Phase-field description of brittle fracture in plates and shells

Abstract

We present an approach for phase-field modeling of fracture in thin structures like plates and shells, where the kinematics is defined by midsurface variables. Accordingly, the phase field is defined as a two-dimensional field on the midsurface of the structure. In this work, we consider brittle fracture and a Kirchhoff-Love shell model for structural analysis. We show that, for a correct description of fracture, the variation of strains through the shell thickness has to be considered and the split into tensile and compressive elastic energy components, needed to prevent cracking in compression, has to be carried out at various points through the thickness, which prohibits the typical separation of the elastic energy into membrane and bending terms. For numerical analysis, we employ isogeometric discretizations and a rotation-free Kirchhoff-Love shell formulation. In several numerical examples we show the applicability of the approach and detailed comparisons with 3D solid simulations confirm its accuracy and efficiency.

A non-intrusive global/local approach applied to phase-field modeling of brittle fracture

“…We mention the papers by Amor et al [7], Miehe et al [8,9], Kuhn and Müller [10], Pham et al [11], Borden et al [12], Mesgarnejad et al [13], Kuhn et al [14], Ambati et al [15], Wu et al [16], where various formulations are developed and validated. Recently, the framework has been also extended to ductile (elasto-plastic) fracture [17][18][19][20][21][22], pressurized fracture in elastic and porous media [23,24], fracture in films [25] and shells [26][27][28], and multi-field fracture [29][30][31][32][33][34][35][36]. Non-intrusive global/local approaches have also been applied to a quite large number of situations: the computation of the propagation of cracks in a sound model using the extended finite element method (XFEM) [37], the computation of assembly of plates introducing realistic non-linear 3D modeling of connectors [38], the extension to non-linear domain decomposition methods [39] and to explicit dynamics [40,41] with an application to the prediction of delamination under impact using Abaqus [42].…”

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

“…In the work of Miehe et al (2010a), a spectral decomposition of the strain tensor is introduced in which only positive strains contribute to the fracture process. Likewise, Kiendl et al (2016) establish a spectral decomposition within a small deformation framework in plates and shells. They have outlined that it is not possible to consider a split into tension and compression as well as a split into membrane and bending contributions at the same time if such a spectral decomposition of the total strain is used.…”

“…In the following, we show an example taken from Kiendl et al (2016) that they use to motivate the need for a thickness integration for the energy split. We use their example to motivate the proposed split of the bending energy density.…”

“…The proposed higher order phase field model of Borden et al (2014) is adopted because of its higher rate of convergence and it is formulated on the shell's mid-plane. Motivated by the work of Kiendl et al (2016), bending effects on the fracture process are modeled based on thickness integration. Adaptive spatial refinement is based on LR NURBS (Zimmermann and Sauer, 2017) and temporal discretization is based on the generalized-α scheme (Chung and Hulbert, 1993).…”

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

“…Initially, energies like (5) have been used in image segmentation problems, e.g. [31], later, after [11], they spread in fracture mechanics, see e.g., [32,28,37,9,30,33,26], the book [12] and the review [2]. In this perspective, Γconvergence provides a rigorous mathematical framework to prove that phase-field energies are consistent with sharp-crack (free discontinuity) energies.…”