Thermal effects on nonlinear acceleration waves in the Biot theory of porous media

Abstract

We generalize a theory of Biot for a porous solid based on nonlinear elasticity theory to incorporate temperature effects. Acceleration waves are studied in detail in the fully nonlinear theory. The wavespeeds are found explicitly and the amplitudes are then determined. The possibility of shock formation is discussed.

Anisotropic Rock Poroelasticity Evolution in Ultra‐low Permeability Sandstones under Pore Pressure, Confining Pressure, and Temperature: Experiments with Biot's Coefficient

“…The higher the Biot coefficient is, the bigger the stiffness of the pore is, the more difficult the pore is to be compressed. On the contrary, the lower the Biot coefficient, the smaller the stiffness of the pore is, the easier the pore is to be compressed (Tan et al, 2014;Yang et al, 2015;Luo et al, 2015;Pimienta et al, 2015;Straughan et al, 2018).…”

Jordan–Cattaneo waves: Analogues of compressible flow

“…Indeed, acceleration waves have been studied recently in many different areas of continuum mechanics or even in biology. For example, they have been proved to be useful in random materials, Nishawala and Ostoja Starzewski [6], Ostoja Starzewski and Trebicki [7,8]; in saturated porous media, Jordan [9,10], Jordan et al [11], Ciarletta and Straughan [12], Ciarletta et al [13], Straughan and Tibullo [14], Straughan et al [15]; in hypoplastic materials, Weingartner et al [16,17]; in viscoelastic fluids, Gültop et al [18], Morro [19]; in inhomogeneous fluids, Keiffer et al [20]; in layers of isotropic solids Currò et al [21]; in chemotaxis Barbera and Valenti [22]; in plasticity Loret et al [23]; in perfect gases, relaxing gases and in polytropic gases, Mentrelli et al [24], Christov et al [25], Saxena and Jena [26], Shah and Singh [27]; in micro-structured media, Altenbach et al [28], Eremeyev [29,30], Eremeyev et al [31]; in complex materials, Paoletti [32]; in soft materials, Ziv and Shmuel [33]; and in Green-Naghdi fluids, Christov [34], Jordan and Straughan [35].…”