An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

Abstract

We present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff-Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell's mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith's theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C 1 -continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton-Raphson scheme. The interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.

FFT phase-field model combined with cohesive composite voxels for fracture of composite materials with interfaces

“…In this regard, techniques of automatic loading step control have been explored in several previous contributions. Interested readers are referred to [63][64][65][66] for more details. Alternatively, a fracture-controlled (instead of displacement-controlled) staggered scheme has been proposed by Singh et al [67], which inherits the property of its underlying monolithic scheme, thus simplifying the choice of loading increment.…”

Γ-convergence for high order phase field fracture: Continuum and isogeometric formulations

“…The condition h = o(ε), which appears also in [8], allows to have an accurate approximation of the transition layer of the phase-field variable; in practice it should be satisfied only in a neighbourhood on the discontinuity set and often is obtained by local h-refinement, e.g. [4,10,15,35].…”

Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

“…Further approaches to deal with the thinness of the structure in the context of phase-field modeling exist, such as a formulation with a mixed interpolation of tensorial components (MITC)4+ RM degenerated shell 35 and a solid-shell approach. 36,37 Taken together, the phase-field approach to fracture applied to shells has been subject of extensive research in the recent years, focusing mainly on the extension to specific problems, namely ductile fracture, 38 finite strains, 39 functionally graded materials, 40 thick shells, 41 dynamic problems 42,43 as well as the isogeometric implementation with adaptive refinement 44 or multipatch coupling techniques. 45 However, the application of the phase-field approach to model cracks along the thickness direction of shells has been given very limited attention up until now.…”