Finite elements augmented with embedded interphases for application in quasi-brittle materials

Quasi-brittle materials mainly fail under shear or tensile stress state. When the stress limit is reached, fractures propagate and the stress-strain relation exhibits a softening branch until failure. In the framework of finite elements, discrete crack models and continuous smeared crack models have been implemented to best capture material’s response. In this ambit, we propose a strategy based on the Augmented Finite Element Method (A-FEM, [1]), which can be placed among the discrete crack models, since intra-element weak discontinuity is considered and modelled through a zero-thickness interphase model (IPH, [2, 3]). The original element is in practice divided in two elastic sub-elements with an interposed nonliner IPH element, governed by the damage model proposed by Jir´asek [4]. The additional degrees of freedom introduced to decompose the cracked element are condensed at the equilibrium level, therefore are not present at the global level, as for the embedded crack models. The crack-tracking algorithm is based on the strain state at Gauss points and crack orientation evaluated on the basis of the spectral analysis of the fracture tensor built at the element level. Examples are reported to illustrate the main features of the adopted strategy, among which the absence of a global remeshing phase, mesh independency on the results, and versality of the model in simulating some relevant cases.