1 00:00:00,030 --> 00:00:02,470 The following content is provided under a Creative 2 00:00:02,470 --> 00:00:04,000 Commons license. 3 00:00:04,000 --> 00:00:06,330 Your support will help MIT OpenCourseWare 4 00:00:06,330 --> 00:00:10,690 continue to offer high quality educational resources for free. 5 00:00:10,690 --> 00:00:13,300 To make a donation or view additional materials 6 00:00:13,300 --> 00:00:17,025 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,025 --> 00:00:17,650 at ocw.mit.edu. 8 00:00:26,392 --> 00:00:28,975 LORNA GIBSON: All right, well, I guess I may as well start. 9 00:00:28,975 --> 00:00:31,050 I don't know if anybody else is going to come. 10 00:00:31,050 --> 00:00:33,050 So I wanted to finish up by talking a little bit 11 00:00:33,050 --> 00:00:34,180 about the biomimicking. 12 00:00:34,180 --> 00:00:36,156 And some of these examples, you've seen before. 13 00:00:36,156 --> 00:00:38,030 But I just thought I'd put them all together, 14 00:00:38,030 --> 00:00:41,354 and we could look at them as one thing. 15 00:00:41,354 --> 00:00:42,770 So if you remember, when we talked 16 00:00:42,770 --> 00:00:45,880 about wood, one of the things that I showed 17 00:00:45,880 --> 00:00:48,850 you was that people have taken wood and pyrolized it. 18 00:00:48,850 --> 00:00:52,120 So they get a carbon template of the wood cells. 19 00:00:52,120 --> 00:00:57,510 And then they infiltrate that with silicon carbide-- 20 00:00:57,510 --> 00:00:59,730 or, with a silicon vapor infiltration. 21 00:00:59,730 --> 00:01:01,600 And they make a silicon carbide ceramic. 22 00:01:01,600 --> 00:01:04,107 So they can get a replica of the structure. 23 00:01:04,107 --> 00:01:05,940 So sometimes when people say "biomimicking," 24 00:01:05,940 --> 00:01:08,390 some people think of it as replicating something. 25 00:01:08,390 --> 00:01:11,050 But it doesn't have to be just replicating something. 26 00:01:11,050 --> 00:01:13,680 It can be also just some design inspired 27 00:01:13,680 --> 00:01:16,220 by the biological material. 28 00:01:16,220 --> 00:01:18,190 But this thing really is a replica. 29 00:01:18,190 --> 00:01:19,780 And this was another version where 30 00:01:19,780 --> 00:01:24,700 there was the-- they took the silicon carbide material 31 00:01:24,700 --> 00:01:28,590 and then infiltrated that with liquid silicon 32 00:01:28,590 --> 00:01:32,140 to get a fiber-reinforced material, really. 33 00:01:32,140 --> 00:01:36,140 So there was the wood composites we talked about. 34 00:01:36,140 --> 00:01:38,300 Jennifer Lewis's group up at Harvard 35 00:01:38,300 --> 00:01:41,530 is doing 3-D printing of honeycombs. 36 00:01:41,530 --> 00:01:43,850 And one of the things they've been interested in 37 00:01:43,850 --> 00:01:46,630 is not just printing of the pure resin, 38 00:01:46,630 --> 00:01:48,950 but having a fiber-reinforced resin. 39 00:01:48,950 --> 00:01:50,510 And the first thing they did was they 40 00:01:50,510 --> 00:01:52,960 made these honeycombs like this. 41 00:01:52,960 --> 00:01:56,091 And they had small silicon carbon fibers-- 42 00:01:56,091 --> 00:01:57,340 or, were they silicon carbide? 43 00:01:57,340 --> 00:02:00,060 Maybe it was carbon fibers-- in the ink. 44 00:02:00,060 --> 00:02:02,400 And so they would just-- if the ink was being laid down, 45 00:02:02,400 --> 00:02:04,910 the fibers would just line up in the direction of the ink. 46 00:02:04,910 --> 00:02:07,848 And so the fibers tended to be in the plane of the honeycomb. 47 00:02:07,848 --> 00:02:09,389 And if you think of things like wood, 48 00:02:09,389 --> 00:02:12,420 you want the fibers to normal to that plane. 49 00:02:12,420 --> 00:02:15,040 And more recently, they've-- hello. 50 00:02:15,040 --> 00:02:15,750 Oh, hello. 51 00:02:15,750 --> 00:02:16,250 Oh, look. 52 00:02:16,250 --> 00:02:19,740 Oh, look, almost everybody is here. 53 00:02:19,740 --> 00:02:22,060 So more recently, they've got a technology now 54 00:02:22,060 --> 00:02:23,890 where they're rotating the nozzle 55 00:02:23,890 --> 00:02:26,480 as they print the honeycomb. 56 00:02:26,480 --> 00:02:28,200 And as they rotate the nozzle, they 57 00:02:28,200 --> 00:02:31,580 get some change in the orientation of the fiber. 58 00:02:31,580 --> 00:02:34,180 So they're beginning to be able to make honeycombs 59 00:02:34,180 --> 00:02:35,900 that are fiber-reinforced. 60 00:02:35,900 --> 00:02:38,110 And they can get the fibers aligned with the prism 61 00:02:38,110 --> 00:02:41,670 axis of the honeycomb, which is more or less what 62 00:02:41,670 --> 00:02:42,740 the wood does. 63 00:02:42,740 --> 00:02:44,390 So I wasn't going to write anything on the board today. 64 00:02:44,390 --> 00:02:46,306 I was just going to go over some of the slides 65 00:02:46,306 --> 00:02:47,480 and do the review. 66 00:02:47,480 --> 00:02:49,380 So they're beginning to make honeycombs 67 00:02:49,380 --> 00:02:52,980 that have the same sort of structure on the cell wall 68 00:02:52,980 --> 00:02:54,980 level, or at least a similar structure, 69 00:02:54,980 --> 00:02:57,690 as to what the wood composites have. 70 00:02:57,690 --> 00:02:59,800 So that's another example there. 71 00:02:59,800 --> 00:03:04,180 This is just another close-up of their fiber-reinforced walls 72 00:03:04,180 --> 00:03:06,570 in honeycomb specimens. 73 00:03:06,570 --> 00:03:09,520 We talked about trabecular bone, and we talked about the fact 74 00:03:09,520 --> 00:03:11,630 that people are starting to look at using 75 00:03:11,630 --> 00:03:16,092 foamed metals as coatings on orthopedic implants. 76 00:03:16,092 --> 00:03:17,800 And there's been some interest in looking 77 00:03:17,800 --> 00:03:25,270 at using foamed metals for more permanent parts of the body, 78 00:03:25,270 --> 00:03:28,540 more permanent bone parts, things like vertebral cages, 79 00:03:28,540 --> 00:03:30,510 stuff like that. 80 00:03:30,510 --> 00:03:32,110 And so this is just an example here, 81 00:03:32,110 --> 00:03:33,770 with the trabecular bone on the left 82 00:03:33,770 --> 00:03:35,770 and the tantalum foam that's made 83 00:03:35,770 --> 00:03:39,119 by replicating an open-celled polyurethane foam on the right. 