TY - JOUR

T1 - An adaptive global–local approach for phase-field modeling of anisotropic brittle fracture

AU - Noii, Nima

AU - Aldakheel, Fadi

AU - Wick, Thomas

AU - Wriggers, Peter

N1 - Funding Information: NN was partially supported by the Priority Program DFG - SPP 1748 under the project WI 4367/2-1 . FA was founded by the Priority Program DFG - SPP 2020 under the project WR 19/58-1 . TW and PW were funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122) , project ID 390833453 . Appendix A

PY - 2020/4/1

Y1 - 2020/4/1

N2 - This work addresses an efficient Global–Local approach supplemented with predictor–corrector adaptivity applied to anisotropic phase-field brittle fracture. The phase-field formulation is used to resolve the sharp crack surface topology on the anisotropic/non-uniform local state in the regularized concept. To resolve the crack phase-field by a given single preferred direction, second-order structural tensors are imposed to both the bulk and crack surface density functions Accordingly, a split in tension and compression modes in anisotropic materials is considered. A Global–Local formulation is proposed, in which the full displacement/phase-field problem is solved on a lower (local) scale, while dealing with a purely linear elastic problem on an upper (global) scale. Robin-type boundary conditions are introduced to relax the stiff local response at the global scale and enhancing its stabilization. Another important aspect of this contribution is the development of an adaptive Global–Local approach, where a predictor–corrector scheme is designed in which the local domains are dynamically updated during the computation. To cope with different finite element discretizations at the interface between the two nested scales, a non-matching dual mortar method is formulated. Hence, more regularity is achieved on the interface. Several numerical results substantiate our developments.

AB - This work addresses an efficient Global–Local approach supplemented with predictor–corrector adaptivity applied to anisotropic phase-field brittle fracture. The phase-field formulation is used to resolve the sharp crack surface topology on the anisotropic/non-uniform local state in the regularized concept. To resolve the crack phase-field by a given single preferred direction, second-order structural tensors are imposed to both the bulk and crack surface density functions Accordingly, a split in tension and compression modes in anisotropic materials is considered. A Global–Local formulation is proposed, in which the full displacement/phase-field problem is solved on a lower (local) scale, while dealing with a purely linear elastic problem on an upper (global) scale. Robin-type boundary conditions are introduced to relax the stiff local response at the global scale and enhancing its stabilization. Another important aspect of this contribution is the development of an adaptive Global–Local approach, where a predictor–corrector scheme is designed in which the local domains are dynamically updated during the computation. To cope with different finite element discretizations at the interface between the two nested scales, a non-matching dual mortar method is formulated. Hence, more regularity is achieved on the interface. Several numerical results substantiate our developments.

KW - Anisotropic brittle fracture

KW - Global–local formulation

KW - Non-matching dual mortar method

KW - Phase-field modeling

KW - predictor–corrector adaptivity

KW - Robin-type boundary condition

UR - http://www.scopus.com/inward/record.url?scp=85075817393&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1905.07519

DO - 10.48550/arXiv.1905.07519

M3 - Article

AN - SCOPUS:85075817393

VL - 361

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 112744

ER -