A convex anisotropic damage model based on the compliance tensor

This work is devoted to anisotropic continuum-damage mechanics in the quasi-static, isothermal, small-strain setting. We propose a framework for damage evolution based on compliance tensor as primary variable, context of generalized standard models dissipative solids. Based observation that Hookean strain energy density linear elasticity jointly convex and tensor, we design thermodynamically consistent satisfy Wulfinghoff’s damage-growth criterion feature free energy. The latter property permits obtaining mesh-independent results component scale without necessity introducing gradients field. introduce concepts stress-extraction tensors damage-hardening functions, implicitly describing rigorous damage-analogue yield surfaces elastoplasticity. These may be combined modular fashion give rise complex damage-degradation behavior. discuss how efficiently integrate Biot’s equation implicitly, show specific functions Puck’s failure criteria. Last but not least demonstrate versatility our proposed model efficiency integration procedure variety examples interest.