Effective behavior, microstructure evolution and macroscopic instabilities

in elastomeric composites

 

P. Ponte Castañeda

 

Department of Mechanical Engineering and Applied Mechanics

University of Pennsylvania

Philadelphia, PA 19104-6315, USA

 

and

 

Département de Mécanique

Laboratoire de Mécanique des Solides

École Polytechnique

91128 Palaiseau. France

 

 

 

Abstract

 

This talk will present the application of a recently developed “second-order” homogenization method to generate estimates for effective behavior, microstructure evolution and loss of ellipticity in hyperelastic composites with random and periodic microstructures that are subjected to finite deformations. Two extreme cases are considered that are illustrative of the physics of the problem: porous elastomers and fiber-reinforced elastomers. The main concept behind the method is the introduction of an optimally selected “linear comparison composite,” which can then be used to convert standard linear homogenization estimates into new estimates for the nonlinear hyperelastic composite. Explicit results are provided for materials with isotropic and strongly elliptic constituents. It is found that their overall behavior may lose ellipticity at sufficiently large deformations, which corresponds to the possible development of shear band-type instabilities. The reasons for this result have been linked to the evolution of the microstructure, which, under appropriate loading conditions, can induce “geometric softening” leading to the overall loss of ellipticity.