Phase-field simulation of ductile fracture in shell structures

Davide Proserpio,Marreddy Ambati,Laura De Lorenzis,Josef Kiendl

doi:10.1016/j.cma.2021.114019

Abstract

In this paper, a computational framework for simulating ductile fracture in multipatch shell structures is presented. A ductile fracture phase-field model at finite strains is combined with an isogeometric Kirchhoff–Love shell formulation. For the application to complex structures, we employ a penalty approach for imposing, at patch interfaces, displacement and rotational continuity and C0 and C1 continuity of the phase-field, the latter required if a higher-order phase-field formulation is adopted. We study the mesh dependency of the numerical model and we show that mesh refinement allows for capturing important features of ductile fracture such as cracking along shear bands. Therefore, we investigate the effectiveness of a predictor–corrector algorithm for adaptive mesh refinement based on LR NURBS. Thanks to the adoption of time- and space-adaptivity strategies, it is possible to simulate the failure of complex structures with a reasonable computational effort. Finally, we compare the predictions of the numerical model with experimental results.

Highlights

The numerical prediction of the fracture and post-failure behavior of shell structures constituted by ductile materials like metals requires sophisticated simulation tools
We have presented an approach for the simulation of ductile fracture in shell structures
An isogeometric rotationfree Kirchhoff–Love shell formulation was combined with an elasto-plasticity material model and with a phase-field ductile fracture formulation at finite strains, here extended to the higher-order version

Summary

Introduction

The numerical prediction of the fracture and post-failure behavior of shell structures constituted by ductile materials like metals requires sophisticated simulation tools. Adequate formulations for the description of ductility and fracture, in combination with structural models, are needed. The phase-field approach for the simulation of fracture has been the object of several studies in the last years. The formulation, stemming directly from Griffith’s theory [1], is based on the description of brittle fracture in a variational framework presented by Francfort and Marigo [2], later regularized by Bourdin et al [3]. The competition between the strain and the fracture surface energy controls the nucleation and growth of cracks, which are described by the smooth variation, between the intact and broken material states, of a continuous scalar parameter, the so-called phase-field.

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Conclusion