Formulation of a finite deformation model for the dynamic response of open cell biphasic media

A Rational Procedure for the Experimental Evaluation of the Elastic Coefficients in a Linearized Formulation of Biphasic Media with Compressible Constituents

“…This section summarizes the formulation provided by Serpieri and Rosati (2011) by briefly recalling the relevant state variables, the governing equations, and the boundary conditions of the geometrically nonlinear model. For further details on the general formulation, the reader is referred to the original work.…”

“…The meaning of the quantities introduced in the governing equations above and the relevant notation conventions are briefly recalled below advising that the interested reader can refer to Serpieri and Rosati (2011) for a detailed discussion of the governing equations and a thorough description of the associated physical and mechanical quantities. The accent convention introduced in the companion article is used also in the present one.…”

“…Recently, a least-action variational principle has been also exploited by Serpieri and Rosati (2011) to derive a biphasic formulation with microscopically compressible materials. In such work, by addressing macroscopic homogeneity in a deterministic sense, it is recognized, via an analysis of the kinematics at the microscale, the necessity to take into account two different macroscopic measures of the volume changes of the solid phase, denominated apparent and effective Jacobians, to properly address a global volumetric balance.…”

“…In the present article, the general formulation of Serpieri and Rosati (2011) is further investigated with the main objective of defining a rational procedure to evaluate the elastic moduli of the linearized model on the basis of a set of three macroscopic static tests under spherical symmetry conditions. The definition of such a procedure, dates back to Biot and Willis (1957) and has been addressed by several authors since it constitutes a fundamental step to assess and calibrate a biphasic theory.…”

Formulation of a nonlinear porosity law for fully saturated porous media at finite strains

“…Several extensions have been proposed in a relevant long literature, among others, partially saturated poromechanics, see for example (Borja, 2004;Coussy, 2005;Coussy and Monteiro, 2007), higher order poromechanics, see for example (Ito, 2008;Mroginski et al, 2011), and finite strain poromechanics in different domains ranging from soil mechanics applications, see for example (Armero, 1999;Karrech et al, 2012), to deformation of soft media, see for example (Hong et al, 2008;Serpieri and Rosati, 2011). In parallel, much interest has been devoted to the field of computational poromechanics in order to provide tools for structural finite element simulations, see for example (Armero, 1999;Borja, 1986;Lewis and Schrefler, 1998;Ferronato et al, 2010;Korsawe et al, 2006;White and Borja, 2008) among many others.…”