A multi-temporal series high-accuracy numerical manifold method for transient thermoelastic fracture problems

Abstract This paper presents a multi-temporal series high-accuracy numerical manifold method (NMM) for fracture analysis of solid materials under highly time-dependent thermal loadings. In the present method, the framework of NMM is used to perform space discretization of the thermo-mechanical coupling system, due to its advantages in accurately calculating field variables and describing discontinuity. An explicit direct integration scheme based on the precise time step integration method (or PTSIM scheme for short) is constructed for discretization in the time domain. In the present PTSIM scheme, the time-dependent thermal loadings are expressed by means of the basic function in a polynomial form. Highly accurate calculation of the response matrix for the load item is achieved by introducing the exponential transfer matrix. The results of stability, error and convergence analyses indicate that the proposed method is unconditionally stable and convergent. The superior advantages of present method are firstly verified by one example for transient thermal analysis, then four numerical examples with different time-dependent thermal boundary conditions and crack configurations are used for fracture analysis. The results show that the present method is unconditionally stable and time-independent, and high-accuracy can be achieved even for highly time-dependent thermal loadings and large time-step sizes.