The MLS-based numerical manifold method with applications to crack analysis

In order to solve problems, from a continuum point of view and in a unified way, involving continuum and discontinuum deformation, and small deformation and large movement, the numerical manifold method (NMM) introduces two covers, namely the mathematical cover (MC) and the physical cover (PC). This study generates the MC with the influence domains of nodes in the moving least squares (MLS) interpolation instead of commonly-used finite element meshes, significantly simplifying the generation of PCs and the simulation of crack growth. Advantageous over the conventional meshfree method, the MLS-based NMM can naturally treat complex geometry without recourse to those complicated but contrived criteria or operations. Moreover, the treatment of large movement caused by cracking is much easier with the MLS-based NMM than with the FE-based NMM.