COMPUTATIONAL HOMOGENISATION FOR NON-LINEAR HETEROGENEOUS SOLIDS

Author(s):  
V. G. Kouznetsova ◽  
M. G. D. Geers ◽  
W. A. M. Brekelmans
2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Weijian Ge ◽  
Vito L. Tagarielli

AbstractWe propose and implement a computational procedure to establish data-driven surrogate constitutive models for heterogeneous materials. We study the multiaxial response of non-linear n-phase composites via Finite Element (FE) simulations and computational homogenisation. Pseudo-random, multiaxial, non-proportional histories of macroscopic strain are imposed on volume elements of n-phase composites, subject to periodic boundary conditions, and the corresponding histories of macroscopic stresses and plastically dissipated energy are recorded. The recorded data is used to train surrogate, phenomenological constitutive models based on neural networks (NNs), and the accuracy of these models is assessed and discussed. We analyse heterogeneous composites with hyperelastic, viscoelastic or elastic–plastic local constitutive descriptions. In each of these three cases, we propose and assess optimal choices of inputs and outputs for the surrogate models and strategies for their training. We find that the proposed computational procedure can capture accurately and effectively the response of non-linear n-phase composites subject to arbitrary mechanical loading.


2003 ◽  
Vol 58 (9) ◽  
pp. 1321-1346 ◽  
Author(s):  
Kenjiro Terada ◽  
Mitsuteru Asai ◽  
Michihiro Yamagishi

1967 ◽  
Vol 28 ◽  
pp. 105-176
Author(s):  
Robert F. Christy

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)


1997 ◽  
Vol 161 ◽  
pp. 179-187
Author(s):  
Clifford N. Matthews ◽  
Rose A. Pesce-Rodriguez ◽  
Shirley A. Liebman

AbstractHydrogen cyanide polymers – heterogeneous solids ranging in color from yellow to orange to brown to black – may be among the organic macromolecules most readily formed within the Solar System. The non-volatile black crust of comet Halley, for example, as well as the extensive orangebrown streaks in the atmosphere of Jupiter, might consist largely of such polymers synthesized from HCN formed by photolysis of methane and ammonia, the color observed depending on the concentration of HCN involved. Laboratory studies of these ubiquitous compounds point to the presence of polyamidine structures synthesized directly from hydrogen cyanide. These would be converted by water to polypeptides which can be further hydrolyzed to α-amino acids. Black polymers and multimers with conjugated ladder structures derived from HCN could also be formed and might well be the source of the many nitrogen heterocycles, adenine included, observed after pyrolysis. The dark brown color arising from the impacts of comet P/Shoemaker-Levy 9 on Jupiter might therefore be mainly caused by the presence of HCN polymers, whether originally present, deposited by the impactor or synthesized directly from HCN. Spectroscopic detection of these predicted macromolecules and their hydrolytic and pyrolytic by-products would strengthen significantly the hypothesis that cyanide polymerization is a preferred pathway for prebiotic and extraterrestrial chemistry.


Optimization ◽  
1975 ◽  
Vol 6 (4) ◽  
pp. 549-559
Author(s):  
L. Gerencsér

1979 ◽  
Author(s):  
George W. Howe ◽  
James H. Dalton ◽  
Maurice J. Elias
Keyword(s):  

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