We derive a finite element formulation for modelling fracture in 2d quasi-brittle solids. The kinematics of isoparametric quadrilateral is enriched by strong discontinuity in displacements in order to capture the discrete crack opening and sliding. To describe both the bulk and crack-surface dissipative phenomena induced by the crack propagation, a combination of continuum and discrete damage models is used. The continuum damage model describes dissipation in the bulk, which mainly occurs ahead of the crack front. The discrete damage model includes two uncoupled rigid-damage cohesive laws to deal with fracture energy release due to crack propagation in modes I and II. The numerical solution strategy is based on a local-global operator-split procedure and incorporates a crack-tracking algorithm for enforcing continuity of the crack path. Numerical examples illustrate very satisfying performance of the derived formulation in terms of mesh independency and robustness. The sensitivity of results on material parameters for mixed mode fracture is also illustrated.
COBISS.SI-ID: 9088609
We compare three nearly optimal quadrilateral finite elements for geometrically exact inextensible-director shell model. Two of them are revisited and one is novel. The assumed natural strain (ANS) element of Ko et al. (Comput Struct 185:1-14, 2017) shows low sensitivity to mesh distortion and excellent convergence behavior for most types of shell problems. The Hu Washizu element with ANS shear strains of Wagner and Gruttmann (Int J Numer Methods Eng, 64:635-666, 2005) allows for large solution steps and is computationally fast. However, both formulations have undesirable weak spots, which we clearly identify by a comprehensive set of numerical examples. We show that a straightforward combination of both formulations results in a novel element that synergizes the positive features and eliminates the weak spots of its predecessors.
COBISS.SI-ID: 8875617