An adaptively refined XFEM with virtual node polygonal elements for dynamic crack problems

A Brief Review on Polygonal/Polyhedral Finite Element Methods

“…The method has been extended to 3D polyhedral (VPHE) and hexahedral forms and implemented in adaptive computations as can be seen in the literature [123,125,126]. Recently, the method has been coupled with extended FEM (XFEM) [127,128].…”

Dynamic fracture analysis of the linearly uncoupled and coupled physical phenomena by the variable-node multiscale XFEM

“…In order to improve computing efficiency and accuracy, multiscale mesh, i.e., mesh locally refined in the vicinity of cracks, is used and the variable-node elements [23,26] are adopted to as linking elements (or transition elements) between large scale elements and small scale elements, which is schematically sketched in Fig. 1.…”

“…[22] constructed a multiscale XFEM for modeling heterogeneous materials using the multiscale basis functions as a bridge between two scales. Teng et al [23] integrated the virtual node polygonal elements with XFEM for modelling dynamic crack growth. Kumar et al [24] developed a homogenized multigrid XFEM for the crack growth simulations in ductile materials, in which the domain contains the microstructural defects is simulated by fine mesh while other domains are simulated by coarse mesh with homogenized properties.…”

On a Computational Approach to Micro- and Macro-modelling of Damage in Brittle and Quasi-brittle Materials

“…Moreover (24) contains the special sign functions H j with values ±1 only, the crack surface functions F j referring to all parts of Λ and some branch functions F l extracted from asymptotic fields; for more details of such functions and instructive examples cf. [55], [56] and [57]. The singularity-based approach by [58] pays special attention to the 3rd additive term of (24), whose specification, namely the reasonable form of F l from both the point of view of physical justification and that of practical reliable setting of selected material parameters, can be derived the detailed analysis of various modes of stress singularities on crack tips following [59].…”