Meshfree thermomechanical crack growth simulations with new numerical integration scheme

摘要

This paper presents for the first time an improved meshfree particle method without the need for background cells in terms of numerical integration for thermal-mechanical crack growth analysis. In this work, both adiabatic and isothermal crack surfaces are considered. Asymptotic solutions-based enriched functions are incorporated into the approximation scheme to mathematically capture jump across crack surfaces of both the temperature and displacements, as well as the singularities of heat fluxes and stresses in the vicinity of crack tip. Once the stress intensity factors (SIFs) are evaluated, the direction of crack growth can be determined. The meshfree analysis is based on radial point interpolation method (RPIM), in which Cartesian transformation method (CTM) is adopted for numerical integration, instead of the conventional Gaussian quadrature. The utilization of Gaussian scheme requires background cells in shape of quadrilaterals or triangles. In contrast, the CTM is advantageous in the manner that the background cells are no longer required, leading to truly meshfree formulation. The novel contribution of the current work is the extension of CTM scheme in which the integration domain is updated according to crack growth. The crack surfaces are viewed as part of the boundaries of the problem domain. Therefore, it is guaranteed that no discontinuities exist within the domain. The accuracy of the proposed approach is demonstrated by comparison of computed results with reference ones from analytical solution, and other existing numerical methods.