Anisotropy is inherent in many materials, either because of the manufacturing process, or due to their microstructure, and can markedly influence failure behavior. Anisotropic materials obviously possess both anisotropic elasticity fracture surface energy. Phase-field methods are elegant mathematically well-grounded, have become popular for simulating isotropic brittle fracture. Here, we develo...

The compliance technique has been used to monitor crack length during fracture and fatigue testing of materials. Difficulties arise when this technique is applied to anisotropic biological materials such as bone. In this tutorial, two different methods of analyzing compliance calibration data are described: the standard ASTM method and a new approach developed by the authors specifically for an...

The numerical simulation of quasistatic fracturing of brittle material, where no predefined crack path is imposed, is a challenging problem. In particular, we deal with the Francfort-Marigo model which requires the minimization of the well-known nonconvex and nonsmooth Mumford-Shah functional. To deal with a smoother problem which eases the minimization process of the energy, we consider the Γ-...

A microscopic framework for developing phenomenological constitutive models was recently developed for granular materials. The plastic strains are computed from relative sliding and rolling of particles, and the resulting microscopic theory is called the sliding-rolling theory. Within this framework, a phenomenological constitutive model was then developed to describe the anisotropic stress-str...

a School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China b Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China c Department of Mathematics, National University of Singapore, 119076, Singapore d Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA e Department of Mechanical Engineering and Appl...

We use a concrete simulation scenario to study the effect of hexahedral mesh size and mesh quality on the accuracy of the solution of a finite element analysis (FEA). Our test cases stem from biomedical research. We investigate a composite two-material model of a piece of bone from the human mandible on which we simulate a bite. In particular, we are interested whether material properties (soft...