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A gradient theory of porous elastic solids
Author(s) -
Ieşan D.
Publication year - 2020
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900241
Subject(s) - positive definiteness , isotropy , uniqueness , mathematics , nonlinear system , mathematical analysis , constitutive equation , mixture theory , galerkin method , classical mechanics , physics , positive definite matrix , eigenvalues and eigenvectors , finite element method , thermodynamics , statistics , quantum mechanics , mixture model
This paper is concerned with a theory of elastic materials with voids where the second gradient of deformation and the second gradient of volume fraction field are added to the set of independent constitutive variables. First, we establish the nonlinear theory and study the continuous dependence of solutions upon initial state and body loads. Then, we derive the linear theory and establish a uniqueness theorem with no definiteness assumption on the constitutive coefficients. We present the equations for homogeneous and isotropic solids and establish a counterpart of the Boussinesq‐Somigliana‐Galerkin solution in the classical elastostatics. The effects of concentrated body loads acting in an infinite space are investigated.