TY - CHAP

T1 - Efficient Low Order Virtual Elements for Anisotropic Materials at Finite Strains

AU - Wriggers, P.

AU - Hudobivnik, B.

AU - Korelc, J.

N1 - Funding information: The paper is a contribution to honor Professor Roger Owen on behalf of his 75th birthday. The authors like to thank Roger Owen for his continuous support and friendship throughout the last four decades of research on finite element methods. The first author would like to thank for the support of the DFG within the priority program SPP 1748 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 - 2017/9/10

Y1 - 2017/9/10

N2 - Virtual elements were introduced in the last decade and applied to problems in solid mechanics. The success of this methodology when applied to linear problems asks for an extension to the nonlinear regime. This work is concerned with the numerical simulation of structures made of anisotropic material undergoing large deformations. Especially problems with hyperelastic matrix materials and transversly isotropic behaviour will be investigated. The virtual element formulation is based on a low-order formulations for problems in two dimensions. The elements can be arbitrary polygons. The formulation considered relies on minimization of energy, with a novel construction of the stabilization energy and a mixed approximation for the fibers describing the anisotropic behaviour. The formulation is investigated through a several numerical examples, which demonstrate their efficiency, robustness, convergence properties, and locking-free behaviour.

AB - Virtual elements were introduced in the last decade and applied to problems in solid mechanics. The success of this methodology when applied to linear problems asks for an extension to the nonlinear regime. This work is concerned with the numerical simulation of structures made of anisotropic material undergoing large deformations. Especially problems with hyperelastic matrix materials and transversly isotropic behaviour will be investigated. The virtual element formulation is based on a low-order formulations for problems in two dimensions. The elements can be arbitrary polygons. The formulation considered relies on minimization of energy, with a novel construction of the stabilization energy and a mixed approximation for the fibers describing the anisotropic behaviour. The formulation is investigated through a several numerical examples, which demonstrate their efficiency, robustness, convergence properties, and locking-free behaviour.

UR - http://www.scopus.com/inward/record.url?scp=85029219912&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-60885-3_20

DO - 10.1007/978-3-319-60885-3_20

M3 - Contribution to book/anthology

AN - SCOPUS:85029219912

T3 - Computational Methods in Applied Sciences

SP - 417

EP - 434

BT - Advances in Computational Plasticity

PB - Springer Basel AG

ER -