Modelling questions in multi-porosity elasticity

Fundamental solutions in the linear theory of thermoelasticity for solids with triple porosity

“…The matrix (s) (x) is constructed explicitly by means of five elementary functions φ (j) (j = 1, 2, 3),γ (5) and γ (6) (see equations ( 43) and ( 46)).…”

“…The mathematical models of multi-porosity media, as originally developed for the mechanics of naturally fractured reservoirs, have found applications in many branches of engineering, technology and biomechanics [1][2][3][4][5].…”

“…Mathematical formulation of flow through triple porosity media with macro-, meso-and microporosity structure was first introduced three decades ago by Liu [31]. Several new triple porosity models for solids with these hierarchical structures are presented by Liu et al [32], Straughan [5,33], Svanadze [34,35] and Wu et al [36]. Moreover, in the work of Straughan [33] the fully coupled linear theory of thermoelasticity for triple porosity anisotropic materials is developed.…”

External boundary value problems in the quasi static theory of triple porosity thermoelasticity

“…We consider an isotropic and homogeneous elastic solid with macro-, meso-and microporosity structure occupies a region of R 3 . The governing system of homogeneous equations of steady vibrations in the quasi static linear theory of thermoelasticity for triple porosity materials with macro-, meso-and micropores consists of the following equations [2]:…”

“…The BVPs of quasi-static theory of thermoelasticity for solids with triple porosity are studied by Svanadze [5]. The general models for anisotropic thermoelastic solids with triple, quadruple and quintuple porosity structures are presented by Straughan [2]. Recently, the mathematical models of double porosity materials are studied by several authors [6][7][8][9][10][11][12][13].…”