An exact result for the macroscopic response of porous Neo-Hookean solids

M. I. IDIART; O. LOPEZ-PAMIES

Blacksburg (VA)

Conferencia; The 2009 Joint ASCE-ASME-SES Conference on Mechanics and Materials; 2009

Society of Engineering Science

The stored-energy function of a finitely strained hyperelastic solid can be significantly affected by the presence of random micro-porosity. Thus far, exact results for the resulting stored-energy function have been limited to very simple porous microgeometries and loading conditions, while approximations have remained elusive until very recently. In this work, we consider a novel and fairly general class of microgeometries for which the stored-energy function can be computed exactly to a large degree of generality: infinite-rank laminate microgeometries. Their stored-energy function is solution to a Hamilton-Jacobi equation where the initial volume fraction of pores and the macroscopic deformation gradient tensor play the roles of time and space,  respectively. As a first application of the proposed formulation, we derive an exact closed-form result for the macroscopic response of a porous Neo-Hookean solid containing an isotropic distribution of pores. The main theoretical and practical aspects of this result are discussed.