Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: I-Analysis

O. Lopez-Pamies, P. Ponte Castañeda

Research output: Contribution to journalArticlepeer-review


The purpose of this paper is to provide homogenization-based constitutive models for the overall, finite-deformation response of isotropic porous rubbers with random microstructures. The proposed model is generated by means of the "second-order" homogenization method, which makes use of suitably designed variational principles utilizing the idea of a "linear comparison composite." The constitutive model takes into account the evolution of the size, shape, orientation, and distribution of the underlying pores in the material, resulting from the finite changes in geometry that are induced by the applied loading. This point is key, as the evolution of the microstructure provides geometric softening/stiffening mechanisms that can have a very significant effect on the overall behavior and stability of porous rubbers. In this work, explicit results are generated for porous elastomers with isotropic, (in)compressible, strongly elliptic matrix phases. In spite of the strong ellipticity of the matrix phases, the derived constitutive model may lose strong ellipticity, indicating the possible development of shear/compaction band-type instabilities. The general model developed in this paper will be applied in Part II of this work to a special, but representative, class of isotropic porous elastomers with the objective of exploring the complex interplay between geometric and constitutive softening/stiffening in these materials.

Original languageEnglish (US)
Pages (from-to)1677-1701
Number of pages25
JournalJournal of the Mechanics and Physics of Solids
Issue number8
StatePublished - Aug 2007
Externally publishedYes


  • Constitutive behavior
  • Finite strain
  • Microstructures
  • Porous material
  • Soft matter

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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