Correspondence principle between anisotropic poroviscoelasticity and poroelasticity using micromechanics and application to compression of orthotropic rectangular strips

Abstract

In this paper, the correspondence principle between poroviscoelasticity and poroelasticity in both time domain and Laplace transform domain is established for the general case of matrix anisotropy as well as solid constituent anisotropy using micromechanics considerations. Using this correspondence principle, any constitutive relation or formula for material coefficient of linear anisotropic poroviscoelasticity can be obtained from the corresponding expression in poroelasticity. Numerical examples of the complex behavior of the poroviscoelastic Biot’s effective stress coefficient for geomaterials and biomaterials are included as illustration. Moreover, analytical solutions for initial and boundary value problems in the Laplace transform domain in poroelasticity can now be readily transferred to poroviscoelasticity and vice versa. To illustrate this technique, analytical solutions for orthotropic poroelastic rectangular strips under either unconfined compression (Mandel’s problem) or confined compression (1D consolidation problem) subjected to either time-dependent force or time-dependent displacement loading have been derived and then transferred to poroviscoelasticity herein. Finally, a biomechanics analysis of laboratory testing on orthotropic articular cartilage illustrates the usefulness of the newly derived solutions.