S.S. Xu, Y. Dong, Y. Zhang

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.1, pp. 17-26, 2008, DOI:10.3970/cmes.2008.030.017

Abstract A meshless method for arbitrary crack growths is presented. The new method is based on a local partition of unity by introducing additional degrees of freedom that determine the opening of the crack. The crack is modeled with overlapping crack segments located at the nodes. The crack segments are rotated at directional changes of the principal tensile stress such that smearing of the crack is avoided. Such smearing occurs in fixed crack method probably because of inaccurate stress state around the crack tip when the crack propagates. The key feature of our method is that it does not require algorithms… More >

Shardool U. Chirputkar¹, Dong Qian²

CMES-Computer Modeling in Engineering & Sciences, Vol.24, No.2&3, pp. 185-202, 2008, DOI:10.3970/cmes.2008.024.185

Abstract A multiscale method based on the extended space-time finite element method is developed for the coupled atomistic/continuum simulation of nanoscale material systems. Existing single scale approach such as the finite element method has limited capability of representing the fine scale physics in both the spatial and temporal domains. This is a major disadvantage for directly incorporating FEM in coupled atomistic/continuum simulations as it results in errors such as spurious wave reflections at the atomistic/continuum interface. While numerous efforts have been devoted to eliminating the interfacial mismatch effects, less attention has been paid to developing fine scale, atomistic level representations within… More >

Xue-cong Liu¹, Qing Zhang^1,*, Xiao-zhou Xia¹

CMC-Computers, Materials & Continua, Vol.53, No.3, pp. 187-206, 2017, DOI:10.3970/cmc.2017.053.203

Abstract This paper focuses on the study of the stability of explicit time integration algorithm for dynamic problem by the Extended Finite Element Method (XFEM). A new enrichment scheme of crack tip is proposed within the framework of XFEM. Then the governing equations are derived and evolved into the discretized form. For dynamic problem, the lumped mass and the explicit time algorithm are applied. With different grid densities and different forms of Newmark scheme, the Dynamic Stress Intensity Factor (DSIF) is computed by using interaction integral approach to reflect the dynamic response. The effectiveness of the proposed scheme is demonstrated through… More >

E. Ferretti¹

CMC-Computers, Materials & Continua, Vol.36, No.1, pp. 49-72, 2013, DOI:10.3970/cmc.2013.036.049

Abstract In several recent papers studying the Cell Method (CM), which is a numerical method based on a truly algebraic formulation, it has been shown that numerical modeling in physics can be achieved even without starting from differential equations, by using a direct algebraic formulation. In the present paper, our focus will be above all on highlighting some of the theoretical features of this algebraic formulation to show that the CM is not simply a new numerical method among many others, but a powerful numerical instrument that can be used to avoid spurious solutions in computational physics. More >