Abstract
An approximate homogenization solution is put forth for the effective stored-energy function describing the macroscopic elastic response of isotropic porous elastomers comprised of incompressible non-Gaussian elastomers embedding equiaxed closed-cell vacuous pores. In spite of its generality, the solution — which is constructed in two successive steps by making use first of an iterative technique and then of a nonlinear comparison medium method — is fully explicit and remarkably simple. Its key theoretical and practical features are discussed in detail and its accuracy is demonstrated by means of direct comparisons with novel computational solutions for porous elastomers with four classes of physically relevant isotropic microstructures wherein the underlying pores are: (i) infinitely polydisperse in size and of abstract shape, (ii) finitely polydisperse in size and spherical in shape, (iii) monodisperse in size and spherical in shape, and (iv) monodisperse in size and of oblate spheroidal shape.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 364-380 |
| Number of pages | 17 |
| Journal | Journal of the Mechanics and Physics of Solids |
| Volume | 122 |
| DOIs | |
| State | Published - Jan 2019 |
Funding
Support for this work by the National Science Foundation through the Grant CMMI–1661853 is gratefully acknowledged. Part of this work was performed while V.L. was the Hibbitt Engineering Fellow at Brown University. Support from this fellowship is gratefully acknowledged. Support for this work by the National Science Foundation through the Grant CMMI–1661853 is gratefully acknowledged. Part of this work was performed while V.L. was the Hibbitt Engineering Fellow at Brown University. Support from this fellowship is gratefully acknowledged.
Keywords
- Constitutive modeling
- Elastomers
- Hamilton–Jacobi equations
- Microstructures
- Porosity
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering