Reduction of Macroscale Calibration Experiments Through Constraints on Anisotropic Elastic Stiffnesses Available to Purchase

Geomaterials that are assumed to have symmetry about a single preferred direction have five independent transversely isotropic elastic constants. These elastic constants can be determined from data obtained through a series of macroscale calibration experiments, but only a subset of these five constants can be found directly from axial and lateral stressstrain measurements on a single cylindrical sample of material. Substructural axisymmetric inhomogeneities present in the material and decoupling methods used in modeling can imply constraints on transversely isotropic elastic constants, potentially reducing the number of macroscale experiments needed to characterize a geomaterial model. Morphology of substructural heterogeneities, such as distributions of microscale inclusions, cracks, pores and fibers, lead to homogenization or distribution parameters that affect the fourth-order elastic stiffness of the material. Constitutive models that decouple the elastic stiffness often neglect interaction components, which impose constraints on the transversely isotropic elastic constants. We consider the mathematically motivated decoupling of tensorially linear and non-linear functions of a structural or fabric tensor. Neglecting the non-linear components, as often done for rock models, imposes a constraint that the lateral shear modulus depends on the remaining elastic constants. We also consider the mathematically motivated decoupling of purely-volumetric and purely-deviatoric components, often used in the field of biomechanics. When the mixed volumetric-deviatoric components are neglected, the axial and lateral Poisson’s ratios are constrained to become dependent on the two tensile moduli and a new independent bulk modulus type parameter. The described constraints reduce the number of independent elastic constants from five to four. In biomechanics, the accuracy of the approximation from the constraints can be verified through knowledge that the substructural source of anisotropy is fibers embedded in a mostly incompressible water matrix. The potential for using similar techniques to investigate approximations that use constraints on elastic constants is discussed for geomaterials, specifically non-interacting cracked solids, with the goal of reducing the number of macroscale experiments needed to characterize a geomaterial model.