Finite strain analysis of limestone / basaltic magma interaction and fracture: Low order mixed tetrahedron and remeshing

Abstract

In this investigation, we use a recent constitutive framework and remeshing technique for tetrahedra to analyze the pressure-driven crack propagation of limestone intruded by basaltic magma. Limestone is represented by an elasto-plastic capped Drucker-Prager model with an hypoelastic term in order to account for inelastic effects from plastic signature. Kinematic hardening is considered for limestone, whereas magma is modeled by means of a compressible Bingham fluid. Classical limit surfaces of the capped model are used to initiate the crack events in the limestone. Propagation is performed by a local remeshing technique with mesh smoothing for uncracked elements. Arnold's MINI element is used to avoid locking in the quasiincompressible case. Verification (for limestone) examples and a crack propagation example in 3D are performed. A mesh convergence study is performed, exhibiting very promising results.

Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase-field fracture by nonlocal operator method

“…Around the fracture front tip, the stress singularity happens for local theory. To model fracture and its evolution, various local theories have been proposed, for example, finite element method (FEM) [4], extended finite element method [5], phase-field fracture method [6][7][8], cracking particle method [9,10], extended finite element method [11], numerical manifold method [12], extended isogeometric analysis (XIGA) for three-dimensional crack [13], meshfree methods [14][15][16]. Another approach for fracture modeling is the nonlocal method.…”

Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase field fracture by nonlocal operator method

“…Around the fracture front tip, the stress singularity happens for local theory. In order to model fracture and its evolution, various local theories have been proposed, for example, finite element method (FEM) [4], extended finite element method [5], phase-field fracture method [6,7,8], cracking particle method [9,10], extended finite element method [11], numerical manifold method [12], extended isogeometric analysis (XIGA) for three-dimensional crack [13], meshfree methods [14,15,16]. Another approach for fracture modeling is the nonlocal method.…”