Cracking particles: a simplified meshfree method for arbitrary evolving cracks

Abstract

SUMMARYA new approach for modelling discrete cracks in meshfree methods is described. In this method, the crack can be arbitrarily oriented, but its growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed. The crack is modelled by a local enrichment of the test and trial functions with a sign function (a variant of the Heaviside step function), so that the discontinuities are along the direction of the crack. The discontinuity consists of cylindrical planes centred at the particles in three dimensions, lines centred at the particles in two dimensions. The model is applied to several 2D problems and compared to experimental data.

A meshfree thin shell method for non‐linear dynamic fracture

“…Due to higher order displacement continuity of meshfree methods, when compared with finite elements, the incorporation of strong discontinuities is especially simple. We proposed two methodologies, a cracking particle method [8,13] where the crack is introduced at the particle position and a local partition of unity PU method as in Ventura et al [11]. In the latter case, the crack is modelled as a continuous line.…”

“…Since at least second order complete basis polynomials have to be used, the domains of influence are large and the cracked particles will influence more particles than in the continuum version of this method [8]. Note also, that in [8,13], the method was developed for a stress point integration where stresses are evaluated at nodes and stress points. In this approach, the nodal stresses are obtained by MLS fits.…”

“…We use two methods; both were already used to model cracks in continua, see Rabczuk and Belytschko [8], Ventura et al [11], Rabczuk and Belytschko [13]. The last one was used in linear fracture mechanics and is here modified to deal with cohesive cracks.…”

“…We include in the shell the capability to model cracks, which are modeled either by cracked particles as in Rabczuk and Belytschko [8] or by a local partition of unity [9,10,11]. Due to the higher order continuity of meshfree methods, which enables the use of KirchhoffLove shell theories in pristine form, the incorporation of discontinuities is very simple and straight forward.…”

Phase-field modeling of fracture in linear thin shells

“…Since analytical solutions provide limited information, there has been a keen interest in numerically simulating fracture in thin shells in recent years. However, despite the advances made in modeling fracture for solid bodies [1,2,3,4,5], fracture in thin bodies remains a challenge due to the complex interplay between cracks and the shell kinematics and geometry.…”