84 00:03:39,119 --> 00:03:41,660 And you can see the similarity in the structures of those two 85 00:03:41,660 --> 00:03:43,720 things there. 86 00:03:43,720 --> 00:03:46,010 Then we talked about tissue engineering scaffolds. 87 00:03:46,010 --> 00:03:49,540 And if you remember, these two scaffolds here on the bottom 88 00:03:49,540 --> 00:03:52,460 were made from pig heart tissue. 89 00:03:52,460 --> 00:03:54,720 And they're made by just removing all the cells. 90 00:03:54,720 --> 00:03:57,850 So that actually is the natural extracellular matrix. 91 00:03:57,850 --> 00:04:00,010 And then, these other structures up here, these 92 00:04:00,010 --> 00:04:03,160 were all engineered tissue engineering scaffolds that 93 00:04:03,160 --> 00:04:05,600 are made in a synthetic way. 94 00:04:05,600 --> 00:04:09,720 And the idea is to try to mimic the extracellular 95 00:04:09,720 --> 00:04:11,020 matrix in the body. 96 00:04:11,020 --> 00:04:14,580 So you can see the similarities there. 97 00:04:14,580 --> 00:04:17,560 And then more recently, we were talking about sandwich panels. 98 00:04:17,560 --> 00:04:20,200 So this is the example from the helicopter rotor blade. 99 00:04:20,200 --> 00:04:22,330 That's from an aircraft flooring panel. 100 00:04:22,330 --> 00:04:25,107 And this was the Irish leaf, and these were the bird skulls. 101 00:04:25,107 --> 00:04:26,690 So the same sort of idea, that there's 102 00:04:26,690 --> 00:04:29,050 these engineering lightweight structures, and there's 103 00:04:29,050 --> 00:04:33,430 also similar things in nature. 104 00:04:33,430 --> 00:04:36,060 And then, I think, last time, we also were talking about palms. 105 00:04:36,060 --> 00:04:39,100 And the palm stems had density gradients in them. 106 00:04:39,100 --> 00:04:40,560 And one of the things we showed was 107 00:04:40,560 --> 00:04:42,170 that by having that density gradient, 108 00:04:42,170 --> 00:04:46,660 the stress distribution across, say, the radius of the palm 109 00:04:46,660 --> 00:04:48,940 was almost matched by the strength distribution. 110 00:04:48,940 --> 00:04:51,820 So it was a very efficient way to use the material. 111 00:04:51,820 --> 00:04:54,370 And at MIT, that was a student in architecture 112 00:04:54,370 --> 00:04:57,680 who was looking at doing this with concretes with aerated 113 00:04:57,680 --> 00:05:00,740 or foam concretes and making a radial density distribution. 114 00:05:00,740 --> 00:05:01,700 So he made beams. 115 00:05:01,700 --> 00:05:02,400 He made columns. 116 00:05:02,400 --> 00:05:04,417 He made different kinds of things. 117 00:05:04,417 --> 00:05:06,750 With the concrete, there's a little bit of a limitation, 118 00:05:06,750 --> 00:05:08,916 because the concrete is much stronger in compression 119 00:05:08,916 --> 00:05:10,740 than it is in tension. 120 00:05:10,740 --> 00:05:13,840 So if you had a beam loaded in tension 121 00:05:13,840 --> 00:05:16,689 or a concrete column that might buckle, 122 00:05:16,689 --> 00:05:18,980 you'd still have to have some reinforcing bars in there 123 00:05:18,980 --> 00:05:21,610 to take the tensile loads. 124 00:05:21,610 --> 00:05:23,610 And one thing I think I didn't really talk about 125 00:05:23,610 --> 00:05:27,090 was animal quills and other sorts of plants stems. 126 00:05:27,090 --> 00:05:29,070 And many of these have a structure 127 00:05:29,070 --> 00:05:31,020 that's made up of a cylindrical shell 128 00:05:31,020 --> 00:05:33,610 with a foam or a honeycomb core. 129 00:05:33,610 --> 00:05:35,590 So here are some examples in nature. 130 00:05:35,590 --> 00:05:37,990 If you look at grass stems, there's 131 00:05:37,990 --> 00:05:40,021 a dense layer on the outside, and then 132 00:05:40,021 --> 00:05:41,770 a foamy layer on the inside, and then just 133 00:05:41,770 --> 00:05:43,459 a hollow layer in the middle. 134 00:05:43,459 --> 00:05:45,000 And if you look at porcupine quills-- 135 00:05:45,000 --> 00:05:47,330 this is a porcupine quill-- these are made of keratin. 136 00:05:47,330 --> 00:05:49,700 They're like modified hairs. 137 00:05:49,700 --> 00:05:51,810 So it has a dense layer on the outside, 138 00:05:51,810 --> 00:05:53,880 and then this foamy stuff on the inside. 139 00:05:53,880 --> 00:05:55,650 This is a hedgehog spine here. 140 00:05:55,650 --> 00:05:58,108 And again, you can see there's a dense layer on the outside 141 00:05:58,108 --> 00:05:59,380 and these ribs on the inside. 142 00:05:59,380 --> 00:06:01,865 And this is the toucan beak-- you know, the toucans that 143 00:06:01,865 --> 00:06:03,950 live in Central America. 144 00:06:03,950 --> 00:06:06,440 And the beak has a foam core. 145 00:06:06,440 --> 00:06:08,070 Again, they're keratin structures, 146 00:06:08,070 --> 00:06:10,390 and yet the outside is solid. 147 00:06:10,390 --> 00:06:12,090 But the inside has a foamy structure. 148 00:06:12,090 --> 00:06:14,894 And Mark Myers did a paper on this a while ago. 149 00:06:14,894 --> 00:06:16,560 So we got interested in these structures 150 00:06:16,560 --> 00:06:18,810 that have a solid shell on the outside 151 00:06:18,810 --> 00:06:20,620 but a foamy thing on the inside. 152 00:06:20,620 --> 00:06:23,860 And we wondered if there was a mechanical reason for that. 153 00:06:23,860 --> 00:06:26,600 And you can show that, at least in some of them, 154 00:06:26,600 --> 00:06:28,500 if, say, you have a grass stem-- it's 155 00:06:28,500 --> 00:06:29,920 really common in plant stems. 156 00:06:29,920 --> 00:06:31,260 Do I have some more plant stems? 157 00:06:31,260 --> 00:06:31,968 Yeah, here we go. 158 00:06:31,968 --> 00:06:33,340 Here's a milkweed stem. 159 00:06:33,340 --> 00:06:38,200 So it's got these dense fibers with this foamy core here. 160 00:06:38,200 --> 00:06:41,130 And blue jay feathers-- feathers have this as well. 161 00:06:41,130 --> 00:06:45,280 So they have an outside layer on the quill that's solid, 162 00:06:45,280 --> 00:06:47,170 and then an inside layer that's foamy. 