Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Asymptotic rigidity of layered structures and its application in homogenization theory (1808.10494v1)

Published 30 Aug 2018 in math.AP

Abstract: In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff components arranged into fine parallel layers. We show that strict global constraints of anisotropic nature occur in the limit of vanishing layer thickness, and give a characterization of the class of effective deformations. The optimality of the scaling relation between layer thickness and stiffness is confirmed by suitable bending constructions. Beyond its theoretical interest, this result constitutes a key ingredient for the homogenization of variational problems modeling high-contrast bilayered composite materials, where the common assumption of strict inclusion of one phase in the other is clearly not satisfied. We study a model inspired by hyperelasticity via Gamma-convergence, for which we are able to give an explicit representation of the homogenized limit problem. It turns out to be of integral form with its density corresponding to a cell formula.

Summary

We haven't generated a summary for this paper yet.