Computational Morphogenesis: Morphologic constructions using polygonal discretizations

Abstract

To consistently coarsen arbitrary unstructured meshes, a computational morphogenesis process is built in conjunction with a numerical method of choice, such as the virtual element method with adaptive meshing. The morphogenesis procedure is performed by clustering elements based on a posteriori error estimation. Additionally, an edge straightening scheme is introduced to reduce the number of nodes and improve accuracy of solutions. The adaptive morphogenesis can be recursively conducted regardless of element type and mesh generation counting. To handle mesh modification events during the morphogenesis, a topology-based data structure is employed, which provides adjacent information on unstructured meshes. Numerical results demonstrate that the adaptive mesh morphogenesis effectively handles mesh coarsening for arbitrarily shaped elements while capturing problematic regions such as those with sharp gradients or singularity.

Virtual element method for mixed-mode cohesive fracture simulation with element split and domain integral

“…Finally, stresses at the Gauss points of each single virtual grid are obtained using the shape functions of the bilinear quadrilateral element. We remark that the patch-based gradient recovery scheme (Choi et al 2021;Chi et al 2019) may be an alternative choice to evaluate the stress field around the crack-tip region, which can provide a more accurate gradient field than the original VEM solutions. A further comparative study of various stress recovery schemes on VEM for fracture modeling is subjected to future investigation.…”

“…Recently, the virtual element method (VEM) is developed to consistently handle arbitrary polygonal and polyhedral elements (Beira ˜o da Veiga et al 2013). Because of the flexibility on the element shape, VEM has been utilized to solve various engineering problems (Choi et al 2021;Park et al 2019;Chi et al 2020;Wriggers et al 2017Wriggers et al , 2021. For the application to brittle crack propagation problems, a cutting technique is employed on a polygonal mesh (Hussein et al 2019), while some of computational results demonstrated the oscillation in a predicted crack path.…”