163 00:06:47,170 --> 00:06:50,610 If you look at things like plant stems, they blow in the wind. 164 00:06:50,610 --> 00:06:54,590 And you can look at the buckling resistance of the stem. 165 00:06:54,590 --> 00:06:57,631 And because there's this shell with the foam-like core, 166 00:06:57,631 --> 00:06:59,880 it's not just the overall buckling of the whole thing. 167 00:06:59,880 --> 00:07:02,860 You can get that local face-wrinkling mode again. 168 00:07:02,860 --> 00:07:05,050 So the outer shell can wrinkle. 169 00:07:05,050 --> 00:07:07,350 And you can show that having a foam-like core 170 00:07:07,350 --> 00:07:09,700 helps prevent that wrinkling from happening, the same as 171 00:07:09,700 --> 00:07:10,670 with the sandwich panel. 172 00:07:10,670 --> 00:07:11,990 You remember we talked about the face wrinkling 173 00:07:11,990 --> 00:07:13,170 on the sandwich panel? 174 00:07:13,170 --> 00:07:15,190 Well, on these stems, you can get 175 00:07:15,190 --> 00:07:16,840 wrinkling of the outer shell. 176 00:07:16,840 --> 00:07:18,904 And the foam helps prevent that from happening. 177 00:07:18,904 --> 00:07:20,570 And you can show that you can actually-- 178 00:07:20,570 --> 00:07:22,790 for the same buckling load, you can reduce 179 00:07:22,790 --> 00:07:26,340 the weight of the plant stem, or the bird feather quill, 180 00:07:26,340 --> 00:07:29,430 or whatever by having that foamy core. 181 00:07:29,430 --> 00:07:31,829 So people have looked at this too. 182 00:07:31,829 --> 00:07:33,245 And there's a group in Germany who 183 00:07:33,245 --> 00:07:36,330 had looked at the idea of mimicking the horsetail stem. 184 00:07:36,330 --> 00:07:40,690 So this is a plant stem here, the horsetail plant. 185 00:07:40,690 --> 00:07:43,110 And they made something they called a technical plant 186 00:07:43,110 --> 00:07:46,610 stem, where they made this structure here. 187 00:07:46,610 --> 00:07:49,680 And they made it out of fiber-reinforced composites. 188 00:07:49,680 --> 00:07:51,290 And you can see, the little holes 189 00:07:51,290 --> 00:07:55,110 here represent those holes there, in the plant stem. 190 00:07:55,110 --> 00:07:56,910 So the idea was to try to get something 191 00:07:56,910 --> 00:07:59,490 that was good at resisting the buckling, 192 00:07:59,490 --> 00:08:00,880 but at a lower weight. 193 00:08:00,880 --> 00:08:03,500 And they were doing that with this thing here. 194 00:08:03,500 --> 00:08:06,460 And there was a group in Japan that did a similar thing. 195 00:08:06,460 --> 00:08:10,580 They used-- I think they took a copper tube, 196 00:08:10,580 --> 00:08:13,990 and then they took copper and aluminum wires 197 00:08:13,990 --> 00:08:16,400 and filled the copper tube with the wires. 198 00:08:16,400 --> 00:08:17,490 They extruded that. 199 00:08:17,490 --> 00:08:21,980 And then they melted out the aluminum, which, I think, 200 00:08:21,980 --> 00:08:27,790 also helped to soften and make the copper bond together. 201 00:08:27,790 --> 00:08:29,595 And they got these structures here. 202 00:08:29,595 --> 00:08:31,220 And you can see, that's similar to some 203 00:08:31,220 --> 00:08:34,940 of the plant stems as well. 204 00:08:34,940 --> 00:08:38,669 So these are all examples of cellular structures 205 00:08:38,669 --> 00:08:42,000 that have-- mechanically efficient structures. 206 00:08:42,000 --> 00:08:45,000 They're lightweight, and they're strong, and they're stiff. 207 00:08:45,000 --> 00:08:49,460 And these natural structures have been mimicked 208 00:08:49,460 --> 00:08:52,140 in engineering applications. 209 00:08:52,140 --> 00:08:54,305 So that's really all I wanted to talk about today. 210 00:08:54,305 --> 00:08:56,930 But I think we wanted to use the rest of the class as a review. 211 00:09:03,400 --> 00:09:08,070 So I haven't made a one-hour summary of the last six weeks, 212 00:09:08,070 --> 00:09:09,619 because that's not really possible. 213 00:09:09,619 --> 00:09:11,410 So I thought I would just answer questions. 214 00:09:11,410 --> 00:09:13,600 If you have questions, I'll try and answer them. 215 00:09:13,600 --> 00:09:19,100 So for the test-- so, the test is on Wednesday. 216 00:09:19,100 --> 00:09:22,000 You can bring one 8 and 1/2 by 11 sheet. 217 00:09:22,000 --> 00:09:24,350 I wasn't going to give you all those honeycomb and foam 218 00:09:24,350 --> 00:09:28,130 equations, partly because-- the only thing I would really want 219 00:09:28,130 --> 00:09:30,590 you know is open-cell foams. 220 00:09:30,590 --> 00:09:32,680 And I was hoping, by now, that you 221 00:09:32,680 --> 00:09:35,010 might have registered those equations somewhere 222 00:09:35,010 --> 00:09:36,970 in your brain. 223 00:09:36,970 --> 00:09:43,790 So I'm not going to ask you for-- some equations are 224 00:09:43,790 --> 00:09:44,460 obscure. 225 00:09:44,460 --> 00:09:46,262 I might ask you-- expect you to know 226 00:09:46,262 --> 00:09:48,220 what the Young's modulus of an open-celled foam 227 00:09:48,220 --> 00:09:52,403 is by now, or the axial modulus of a honeycomb or something. 228 00:09:52,403 --> 00:09:55,060 But I don't think I'm going to ask you anything 229 00:09:55,060 --> 00:10:01,220 like, calculate air pressure contributions to the modulus 230 00:10:01,220 --> 00:10:02,220 of the closed-cell foam. 231 00:10:02,220 --> 00:10:04,660 I don't think we're going to do that on this test. 232 00:10:04,660 --> 00:10:11,417 So I think you should know what the modulus of a-- the Young's 233 00:10:11,417 --> 00:10:13,250 modulus of an open-celled foam is, the shear 234 00:10:13,250 --> 00:10:15,980 modulus of a foam, because you need 235 00:10:15,980 --> 00:10:17,780 that for the sandwich panels. 236 00:10:17,780 --> 00:10:20,340 But you don't need reams and reams of those equations, 237 00:10:20,340 --> 00:10:23,338 so I wasn't going to give you those this time. 238 00:10:23,338 --> 00:10:24,800 OK? 239 00:10:24,800 --> 00:10:27,300 So Jenny, did you have-- so I finished the biomimicking 240 00:10:27,300 --> 00:10:27,550 thing. 241 00:10:27,550 --> 00:10:28,883 We're just going to do a review. 242 00:10:28,883 --> 00:10:32,004 I don't know if you want to stay or if you want to go. 243 00:10:32,004 --> 00:10:32,926 You want to stay? 244 00:10:32,926 --> 00:10:33,850 Well, whatever. 