Abstract
We present a computational framework for applying the phase-field approach to brittle fracture efficiently to complex shell structures. The momentum and phase-field equations are solved in a staggered scheme using isogeometric Kirchhoff–Love shell analysis for the structural part and isogeometric second- and fourth-order phase-field formulations for the brittle fracture part. For the application to complex multipatch structures, we propose penalty formulations for imposing all the required interface constraints, i.e., displacement (C0) and rotational (C1) continuity for the structure as well as C0 and C1 continuity for the phase field, where the latter is required only in the case of the fourth-order phase-field model. All involved penalty terms are scaled with the corresponding problem parameters to ensure a consistent scaling of the penalty contributions to the global system of equations. As a consequence, all coupling terms are controlled by one global penalty parameter, which can be set to 103 independent of the problem parameters. Furthermore, we present a multistep predictor–corrector algorithm for adaptive local refinement with LR NURBS, which can accurately predict and refine the region around the crack even in cases where fracture fully develops in a single load step, such that rather coarse initial meshes can be used, which is essential especially for the application to large structures. Finally, we investigate and compare the numerical efficiency of loosely vs. strongly staggered solution schemes and of the second- vs. fourth-order phase-field models.
Highlights
The modeling and simulation of crack initiation and propagation for structural members is a challenging research topic of high industrial relevance, as it has applications both during the design process and for the inspection and maintenance of in-service structures
We present an isogeometric approach for the efficient simulation of brittle fracture in complex multipatch shell structures, using Kirchhoff–Love shells coupled with second- and fourth-order phase-field formulations
We presented an efficient simulation framework to apply the phase-field approach to brittle fracture to complex shell structures
Summary
The modeling and simulation of crack initiation and propagation for structural members is a challenging research topic of high industrial relevance, as it has applications both during the design process and for the inspection and maintenance of in-service structures. We present an isogeometric approach for the efficient simulation of brittle fracture in complex multipatch shell structures, using Kirchhoff–Love shells coupled with second- and fourth-order phase-field formulations. This section briefly presents the main features of the phase-field approach for modeling brittle fracture and how this formulation can be coupled with plate and shell models, with a focus on Kirchhoff–Love shells which are considered in this contribution. In each thickness integration point, the total strain is computed as the sum of membrane and bending parts, as in Eq (15), and the spectral split is performed According to this approach, which can be adopted independently of the specific shell formulation, it is possible to describe a nonlinear degradation of stresses and strain energy through the shell thickness (see Fig. 1), assuming only one value of the phase-field variable s and of the degradation function g(s) at the midsurface.
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