Nonlocal Elastic-Damage Interface Mechanical Model

Abstract

The paper presents a nonlocal extension of the elastic-damage interface mechanical model, which is able to describe the effects of the spatially extended microstructure on the decohesion (or fracture) process along a surface. The key feature of the proposed model is an integral constitutive relation between tractions and displacement jumps at the interface. The presence of an integral kernel brings in the model an internal length measure, which characterizes the transition from the microscale, dominated by heterogeneities and discontinuous media, to the mesoscale, characterized as an enhanced homogenized continuum with nonlocal features. The motivations and the fields of applications of the presented approach are rooted on the observation that, in many micromechanical circumstances, the potential process zone, where decohesion might develop, involves a spatial extended and organized microstructure, that produces complex elastic bridging spatial effects. The present model is a generalization of the classical (local) interface and should be adopted when the size of the microstructure, in the interface, is comparable to the size of the process zone. Typically, spatial constitutive interactions can be well modeled by means of integral (nonlocal) relations. In nonlocal constitutive equations, the stress at a point is related to the strain field at the neighboring points, by means of an integral weighting relation. The nonlocal interface constitutive relations are developed following a thermodynamically consistent approach. The damage development along the interface is driven by a nonlocal damage activation function, where the damage driving force is related to a nonlocal strain measure. Namely, a spatial average energy release rate is responsible for the local decohesion development. The model has been implemented in a finite element code, and some numerical applications of microfracture are examined.