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In this paper, we study the preferential stiffness and the crack-tip fieldsfor an elastic porous solid of which material properties are dependent upon thedensity. Such a description is necessary to describe the failure that can becaused by damaged pores in many porous bodies such as ceramics, concrete andhuman bones. To that end, we revisit a new class of implicit constitutiverelations under the assumption of small deformation. Although the constitutiverelationship \textit{appears linear} in both the Cauchy stress and linearizedstrain, the governing equation bestowed from the balance of linear momentumresults in a quasi-linear partial differential equation (PDE) system. For thelinearization and obtaining a sequence of elliptic PDEs, we propose thesolution algorithm comprise a \textit{Newton's method} coupled with a bilinearcontinuous Galerkin-type finite elements for the discretization. Our algorithmexhibits an optimal rate of convergence for a manufactured solution. In thenumerical experiments, we set the boundary value problems (BVPs) with edgecrack {under different modes of loading (i.e., the pure mode-I, II, and themixed-mode). From the numerical results, we find that the density-dependentmoduli model describes diverse phenomena that are not captured within theframework of classical linearized elasticity. In particular,numerical solutionsclearly indicate that the nonlinear \textit{modeling} parameter depending onits sign and magnitude can control preferential mechanical stiffness along withthe change of volumetric strain; larger the parameter is in the positivevalue}, the responses are such that the strength of porous solid gets weakeragainst the tensile loading while stiffer against the in-plane shear (orcompressive) loading, which is vice versa for the negative value of it.

Preferential stiffness and the crack-tip fields of an elastic porous solid based on the density-dependent moduli model