Thermodynamic framework of non-local continuum damage–plasticity model

Abstract

We present a novel non-local continuum damage–plasticity model for predicting numerically the progressive failure behavior of cohesive-frictional materials within the framework of irreversible thermodynamics. The damage driving force is a function of the tensile part of elastic strain energy and a portion of the plastic stored energy, in which the introduction of coefficient ${\chi }_p$ provides the opportunity to quantify how the plastic deformation propels the damage growth. The non-local integral-type damage formulation is adopted to quantitatively describe the degradation of Young’s modulus and cohesive strength. The thermodynamically consistent model arrives at a damage–plasticity relationship that simultaneously provides an interplay description between regularized damage evolution and plastic deformation. A Newton–Raphson method is utilized to solve the nonlinear system of equations, in which an analytical non-local damage–plasticity consistent tangent operator is derived with an implicit return mapping algorithm. A detailed material parameter calibration procedure is performed based on standard laboratory tests considering uniaxial-, biaxial- and conventional triaxial-compressive experiments. Furthermore, simulations of proportional low-cyclic tension and compression loads, and triaxial compressive loads for hexahedron plain concrete specimens, a compacted clay specimen under tension loading, and a slope shear-failure problem are conducted to validate the applicability of the proposed model. Numerical simulations highlight the predictive ability of the model in describing the complex behaviors, including material hardening and softening, frictional shear fracture propagation, significant plastic deformation, brittle–ductile failure transition, confining pressure sensitivity, and material properties degradation. The proposed non-local model effectively addresses mesh sensitivity and non-physical spurious oscillations for all field variables.