Finite elements with embedded interphases for strain localization in quasi-brittle materials

The paper presents a continuous-discontinuous numerical strategy for simulating localized failure in structures made of quasi-brittle materials using finite elements. The strategy is based on observing acting stresses scenarios, when a diffuse degradation is followed by high deformation bands localizing in certain regions of the structure. The numerical strategy should encompass both situations in accordance with the material’s constitutive model. This objective is achieved by introducing a thin layer into a finite element at a certain level of the deformation process. In this study, the thin layer is modeled for the first time by an interphase mechanical device whose consti- tutive behavior is the same as the bulk material. This is possible since the interphase adds internal strains and stresses to the contact ones. As a consequence, no additional constitutive model and parameters are needed, unlike the zero-thickness interface or cohesive zone models commonly employed. The proposed numerical strategy is illustrated in detail both at the element level and at the structural level. A new crack tracking algorithm has been developed based on decomposition of the model into substructures to allow cracks to cross arbitrary meshes. Some benchmark examples are presented showing the mesh-size and mesh-bias independence of results, together with the convergence behavior of the model.