Observed nonlinearities in frictional and brittle solids such as concrete, rocks, ceramics, and some composites arise mainly due to the nucleation and propagation of microvoids and microcracks. Microcrack formation, propagation, and coalescence damage the material and renders it more compliant. Microdefects and cracks are also usually irreversible and cause strong anisotropy in the response to loads. This paper presents a damage mechanics model to capture material anisotropy and damage under multiaxial stress states for proportional and fatigue type loadings. The theory is cast within the generally accepted principles of thermodynamics with internal variables where the dissipation inequality is invoked to develop loading surfaces. Flow rules for the onset of inelastic deformations is provided and specific damage laws are proposed. The model extension to the cyclic and fatigue type loading is presented and numerical results are provided with comparison to the available experimental data.
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