245 00:10:33,850 --> 00:10:35,630 So do you have questions, Jenny? 246 00:10:35,630 --> 00:10:37,986 AUDIENCE: I do. 247 00:10:37,986 --> 00:10:44,116 I just wanted to have question 4 from the last pset reexplained. 248 00:10:44,116 --> 00:10:47,664 Because I know that you explained it to 249 00:10:47,664 --> 00:10:50,080 in office hours, and I know that the solutions are online, 250 00:10:50,080 --> 00:10:51,500 and I looked at them. 251 00:10:51,500 --> 00:10:52,330 I'm still confused. 252 00:10:52,330 --> 00:10:52,560 LORNA GIBSON: OK. 253 00:10:52,560 --> 00:10:54,420 So, you're going to have to remind me what problem 4 is, 254 00:10:54,420 --> 00:10:55,570 because I don't remember. 255 00:10:55,570 --> 00:10:59,606 AUDIENCE: Question 4 says, polymethacrylate foam 256 00:10:59,606 --> 00:11:06,042 at solid strength of 3.0-- or, solid Young's modulus, rather, 257 00:11:06,042 --> 00:11:10,452 of 3.0-- gigapascals is being considered 258 00:11:10,452 --> 00:11:13,862 for the energy absorption layer in a bicycle helmet. 259 00:11:13,862 --> 00:11:14,570 LORNA GIBSON: OK. 260 00:11:14,570 --> 00:11:17,111 I'll tell you what, I think I have it on my little disk here. 261 00:11:17,111 --> 00:11:20,562 Maybe that's easier, because then I can read it. 262 00:11:20,562 --> 00:11:22,000 AUDIENCE: [INAUDIBLE]. 263 00:11:22,000 --> 00:11:26,450 LORNA GIBSON: Yeah, let me just see if that's going to come up. 264 00:11:26,450 --> 00:11:27,170 There it is. 265 00:11:42,966 --> 00:11:43,465 OK. 266 00:11:46,220 --> 00:11:48,614 So this one here about the foam, about the-- 267 00:11:48,614 --> 00:11:50,030 AUDIENCE: The one with the graphs. 268 00:11:50,030 --> 00:11:51,446 LORNA GIBSON: --energy absorption? 269 00:11:51,446 --> 00:11:55,302 AUDIENCE: I'm just a little bit confused by the graphs. 270 00:11:55,302 --> 00:11:56,010 LORNA GIBSON: OK. 271 00:12:04,456 --> 00:12:06,392 Let me see if I can make this bigger. 272 00:12:06,392 --> 00:12:07,975 Hang on a sec, my computer's thinking. 273 00:12:14,080 --> 00:12:14,580 OK. 274 00:12:20,450 --> 00:12:20,950 OK. 275 00:12:20,950 --> 00:12:24,284 And I think I gave you-- right, I gave you this graph here. 276 00:12:24,284 --> 00:12:24,783 Right? 277 00:12:24,783 --> 00:12:25,710 AUDIENCE: Yes. 278 00:12:25,710 --> 00:12:27,100 LORNA GIBSON: OK. 279 00:12:27,100 --> 00:12:29,120 So can you read what I've got here, 280 00:12:29,120 --> 00:12:31,320 or is that-- should I make it bigger? 281 00:12:31,320 --> 00:12:33,670 AUDIENCE: I can't really read it, [INAUDIBLE]. 282 00:12:37,900 --> 00:12:40,930 LORNA GIBSON: Does that help? 283 00:12:40,930 --> 00:12:42,500 OK. 284 00:12:42,500 --> 00:12:44,760 So I have to admit, when I put this together, 285 00:12:44,760 --> 00:12:46,760 somebody-- I can't remember who it was-- told me 286 00:12:46,760 --> 00:12:48,218 you thought it was overconstrained. 287 00:12:48,218 --> 00:12:51,070 And it turned out it was overconstrained. 288 00:12:51,070 --> 00:12:53,521 And then I said, forget the thickness. 289 00:12:53,521 --> 00:12:55,520 Forget that I've given you the thickness, right? 290 00:12:55,520 --> 00:12:56,732 So disregard the thickness. 291 00:12:56,732 --> 00:12:58,285 AUDIENCE: No, the velocity. 292 00:12:58,285 --> 00:12:59,785 LORNA GIBSON: Oh, speed-- the speed? 293 00:12:59,785 --> 00:13:01,687 The speed-- all right, OK, the speed. 294 00:13:04,370 --> 00:13:07,290 No, I don't want to register. 295 00:13:07,290 --> 00:13:08,310 OK. 296 00:13:08,310 --> 00:13:12,310 So from what I gave you, you can figure out the normalized peak 297 00:13:12,310 --> 00:13:13,790 stress, right? 298 00:13:13,790 --> 00:13:15,940 So you can get-- so if I do this, is this good? 299 00:13:15,940 --> 00:13:17,720 You can see what I'm pointing at? 300 00:13:17,720 --> 00:13:20,380 So you can get, the peak stress is just the mass times 301 00:13:20,380 --> 00:13:24,580 the acceleration over the area-- are we good with that-- divided 302 00:13:24,580 --> 00:13:26,590 by Es, which I gave you. 303 00:13:26,590 --> 00:13:31,240 So I think most people probably got the peak stress here. 304 00:13:31,240 --> 00:13:32,760 And then, because I had given you 305 00:13:32,760 --> 00:13:34,720 the velocity and the thickness, I 306 00:13:34,720 --> 00:13:37,400 was thinking you could calculate the strain rate. 307 00:13:37,400 --> 00:13:40,080 But if I don't give you the velocity, 308 00:13:40,080 --> 00:13:42,700 say we're not calculating the strain rate at this point here, 309 00:13:42,700 --> 00:13:44,550 OK? 310 00:13:44,550 --> 00:13:48,987 So here, we're-- did I put this-- 311 00:13:48,987 --> 00:13:51,070 I don't know if I have the graph on this solution. 312 00:13:51,070 --> 00:13:51,569 There we go. 313 00:13:54,020 --> 00:13:57,140 So this point here is the 2.5 times 10 to the minus 4 314 00:13:57,140 --> 00:13:59,100 for the peak stress. 315 00:13:59,100 --> 00:14:04,230 And if you're not given the velocity, 316 00:14:04,230 --> 00:14:07,620 I think what I thought you would do then would be just assume 317 00:14:07,620 --> 00:14:08,120 a velocity. 318 00:14:11,710 --> 00:14:14,140 And then you can check it at the end. 319 00:14:14,140 --> 00:14:17,220 So since I had given you this velocity of 12, 320 00:14:17,220 --> 00:14:19,190 let's just say that's what we assumed. 321 00:14:19,190 --> 00:14:20,510 OK? 322 00:14:20,510 --> 00:14:23,460 So then you get a strain rate of 480 per second. 323 00:14:23,460 --> 00:14:26,280 So let's just say we assumed that velocity. 324 00:14:26,280 --> 00:14:30,350 Then we could scoot back over here. 325 00:14:30,350 --> 00:14:34,330 So we know we're on this line here for the sigma p over Es. 326 00:14:34,330 --> 00:14:37,620 And we want to be up towards the top of these different strain 327 00:14:37,620 --> 00:14:38,120 rates. 328 00:14:38,120 --> 00:14:39,786 So if you look at the strain rates, see, 329 00:14:39,786 --> 00:14:42,410 the very last one at the top is 1,000 per second, 330 00:14:42,410 --> 00:14:44,280 and the next one's 100 per second. 