A Unified Determinant-Preserving Formulation for Compressible/Incompressible Finite Viscoelasticity.

This paper presents a formulation alongside a numerical solution algorithm to describe the mechanical response of bodies made of a large class of viscoelastic materials undergoing arbitrary quasistatic finite deformations. With the objective of having a unified formulation that applies to a wide range of highly compressible, nearly incompressible, and fully incompressible soft organic materials in a numerically tractable manner, the viscoelasticity is described within a Lagrangian setting by a two-potential mixed formulation. In this formulation, the deformation field, a pressure field that ensues from a Legendre transform, and an internal variable of state that describes the viscous part of the deformation are the independent fields.

The effective shear modulus of a random isotropic suspension of monodisperse liquid -spheres: from the dilute limit to the percolation threshold.

A numerical and analytical study is made of the macroscopic or homogenized mechanical response of a random isotropic suspension of liquid -spherical inclusions ( = 2, 3), each having identical initial radius , in an elastomer subjected to small quasistatic deformations. Attention is restricted to the basic case when the elastomer is an isotropic incompressible linear elastic solid, the liquid making up the inclusions is an incompressible linear elastic fluid, and the interfaces separating the solid elastomer from the liquid inclusions feature a constant initial surface tension . For such a class of suspensions, it has been recently established that the homogenized mechanical response is that of a standard linear elastic solid and hence, for the specific type of isotropic incompressible suspension of interest here, one that can be characterized solely by an effective shear modulus in terms of the shear modulus of the elastomer, the initial elasto-capillary number eCa = /2, the volume fraction of inclusions, and the space dimension .

Damage in elastomers: healing of internally nucleated cavities and micro-cracks.

Following on the work of Poulain et al. (Damage in elastomers: Nucleation and growth of cavities, micro-cracks, and macro-cracks, Int. J.