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

Abstract

Thermoelastic fracture of brittle materials is a key concern for many types of engineering structures such as aerospace components and pressure vessels. These problems present difficulties in modelling as they involve coupling of the effects of thermal and mechanical loadings, and usually material behaviours are strongly discontinuous at crack locations, and highly nonlinear during crack propagation. Most current numerical methods applied to these problems use enrichment functions to model discontinuities of temperature and stresses at cracks, however, these enrichments bring extra unknowns into the model and can lead to numerical difficulties in attempting solutions. In this paper, an adaptive cracking particle method is developed for thermoelastic fracture. The method is meshless, so crack discontinuities can be introduced by modifying the influence domains of particles, rather than through external enrichments. Another benefit is an easy implementation of h-adaptivity, since no transition is required for different densities of particles, and it is easy to build dense groups of particles around crack tips. The results demonstrate that this new method can provide the same level of accuracy as others that employ enrichment functions, but using fewer degrees of freedom. A number of examples show the flexibility of the new method to model a range of thermoelastic problems in 2D including multiple cracks and crack propagation.