331 00:14:44,280 --> 00:14:45,770 So we're halfway in between those. 332 00:14:45,770 --> 00:14:47,830 And they're so close together, you can't really 333 00:14:47,830 --> 00:14:48,663 read the difference. 334 00:14:48,663 --> 00:14:50,030 But we're up here somewhere. 335 00:14:50,030 --> 00:14:54,030 So then we read off a w over Es for that. 336 00:14:54,030 --> 00:14:55,240 OK? 337 00:14:55,240 --> 00:14:55,810 Are we good? 338 00:14:59,070 --> 00:15:02,080 Then, if we know the w over Es, this 339 00:15:02,080 --> 00:15:04,180 is the number, here, that I read off. 340 00:15:07,680 --> 00:15:11,570 You know what the Es is, so you can get w. 341 00:15:11,570 --> 00:15:14,460 If you can get w, w is in joules per cubic meter. 342 00:15:14,460 --> 00:15:16,567 It's in energy per unit volume. 343 00:15:16,567 --> 00:15:18,650 But you know the area, and you know the thickness. 344 00:15:18,650 --> 00:15:20,900 So you can get the energy in joules. 345 00:15:20,900 --> 00:15:23,929 And then-- oh, did I-- I must have rubbed that off. 346 00:15:23,929 --> 00:15:25,220 Didn't have it on this version. 347 00:15:25,220 --> 00:15:26,820 The version in my notebook, I think, 348 00:15:26,820 --> 00:15:28,450 calculated what the velocity would 349 00:15:28,450 --> 00:15:30,425 be that corresponds to this. 350 00:15:30,425 --> 00:15:32,550 And I think it turned out to be 8 meters per second 351 00:15:32,550 --> 00:15:33,560 or something. 352 00:15:33,560 --> 00:15:37,280 So I had assumed 12, and I think it worked out to 8. 353 00:15:37,280 --> 00:15:41,550 And on those log log graphs, whether or not 354 00:15:41,550 --> 00:15:45,310 it's a strain rate of 480, or a little bit less, 355 00:15:45,310 --> 00:15:47,470 or a little bit more, you can't read the difference 356 00:15:47,470 --> 00:15:48,390 on these things. 357 00:15:48,390 --> 00:15:48,890 OK? 358 00:15:48,890 --> 00:15:50,556 AUDIENCE: Can you explain how this graph 359 00:15:50,556 --> 00:15:56,719 relates to the other graphs from lecture that were simpler? 360 00:15:56,719 --> 00:16:02,186 Because we had ones that were all density, and ones 361 00:16:02,186 --> 00:16:04,174 that were all the same strain rate. 362 00:16:04,174 --> 00:16:05,670 And I guess I'm just confused why. 363 00:16:05,670 --> 00:16:06,930 LORNA GIBSON: Oh, OK. 364 00:16:06,930 --> 00:16:09,160 Hang on. 365 00:16:09,160 --> 00:16:12,143 So let me see if I can-- hang on. 366 00:16:12,143 --> 00:16:13,620 No, I think I know what you mean. 367 00:16:13,620 --> 00:16:14,120 Let me see. 368 00:16:14,120 --> 00:16:16,439 I want to pull up the lecture notes. 369 00:16:16,439 --> 00:16:20,495 I think I'm finding the right thing. 370 00:16:20,495 --> 00:16:21,851 Here we are. 371 00:16:30,784 --> 00:16:32,200 So in the lecture notes, there was 372 00:16:32,200 --> 00:16:34,440 a thing that looked like this. 373 00:16:34,440 --> 00:16:36,240 Is that what you're talking about? 374 00:16:36,240 --> 00:16:39,040 Yeah. 375 00:16:39,040 --> 00:16:41,310 So the top set are the stress strain curves. 376 00:16:41,310 --> 00:16:42,340 So those are OK. 377 00:16:42,340 --> 00:16:45,400 You do a compression test, you measure that. 378 00:16:45,400 --> 00:16:50,310 Then, the middle set, you take, say, for one density, 379 00:16:50,310 --> 00:16:53,440 for one stress strain curve-- say 380 00:16:53,440 --> 00:16:56,940 that's your curve, the middle one there, 0.03. 381 00:16:56,940 --> 00:16:58,560 Say you loaded it up to some point, 382 00:16:58,560 --> 00:17:01,790 or say you looked at some point here, on the curve. 383 00:17:01,790 --> 00:17:04,869 You would figure out, for that stress, 384 00:17:04,869 --> 00:17:08,450 what's the area under the curve up to that stress. 385 00:17:08,450 --> 00:17:10,609 So you'd have a stress and an area under the curve 386 00:17:10,609 --> 00:17:12,300 up to that stress. 387 00:17:12,300 --> 00:17:15,986 And you could then-- say we know what this foam is. 388 00:17:15,986 --> 00:17:18,069 It's-- I don't know-- a polyurethane or something. 389 00:17:18,069 --> 00:17:20,050 So say we know Es. 390 00:17:20,050 --> 00:17:22,220 Then we could divide those two numbers by Es. 391 00:17:22,220 --> 00:17:24,799 And we would plot that one thing. 392 00:17:24,799 --> 00:17:26,839 Let me just walk over here. 393 00:17:26,839 --> 00:17:28,162 So this is the 0.03. 394 00:17:28,162 --> 00:17:29,870 So if it's in the linear elastic reading, 395 00:17:29,870 --> 00:17:32,260 it would be somewhere in here. 396 00:17:32,260 --> 00:17:35,720 Then I would scoot along, say, to here someplace. 397 00:17:35,720 --> 00:17:38,490 I would do a whole bunch of points all the way along there. 398 00:17:38,490 --> 00:17:41,089 And at every point, I would say, what's the stress, 399 00:17:41,089 --> 00:17:43,130 and what's the energy absorbed up to that stress. 400 00:17:43,130 --> 00:17:44,270 OK? 401 00:17:44,270 --> 00:17:46,800 And then I would plot-- doot, doot, doot, doot, doot-- up 402 00:17:46,800 --> 00:17:49,514 here, I would plot all those points. 403 00:17:49,514 --> 00:17:50,900 OK? 404 00:17:50,900 --> 00:17:53,360 And then when I got to this part here, 405 00:17:53,360 --> 00:17:55,930 that corresponds to that part over there. 406 00:17:55,930 --> 00:17:57,410 OK? 407 00:17:57,410 --> 00:18:00,550 Are we all good with that? 408 00:18:00,550 --> 00:18:01,050 OK. 409 00:18:01,050 --> 00:18:05,550 So then we repeat-- so we get one curve on the middle chart. 410 00:18:05,550 --> 00:18:09,275 Then, for the different densities 411 00:18:09,275 --> 00:18:10,900 and the different stress strain curves, 412 00:18:10,900 --> 00:18:14,230 we plot a different curve for each of the different densities 413 00:18:14,230 --> 00:18:16,110 doing the same process. 414 00:18:16,110 --> 00:18:20,420 And the thing we notice is that these points here 415 00:18:20,420 --> 00:18:22,240 are really the optimum point. 416 00:18:22,240 --> 00:18:24,650 Because at that point there, you absorb as much energy 417 00:18:24,650 --> 00:18:27,160 as you possibly can for that stress. 