TY - JOUR

T1 - Phase-field modeling of brittle fracture using an efficient virtual element scheme

AU - Aldakheel, Fadi

AU - Hudobivnik, Blaž

AU - Hussein, Ali

AU - Wriggers, Peter

N1 - Funding information: The corresponding authors gratefully acknowledgesupport for this research by (i) the collaborative research center CRC 1153 “ Process chain for the production of hybrid high-performance components through tailored forming ”, (ii) the “German Research Foundation” (DFG) in the Priority Program SPP 2020 under the project WR 19/58-1 and (iii) the Deutsche Forschungsgemeinschaft in the Priority Program 1748 “ Reliable simulation techniques in solid mechanics: Development of non- standard discretization methods, mechanical and mathematical analysis ” under the project WR 19/50-1 .

PY - 2018/11/1

Y1 - 2018/11/1

N2 - This work addresses an efficient low order virtual element method (VEM) for the phase-field modeling of isotropic brittle fracture. Virtual elements were introduced in the last decade and applied to various problems in solid mechanics. The phase-field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage modeling with constitutive terms rooted in fracture mechanics, see Miehe et al. [23] and Miehe et al. [29]. In the presented contribution, we propose a rigorous variational-based framework for the phase-field modeling of brittle fracture in elastic solids undergoing small strains. The key goal here, is the extension towards the recently developed virtual element formulation due to the flexible choice of nodes number in an element which can be changed easily during the simulation process, as outlined in Wriggers et al. [11] and Wriggers et al. [18]. To this end, the potential density is formulated in terms of suitable polynomial functions, instead of computing the unknown shape functions for complicated element geometries, e.g. arbitrary convex or concave polygonal elements. An important aspect of this work is the introduction of an incremental minimization principle, with a novel construction of the stabilization density for the coupled multi-field problem. On the computational side, a robust and efficient monolithic scheme is employed using the software tool ACEFEM program in the numerical implementation to compute the unknowns (displacement and crack phase-field), see Korelc and Wriggers [52]. The performance of the formulation is underlined by means of representative examples.

AB - This work addresses an efficient low order virtual element method (VEM) for the phase-field modeling of isotropic brittle fracture. Virtual elements were introduced in the last decade and applied to various problems in solid mechanics. The phase-field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage modeling with constitutive terms rooted in fracture mechanics, see Miehe et al. [23] and Miehe et al. [29]. In the presented contribution, we propose a rigorous variational-based framework for the phase-field modeling of brittle fracture in elastic solids undergoing small strains. The key goal here, is the extension towards the recently developed virtual element formulation due to the flexible choice of nodes number in an element which can be changed easily during the simulation process, as outlined in Wriggers et al. [11] and Wriggers et al. [18]. To this end, the potential density is formulated in terms of suitable polynomial functions, instead of computing the unknown shape functions for complicated element geometries, e.g. arbitrary convex or concave polygonal elements. An important aspect of this work is the introduction of an incremental minimization principle, with a novel construction of the stabilization density for the coupled multi-field problem. On the computational side, a robust and efficient monolithic scheme is employed using the software tool ACEFEM program in the numerical implementation to compute the unknowns (displacement and crack phase-field), see Korelc and Wriggers [52]. The performance of the formulation is underlined by means of representative examples.

KW - Brittle fracture

KW - Phase-field modeling

KW - Stabilization

KW - Virtual element method (VEM)

UR - http://www.scopus.com/inward/record.url?scp=85050464413&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2018.07.008

DO - 10.1016/j.cma.2018.07.008

M3 - Article

AN - SCOPUS:85050464413

VL - 341

SP - 443

EP - 466

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -