Microstructure Evolution In Hyperelastic Laminates And Implications For Overall Behavior And Macroscopic Stability

摘要

In this paper we study the evolution of the underlying microstructure in hyperelastic laminates subjected to finite deformations. To this end, we identify a set of relevant micro-structural variables and derive rigorous formulae for their evolution along finite-deformation paths. Making use of these results we then establish connections between the evolution of the microstructure and the overall stress-strain relation and macroscopic stability in hyperelastic laminates. In particular, we show that the rotation of the layers may lead to a reduction in the overall stiffness of the laminates under appropriate loading conditions. Furthermore, we show that this geometric mechanism is intimately related to the possible loss of strong ellipticity of the overall behavior of these materials, which may occur even in the case when the underlying constituents are taken to be strongly elliptic.