Damage, Material Instabilities, and Failure

Abstract

Abstract This chapter begins with an overview of damage mechanics. Isotropic and anisotropic models are described, as well as the coupling to plasticity, including the algorithmic treatment. Next, the implications of strain softening, which starts at a certain level of damage accumulation, are discussed as regards important notions such as material stability and ellipticity. The consequences of loss of ellipticity in terms of grid sensitivity of computations are illustrated for static and dynamic instabilities. Next, the important role of cohesive‐zone models is highlighted, both in its original (discrete) format, a derived smeared format, and as an embedded discontinuum description. To avoid the loss of ellipticity, the introduction of higher order continua is necessary. Various higher order continua incorporating damage or coupled damage–plasticity models are discussed, including aspects of numerical implementation. Also, various discretization methods are discussed, which can accommodate the higher order gradients that arise in higher order gradient models, including meshless methods and isogeometric analysis. Also, the phase‐field approach to brittle fracture and its close relation to gradient damage models are demonstrated. Finally, the numerical implementation of cohesive‐zone models in a discrete format is considered. Attention is given to conventional interface elements, meshless methods, approaches that exploit the partition‐of‐unity property of finite element shape functions, and isogeometric finite element analysis.