The cracking elements method (CEM) is a novel numerical approach for simulating fracture of quasi-brittle materials. This method is built in the framework of conventional finite element method (FEM) based on standard Galerkin approximation, which models the cracks with disconnected cracking segments. The orientation of propagating cracks is determined by local criteria and no explicit or implic...

1Landau Associates, 130 2nd Ave South, Edmonds, WA 98020, U.S.A. 2Civil and Environmental Engineering and National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, 205 North Mathews Ave Urbana, IL 61801, U.S.A. 3Department of Nuclear, Plasma and Radiological Engineering, University of Illinois at Urbana-Champaign, 216 Talbot Lab, 104 S. Wright St., Urbana, IL ...

For a plane polygonal domain Q and a corresponding (general) triangulation we define classes of functions pmix, v) which are polynomials on each triangle and which are in C^'CQ) and also belong to the Sobolev space ^""^'(n). Approximation theoretic properties are proved concerning these functions. These results are then applied to the approximate solution of arbitrary-order elliptic boundary va...

The fundamental theory of crystal twinning has been long established, leading to a significant advance in understanding the nature of this physical phenomenon. However, there remains a substantial gap between the elaborate theory and the practical determination of twinning elements. This paper proposes a direct and simple method - valid for any crystal structure and based on the minimum shear c...

This work shows that the method of charcteristics is well suited for the numerical solution of first order hyperbolic partial differential equations whose coefficients are approximated by functions piecewise constant on a finite element triangulation of the domain of integration. We apply this method to the numerical solution of Euler's equation and prove convergence when the time step and the ...