418 00:18:27,160 --> 00:18:29,460 OK? 419 00:18:29,460 --> 00:18:32,420 And we notice, happily, that those points 420 00:18:32,420 --> 00:18:36,490 lie on a line, basically, on a straight line. 421 00:18:36,490 --> 00:18:39,080 And we tick of what the different densities 422 00:18:39,080 --> 00:18:42,364 are-- so 0.01, 0.03, 0.1, 0.3. 423 00:18:42,364 --> 00:18:44,150 OK? 424 00:18:44,150 --> 00:18:48,000 And that line there, and all of these stress strain curves, 425 00:18:48,000 --> 00:18:51,390 and all these lines here, curves here, they all 426 00:18:51,390 --> 00:18:53,115 correspond to one strain rate. 427 00:18:53,115 --> 00:18:55,160 All right? 428 00:18:55,160 --> 00:18:57,980 So now I could take that line there for that first strain 429 00:18:57,980 --> 00:19:01,100 rate, and it would be one of these thinner lines 430 00:19:01,100 --> 00:19:03,890 here for a particular strain rate. 431 00:19:03,890 --> 00:19:05,990 And I would mark off-- just the same 432 00:19:05,990 --> 00:19:10,850 as I've got here, 0.01, 0.03-- I'd go 0.01, 0.03, 0.1, 0.3. 433 00:19:10,850 --> 00:19:13,060 All right? 434 00:19:13,060 --> 00:19:15,350 And then I would repeat this whole process again 435 00:19:15,350 --> 00:19:17,090 for a different strain rate. 436 00:19:17,090 --> 00:19:19,330 So I'd go back to doing some mechanical tests 437 00:19:19,330 --> 00:19:21,540 at, now, a new strain rate. 438 00:19:21,540 --> 00:19:23,260 And typically, the new strain rate 439 00:19:23,260 --> 00:19:26,126 is going to be bigger or smaller by a factor of 10 or so, 440 00:19:26,126 --> 00:19:28,750 because you're not going to see much difference in the behavior 441 00:19:28,750 --> 00:19:31,320 unless you get big changes in the strain rate. 442 00:19:31,320 --> 00:19:34,380 So you're going to change the strain rate significantly. 443 00:19:34,380 --> 00:19:38,380 You get a new series of these stress strain curves. 444 00:19:38,380 --> 00:19:41,140 Then you get a similar-- very similar, 445 00:19:41,140 --> 00:19:44,180 but not quite the same-- series of these curves here. 446 00:19:44,180 --> 00:19:46,990 And what you'd find is you'd have another line here 447 00:19:46,990 --> 00:19:49,960 that would be offset a little from the first one. 448 00:19:49,960 --> 00:19:52,190 And the positions of where these densities were 449 00:19:52,190 --> 00:19:55,030 would also be offset a little from the first one. 450 00:19:55,030 --> 00:19:56,730 And then you'd draw the second one. 451 00:19:56,730 --> 00:19:59,740 So the second strain rate line would go here. 452 00:19:59,740 --> 00:20:03,210 And the little density positions would be offset a little bit, 453 00:20:03,210 --> 00:20:05,040 and you would mark them off. 454 00:20:05,040 --> 00:20:07,600 And you basically repeat it for different strain rates, 455 00:20:07,600 --> 00:20:09,290 and then you build this thing up. 456 00:20:09,290 --> 00:20:12,381 And then the density lines connect too. 457 00:20:12,381 --> 00:20:12,880 Is that OK? 458 00:20:15,850 --> 00:20:18,210 So that's how you generate that. 459 00:20:18,210 --> 00:20:22,370 So the idea is, this bottom diagram is really summarizing 460 00:20:22,370 --> 00:20:25,610 all of those shoulder points. 461 00:20:25,610 --> 00:20:29,310 The bottom diagram is really summarizing all of these points 462 00:20:29,310 --> 00:20:32,070 where the stress starts to scoot up 463 00:20:32,070 --> 00:20:35,880 at the densification machine. 464 00:20:35,880 --> 00:20:37,548 Yeah? 465 00:20:37,548 --> 00:20:39,532 AUDIENCE: So in question 3, we were 466 00:20:39,532 --> 00:20:42,508 constructing the graph in the middle for this particular one. 467 00:20:42,508 --> 00:20:46,290 What confused me is that on the graph, 468 00:20:46,290 --> 00:20:51,400 the variable on the x-axis is stress, 469 00:20:51,400 --> 00:20:54,470 whereas in the question, we were given the stress. 470 00:20:54,470 --> 00:21:00,447 So I drew something that looked as it should have looked. 471 00:21:00,447 --> 00:21:03,493 And it turned out to be right, but I'm 472 00:21:03,493 --> 00:21:05,020 very confused as to why. 473 00:21:05,020 --> 00:21:06,100 LORNA GIBSON: OK. 474 00:21:06,100 --> 00:21:07,880 Let me try and get rid of that. 475 00:21:07,880 --> 00:21:09,463 And I'm going to have to remind myself 476 00:21:09,463 --> 00:21:10,650 what the question is again. 477 00:21:10,650 --> 00:21:11,150 OK. 478 00:21:11,150 --> 00:21:15,220 So we have an open filled aluminum foam. 479 00:21:15,220 --> 00:21:18,140 I asked you to write the equations for each 480 00:21:18,140 --> 00:21:19,687 of the different regimes. 481 00:21:19,687 --> 00:21:21,770 And those were straight out of the notes, I think. 482 00:21:21,770 --> 00:21:22,040 Right? 483 00:21:22,040 --> 00:21:24,108 AUDIENCE: Yeah, I think the three inputs were 484 00:21:24,108 --> 00:21:25,610 different relative densities. 485 00:21:25,610 --> 00:21:27,110 LORNA GIBSON: Yeah, and then you had 486 00:21:27,110 --> 00:21:28,910 to construct the energy absorption 487 00:21:28,910 --> 00:21:33,530 curve based on those equations. 488 00:21:33,530 --> 00:21:35,436 And I give you three relative densities. 489 00:21:39,930 --> 00:21:42,760 So this was my solution. 490 00:21:42,760 --> 00:21:46,590 So all this stuff here, I think, was straight out of the notes. 491 00:21:46,590 --> 00:21:48,560 So there was the-- oops, let me back up 492 00:21:48,560 --> 00:21:50,010 so we start at the beginning. 493 00:21:50,010 --> 00:21:51,940 So there was the linear elastic part. 494 00:21:51,940 --> 00:21:53,400 There was the stress plateau. 495 00:21:53,400 --> 00:21:56,187 That was just as it starts to densify. 496 00:21:56,187 --> 00:21:58,270 And then, there's that line joining up the points. 497 00:21:58,270 --> 00:21:59,780 So you were OK with all of that? 498 00:21:59,780 --> 00:22:00,405 AUDIENCE: Yeah. 499 00:22:00,405 --> 00:22:04,770 No, the only part that confused me is because once 500 00:22:04,770 --> 00:22:09,580 I simplified-- I inputted all of what we were given such 501 00:22:09,580 --> 00:22:12,320 that I had equations in terms of the relative density 502 00:22:12,320 --> 00:22:15,075 so I could just apply it to the different ones given. 