For rock-like and asphalt-mixture materials, the differences in Young's moduli and Poisson ratios are large under the tensile and compressive stress states. Therefore, for fracture mechanics, the stress and displacement fields near the crack tip described by William's series for classical elasticity (single-modulus of material) should be investigated. In this paper, a novel 2D/3D complemented algorithm is established by complementing the constitutive equations of shear modulus. The algorithm is implemented in ABAQUS with the subroutine UMAT and extended to bi-modular plate and cylindrical bar ...
