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

The paper presents a continuous-discontinuous numerical strategy for sim- ulating 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 encom- pass 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 conse- quence, 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.