503 00:22:15,075 --> 00:22:20,412 But then I wasn't very sure how-- because I got constants, 504 00:22:20,412 --> 00:22:23,224 I wasn't really sure how-- the slopes should look like, 505 00:22:23,224 --> 00:22:25,674 because they were constants. 506 00:22:25,674 --> 00:22:27,090 LORNA GIBSON: So you got-- I'm not 507 00:22:27,090 --> 00:22:29,510 sure what you mean about you got constants. 508 00:22:29,510 --> 00:22:32,270 So what I did was I said, well, I 509 00:22:32,270 --> 00:22:35,580 know that the diagram has to have this basic shape, right? 510 00:22:35,580 --> 00:22:39,052 In the first part here is where it's linear elastic. 511 00:22:39,052 --> 00:22:40,760 And this part here is the stress plateau. 512 00:22:40,760 --> 00:22:42,920 And that part there is the densification. 513 00:22:42,920 --> 00:22:43,760 OK? 514 00:22:43,760 --> 00:22:46,390 And I said, well, if I can find these two points that 515 00:22:46,390 --> 00:22:48,830 correspond to the change between the linear elastic part 516 00:22:48,830 --> 00:22:51,490 and the stress plateau and the point that corresponds 517 00:22:51,490 --> 00:22:53,960 to the stress plateau and the densification, 518 00:22:53,960 --> 00:22:55,120 then I've got the diagram. 519 00:22:55,120 --> 00:22:56,600 Right? 520 00:22:56,600 --> 00:22:57,900 OK? 521 00:22:57,900 --> 00:22:59,150 AUDIENCE: Yeah, I think that-- 522 00:23:01,660 --> 00:23:03,758 LORNA GIBSON: Oh, can I stop talking now? 523 00:23:03,758 --> 00:23:06,390 AUDIENCE: I mean, if you wanted to-- 524 00:23:06,390 --> 00:23:07,770 LORNA GIBSON: Well, it's for you. 525 00:23:07,770 --> 00:23:08,830 So you're OK? 526 00:23:08,830 --> 00:23:10,210 AUDIENCE: I think. 527 00:23:10,210 --> 00:23:11,180 LORNA GIBSON: You. 528 00:23:11,180 --> 00:23:13,332 AUDIENCE: So what confused me about this question 529 00:23:13,332 --> 00:23:15,040 was that in order to find the two points, 530 00:23:15,040 --> 00:23:18,560 you'd need to know the strain at which that [INAUDIBLE]. 531 00:23:18,560 --> 00:23:20,640 So I wasn't sure how you would find that strain. 532 00:23:20,640 --> 00:23:22,556 LORNA GIBSON: Yeah, I think I didn't tell you. 533 00:23:22,556 --> 00:23:24,910 Let's see. 534 00:23:24,910 --> 00:23:28,650 Well, let's see. 535 00:23:28,650 --> 00:23:31,106 Do you have to have the strain? 536 00:23:31,106 --> 00:23:34,000 You have that. 537 00:23:34,000 --> 00:23:42,360 I think if you have-- I think you don't have to have it 538 00:23:42,360 --> 00:23:43,600 in terms of the strain. 539 00:23:43,600 --> 00:23:46,972 I suppose you could put it in terms of the strain. 540 00:23:46,972 --> 00:23:48,930 I mean, that would be a different way to do it. 541 00:23:48,930 --> 00:23:50,591 AUDIENCE: But isn't the equation for the stress plateau 542 00:23:50,591 --> 00:23:52,460 already in terms of the strain? 543 00:23:52,460 --> 00:23:57,900 LORNA GIBSON: Yeah, but this assumes that the stress plateau 544 00:23:57,900 --> 00:24:00,620 is just perfectly flat, right? 545 00:24:00,620 --> 00:24:06,990 So this thing here would be useful, the strain at which 546 00:24:06,990 --> 00:24:09,760 the plateau starts. 547 00:24:09,760 --> 00:24:12,360 But I think that's the same as saying-- 548 00:24:12,360 --> 00:24:15,200 that's the same point as saying you're at that point 549 00:24:15,200 --> 00:24:17,740 there, because that's where the plateau starts. 550 00:24:17,740 --> 00:24:18,720 OK? 551 00:24:18,720 --> 00:24:20,250 So I think there's different ways 552 00:24:20,250 --> 00:24:24,060 you could try to approach this. 553 00:24:24,060 --> 00:24:32,432 But I think-- let's see, I'm just 554 00:24:32,432 --> 00:24:33,890 trying to remember what I did here. 555 00:24:33,890 --> 00:24:36,810 Yeah, so what I did here-- so to get point a, 556 00:24:36,810 --> 00:24:38,730 I said, well, this is the equation 557 00:24:38,730 --> 00:24:40,540 for the linear elastic bit, right? 558 00:24:40,540 --> 00:24:43,365 And this is the equation for the stress plateau. 559 00:24:46,840 --> 00:24:50,610 Where I'm at point a here, this stress is the stress plateau. 560 00:24:50,610 --> 00:24:53,460 So that's why I've put sigma star plastic there. 561 00:24:53,460 --> 00:24:58,200 And then I said, this is-- the sigma star plastic is-- 562 00:24:58,200 --> 00:25:01,390 and this works out to some number here, 563 00:25:01,390 --> 00:25:04,077 some number times the relative density to the 3/2 power. 564 00:25:04,077 --> 00:25:05,910 And then I just made this little table here, 565 00:25:05,910 --> 00:25:08,370 where I said, OK, these are the densities I 566 00:25:08,370 --> 00:25:11,690 need to get the curve for. 567 00:25:11,690 --> 00:25:14,180 This is going to be my sigma star 568 00:25:14,180 --> 00:25:16,040 plastic for those densities. 569 00:25:16,040 --> 00:25:19,990 And from that, then I can get this column here. 570 00:25:19,990 --> 00:25:21,620 It's basically just that equation 571 00:25:21,620 --> 00:25:23,590 with this substituted in. 572 00:25:23,590 --> 00:25:27,800 And do you see that that corresponds to the point a? 573 00:25:27,800 --> 00:25:30,300 So I mean, you could do it by figuring out 574 00:25:30,300 --> 00:25:32,730 what that strain is and then figuring out 575 00:25:32,730 --> 00:25:37,520 all the points along that line up to that strain. 576 00:25:37,520 --> 00:25:39,760 But you don't have to do it that way. 577 00:25:39,760 --> 00:25:41,930 Do you know what I'm saying? 578 00:25:41,930 --> 00:25:55,890 So you're saying-- if I had-- so say I have my idealized stress 579 00:25:55,890 --> 00:25:58,000 strain curve like that, right? 580 00:25:58,000 --> 00:26:00,270 You're saying, well, I had to know that strain 581 00:26:00,270 --> 00:26:04,330 there so that I know where this stops, right? 582 00:26:04,330 --> 00:26:06,867 And I'm saying that corres-- and you could do it 583 00:26:06,867 --> 00:26:07,950 this way if you wanted to. 584 00:26:07,950 --> 00:26:15,440 You could say that this is the energy absorbed up 585 00:26:15,440 --> 00:26:17,170 to that point. 