Phase-field models for crack propagation enable the simulation of complex crack patterns without complex and expensive tracking and remeshing as cracks grow. In the setting without inertia, the crack evolution is obtained from a variational energetic starting point, and leads to an equation for the order parameter coupled to elastostatics. Careful mathematical analysis has shown that this is co...

Contact problems are among the most difficult issues in mathematics and of crucial practical importance engineering applications. This paper presents a scaled boundary finite-element method with B-differentiable equations for 3D frictional contact small deformation elastostatics. Only boundaries system discretized into surface elements by method. The dimension is reduced one. conditions formula...

We present a Nitche’s method to couple non-conforming two and three-dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for linear elastostatics in two and and three-dimensions. The method can deal with surface-surface or volume-volume coupling, and we show how it can be used to handle heterogeneities such as inclusions. W...

A methodology to model arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries is proposed. The numerical method couples the level set method (Osher and Sethian, 1988) to the eXtended Finite Element Method (X-FEM) (Mo es et al., 1999). In the X-FEM, the nite element approximation is enriched by additional functions through the notion of partition of unity. T...

In this paper several methods of dealing with Cauchy Principal Value integrals in advanced boundary element methods are discussed and compared. An attempt is made to present a comprehensive description of these methods in a unified, systematic manner. It is shown that the methods can be grouped into two basic approaches, the (more classical) indirect approach, such as the rigid-body motion tech...

We propose the use of algebras of generalized functions for the analysis of certain highly singular problems in the calculus of variations. After a general study of extremal problems on open subsets of Euclidean space in this setting we introduce the first and second variation of a variational problem. We then derive necessary (Euler-Lagrange equations) and sufficient conditions for extremals. ...

In this paper we present a new mixed variational formulation for the problem of linear elastostatics. Our formulation is very similar to the classical HellingerReissner formulation, but appears superior for finite element discretization. To make plain the relation between the Hellinger-Reissner formulation and the present one, we consider first an elastic body occupying a region g? in Euclidean...

The aim of this manuscript is to give a practical overview of meshless methods (for solid mechanics) based on global weak forms through a simple and well-structured MATLAB code, to illustrate our discourse. The source code is available for download on our website and should help students and researchers get started with some of the basic meshless methods; it includes intrinsic and extrinsic enr...