Time/Date: 15:00~17:00/ July 21, 2025
Venue: M212, Mathematics Building, Gongguan Campus, NTNU
Speaker: Isaac Vikram Chenchiah, Associate Professor, School of Mathematics, University of Bristol (UK)
Title: Bespoke Elasticity and the Nonlinear Analogue of Cauchy’s Relations
Abstract:
Is it possible to design an architectured material or structure whose elastic energy is arbitrarily close to a specified continuous function? This is possible in one dimension, up to an additive constant [Dixon et al. (2019) https://doi.org/10.1098/rspa.2019.0547]. After a review of that result, we explore the situation in two dimensions: Given (i) a continuous energy function E(C), defined for two-dimensional right Cauchy–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 lattice) 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 generalisation of Cauchy’s relations to nonlinear elasticity.
Ref: Chenchiah IV. Bespoke two-dimensional elasticity and the nonlinear analogue of Cauchy’s relations (2024) https://doi.org/10.1177/10812865231198204