586 00:26:17,170 --> 00:26:21,160 And if you know that the modulus goes 587 00:26:21,160 --> 00:26:25,550 as the relative density squared times Es, 588 00:26:25,550 --> 00:26:35,445 and you know this, if you know those two things, 589 00:26:35,445 --> 00:26:37,070 you can figure out what that strain is. 590 00:26:37,070 --> 00:26:39,220 So you could do it that way if you wanted to, 591 00:26:39,220 --> 00:26:41,800 but I just did it a slightly different way. 592 00:26:41,800 --> 00:26:46,248 AUDIENCE: Yeah, so I don't understand how you just 593 00:26:46,248 --> 00:26:48,936 were able to get rid of the epsilon minus epsilon 594 00:26:48,936 --> 00:26:49,840 on that curve. 595 00:26:49,840 --> 00:26:51,340 LORNA GIBSON: Oh, let's see. 596 00:26:51,340 --> 00:26:57,810 So I think, in the first part, where it's linear elastic, 597 00:26:57,810 --> 00:26:59,470 I just go up to epsilon 0, right? 598 00:26:59,470 --> 00:27:01,890 So this part here doesn't really involve the epsilon, 599 00:27:01,890 --> 00:27:03,514 because I've gotten rid of it by taking 600 00:27:03,514 --> 00:27:04,750 the square of the stress. 601 00:27:04,750 --> 00:27:07,730 And then here, the other point I'm looking at 602 00:27:07,730 --> 00:27:09,340 is this point here. 603 00:27:09,340 --> 00:27:13,230 And I've assumed that epsilon 0 is much smaller than epsilon d, 604 00:27:13,230 --> 00:27:15,220 and I've ignored it. 605 00:27:15,220 --> 00:27:18,560 And that's, I think, how I did it in the notes in the class. 606 00:27:18,560 --> 00:27:19,630 OK? 607 00:27:19,630 --> 00:27:22,300 So when you get to that point, this strain 608 00:27:22,300 --> 00:27:27,480 here is usually a few percent at most. 609 00:27:27,480 --> 00:27:31,480 And this strain here is typically 80% or 90%. 610 00:27:31,480 --> 00:27:34,200 So it's pretty common to do that. 611 00:27:34,200 --> 00:27:36,440 OK? 612 00:27:36,440 --> 00:27:38,330 Other questions? 613 00:27:38,330 --> 00:27:40,490 So don't forget, the test covers everything 614 00:27:40,490 --> 00:27:45,110 from the thermal conductivity of the foams, 615 00:27:45,110 --> 00:27:48,360 it covers the stuff on trabecular bone, sandwich 616 00:27:48,360 --> 00:27:52,282 panels, and then, the energy absorption stuff. 617 00:27:52,282 --> 00:27:55,010 Yeah? 618 00:27:55,010 --> 00:27:58,040 Are you a little exhausted already? 619 00:27:58,040 --> 00:27:59,969 Yeah. 620 00:27:59,969 --> 00:28:02,010 So I'm guessing that this week and next week, you 621 00:28:02,010 --> 00:28:03,970 have everything due. 622 00:28:03,970 --> 00:28:06,530 You have papers, and projects, and tests. 623 00:28:06,530 --> 00:28:11,300 Do you have very many exams left, like final exams? 624 00:28:11,300 --> 00:28:12,350 Yeah, you've got finals? 625 00:28:12,350 --> 00:28:13,280 AUDIENCE: [INAUDIBLE]. 626 00:28:13,280 --> 00:28:13,988 LORNA GIBSON: Oh. 627 00:28:17,940 --> 00:28:19,490 All right. 628 00:28:19,490 --> 00:28:22,350 Anybody else have any questions? 629 00:28:22,350 --> 00:28:24,640 Because I think we can just go and do other things 630 00:28:24,640 --> 00:28:27,540 if nobody has any other questions. 631 00:28:27,540 --> 00:28:29,954 So the test is on-- so let's just review where we're 632 00:28:29,954 --> 00:28:31,120 at for the rest of the term. 633 00:28:31,120 --> 00:28:33,474 So the test's on Wednesday. 634 00:28:33,474 --> 00:28:34,890 And you can bring one cheat sheet, 635 00:28:34,890 --> 00:28:36,980 but I am not giving you all those equations 636 00:28:36,980 --> 00:28:38,250 with honey combs and foams. 637 00:28:38,250 --> 00:28:39,750 So I think, on your cheat sheet, you 638 00:28:39,750 --> 00:28:42,370 would want to put Young's modulus of an open-celled foam, 639 00:28:42,370 --> 00:28:44,907 shear modulus of an open-celled foam, 640 00:28:44,907 --> 00:28:46,740 compressive strength of an open-celled foam, 641 00:28:46,740 --> 00:28:48,730 shear strength of an open-celled foam. 642 00:28:48,730 --> 00:28:51,750 But I don't think there's going to be anything more complicated 643 00:28:51,750 --> 00:28:53,680 than that. 644 00:28:53,680 --> 00:28:57,370 And Monday, I was going to do the 645 00:28:57,370 --> 00:28:59,307 how I became a professor talk. 646 00:28:59,307 --> 00:29:01,640 So if you've seen it and you don't want to see it again, 647 00:29:01,640 --> 00:29:03,290 you're welcome to not come. 648 00:29:03,290 --> 00:29:06,662 But for you guys, I just talk about how I got here. 649 00:29:06,662 --> 00:29:07,620 And it's about my life. 650 00:29:07,620 --> 00:29:10,600 It's not about cellular solids or anything. 651 00:29:10,600 --> 00:29:12,100 And I don't know, you guys liked it. 652 00:29:12,100 --> 00:29:12,650 You like it, don't you? 653 00:29:12,650 --> 00:29:13,120 AUDIENCE: Yeah. 654 00:29:13,120 --> 00:29:13,850 LORNA GIBSON: Yeah. 655 00:29:13,850 --> 00:29:14,350 Yeah. 656 00:29:14,350 --> 00:29:16,420 So if you want to come, I'll do that. 657 00:29:16,420 --> 00:29:17,970 And then Wednesday, I thought, I just 658 00:29:17,970 --> 00:29:19,178 need to collect the projects. 659 00:29:19,178 --> 00:29:21,462 I wasn't going to do anything on Wednesday. 660 00:29:21,462 --> 00:29:22,920 And so I've been thinking about the 661 00:29:22,920 --> 00:29:24,750 how I became a professor talk. 662 00:29:24,750 --> 00:29:27,880 And I think-- so I have this idea that students 663 00:29:27,880 --> 00:29:30,589 would like to hear more of these talks from other faculty. 664 00:29:30,589 --> 00:29:31,380 Would that be true? 665 00:29:31,380 --> 00:29:32,083 AUDIENCE: Yes. 666 00:29:32,083 --> 00:29:32,930 LORNA GIBSON: Ah. 667 00:29:32,930 --> 00:29:35,304 Because I've been in touch with Cindy Barnhart, and we're 668 00:29:35,304 --> 00:29:37,541 going to try and organize something for the fall. 669 00:29:37,541 --> 00:29:39,540 So I'm going to approach some other professors-- 670 00:29:39,540 --> 00:29:41,640 not just in our department, across all of MIT-- 671 00:29:41,640 --> 00:29:43,431 and see if I can get other people to do the 672 00:29:43,431 --> 00:29:45,550 how I became a professor talk. 673 00:29:45,550 --> 00:29:47,390 So you would like that? 674 00:29:47,390 --> 00:29:48,330 OK, yeah. 675 00:29:48,330 --> 00:29:50,740 So we'll see if we can make that happen.