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SUMMARY:MechE Colloquium: Bespoke Elasticity and the Nonlinear Analogue of
  Cauchy’s Relations
DTSTART:20240416T120000
DTEND:20240416T130000
DTSTAMP:20260501T141529Z
UID:9e2d49673a06951ce0f5fa7ed4180caa6447d17617a4689ae6cfabbc
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Isaac Chenchiah\, University of Bristol\, UK\nAbstract:
  \n\nIs it possible to design an architectured material or structure whos
 e elastic energy is arbitrarily close to a specified continuous function? 
 This is possible in one dimension\, up to an additive constant [Dixon et a
 l.\, Bespoke extensional elasticity through helical lattice systems\, Proc
 . R. Soc. A. (2019) https://doi.org/10.1098/rspa.2019.0547]. After a revi
 ew of that result\, we explore the situation in two dimensions: Given (i) 
 a continuous energy function E(C)\, defined for two-dimensional right Cauc
 hy–Green deformation tensors C contained in some compact set\, and (ii) 
 a tolerance ϵ > 0\, can we construct a spring-node unit cell (of a lattic
 e) whose energy is approximately E\, up to an additive constant\, with L
 ∞ -error no more than ϵ? We show that the answer is yes for affine Es (
 i.e.\, for energies E that are quadratic in the deformation gradient) but 
 that the general situation is more subtle and is related to the generalisa
 tion of Cauchy’s relations to nonlinear elasticity. If time permits\, we
  will also explore the three-dimensional situation.\n[Reference]: Chenchia
 h IV. Bespoke two-dimensional elasticity and the nonlinear analogue of Cau
 chy’s relations. Mathematics and Mechanics of Solids. https://doi.org/1
 0.1177/10812865231198204\n\n\nBiography: \n\nAfter undergraduate educatio
 n at IIT Madras (India)\, I received a PhD from Caltech (USA) and was a po
 st-doctoral associate at the Max Planck Institute for Mathematics in the S
 ciences (Germany).\nIn addition to interests in mathematics\, engineering 
 and science\, in my leisure time\, I enjoy reading about ancient Greek Phi
 losophy and Western medieval thought\, especially Thomas Aquinas.\n 
LOCATION:MED 0 1418 https://plan.epfl.ch/?room==MED%200%201418 https://epf
 l.zoom.us/j/61626448592
STATUS:CONFIRMED
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