No abstract

No abstract

No abstract

A novel variational framework to model the fatigue behavior of brittle materials based on a phase-field approach to fracture is presented. The standard regularized free energy functional is modified introducing a fatigue degradation function that effectively reduces the fracture toughness as a proper history variable accumulates. This macroscopic approach allows to reproduce the main known features of fatigue crack growth in brittle materials. Numerical experiments show that the Wöhler curve, the crack growth rate curve and the Paris law are naturally recovered, while the approximate Palmgren-Miner criterion and the monotonic loading condition are obtained as special cases.

We present an approach for phase-field modeling of fracture in thin structures like plates and shells, where the kinematics is defined by midsurface variables. Accordingly, the phase field is defined as a two-dimensional field on the midsurface of the structure. In this work, we consider brittle fracture and a Kirchhoff-Love shell model for structural analysis. We show that, for a correct description of fracture, the variation of strains through the shell thickness has to be considered and the split into tensile and compressive elastic energy components, needed to prevent cracking in compression, has to be carried out at various points through the thickness, which prohibits the typical separation of the elastic energy into membrane and bending terms. For numerical analysis, we employ isogeometric discretizations and a rotation-free Kirchhoff-Love shell formulation. In several numerical examples we show the applicability of the approach and detailed comparisons with 3D solid simulations confirm its accuracy and efficiency.

In the last few years several authors have proposed different phasefield models aimed at describing ductile fracture phenomena. Most of these models fall within the class of variational approaches to fracture proposed by Francfort and Marigo [13]. For the case of brittle materials, the key concept due to Griffith consists in viewing crack growth as the result of a competition between bulk elastic energy and surface energy. For ductile materials, however, an additional contribution to the energy dissipation is present and is related to plastic deformations. Of crucial importance for the performance of the modeling approaches is the way the coupling is realized between plasticity and phase field evolution. Our aim is a critical revision of the main constitutive choices underlying the available models and a comparative study of the resulting predictive capabilities.

No abstract

An isogeometric thin shell formulation allowing for large-strain plastic deformation is presented. A stress-based approach is adopted, which means that the constitutive equations are evaluated at different integration points through the thickness, allowing the use of general 3D material models. The plane stress constraint is satisfied by iteratively updating the thickness stretch at the integration points. The deformation of the shell structure is completely described by the deformation of its midsurface, and, furthermore, the formulation is rotation-free, which means that the discrete shell model involves only three degrees of freedom. Several numerical benchmark examples, with comparison to fully 3D solid simulations, confirm the accuracy and efficiency of the proposed formulation.