Partition of unity-based thermomechanical meshfree method for two-dimensional crack problems

Abstract

We present a partition of unity-enriched element-free Galerkin method for thermoelastic twodimensional crack problems. Therefore, the displacement field is enriched by the step enrichment. In the vicinity of the crack tip, the asymptotic branch enrichment functions commonly used in linear elastic fracture mechanics are employed. The same enrichment strategy is employed for the temperature field. Level set functions are used in order to model the crack surface. The accuracy of the method is demonstrated for three examples, one involves the crack propagation due to temperature and mixed traction-temperature loading conditions with complex curved crack paths.

Thermoelastic fracture modelling in 2D by an adaptive cracking particle method without enrichment functions

“…External enrichment functions have been widely used in numerical methods including the XFEM [4,12,13] and the EFGM [14][15][16][17] to model the temperature discontinuities at cracks. Generally, two different types of cracks are studied in steady heat flux problems namely adiabatic and isothermal cracks, and the two cases result in different enrichment functions, which are applied according to the boundary conditions of the problem.…”

“…The boundary element method (BEM) is an alternative (as in [10]), but meets dilemmas for modelling thermal nonlinearity [11]. Much success has been achieved via the use of enrichment functions within finite elements and meshless methods to model thermal fracture following their success for the purely mechanical case, for instance, in the extended finite element method (XFEM) [4,12,13], the element free Galerkin method (EFGM) [14][15][16][17], the numerical manifold method (NMM) [18,19], and the isogeometric analysis method (IGA) [20].…”

Fourth order phase-field model for local max-ent approximants applied to crack propagation

“…However, they also do not resolve the issue of complex track cracking procedures. An alternative to model complex fracture are meshfree methods [1,4,5,35,49,50,51,52,53,58,61,62,66]. While those contributions also rely on the representation of the crack surface, some meshfree methods such as the Cracking Particles Method [56,57] model fracture as a set of crack segments and therefore can capture -on cost of the accuracy in the crack kinematics -complex fracture patterns quite naturally.…”