TY - JOUR

T1 - Nearly-constrained transversely isotropic linear elasticity

T2 - energetically consistent anisotropic deformation modes for mixed finite element formulations

AU - Marino, Michele

AU - Wriggers, Peter

N1 - Funding Information: M. Marino acknowledges that this work has been funded partially by the Masterplan SMART BIOTECS (Ministry of Science and Culture of Lower Saxony, Germany) and partially by the Rita Levi Montalcini Program for Young Researchers (Ministry of Education, University and Research, Italy). P. Wriggers gratefully acknowledges the support of the German Research foundation within the Priority Program SPP 1748 under the project WR19/50-2.

PY - 2020/10/1

Y1 - 2020/10/1

N2 - Strong anisotropies and/or near-incompressibility properties introduce internal constraints in material deformation. Numerical simulations comprising such a constrained behaviour show an overstiff structural response, referred to as element locking. Implementations based on mixed variational methods can heal locking but available solutions in the state-of-the-art are still non-optimal for anisotropic materials. This paper addresses this issue, by proposing a novel decomposition of anisotropic deformation modes on the basis of kinematic and energy requirements. Theoretical results exploit the Walpole's formalism. The proposed kinematic split allows to introduce a new class of variational principles, referred to as energetically decoupled, for nearly-constrained transversely isotropic materials in linear elasticity. Low-order mixed finite element models are thus derived for treating near-inextensibility and/or near-incompressibility. Two-dimensional benchmark tests reproducing pure-bending and Cook's membrane problems are conducted. Numerical results show that the accuracy of energetically decoupled formulations is high and robust with respect to variations of material properties, while the accuracy of non-energetically decoupled formulations is more sensitive.

AB - Strong anisotropies and/or near-incompressibility properties introduce internal constraints in material deformation. Numerical simulations comprising such a constrained behaviour show an overstiff structural response, referred to as element locking. Implementations based on mixed variational methods can heal locking but available solutions in the state-of-the-art are still non-optimal for anisotropic materials. This paper addresses this issue, by proposing a novel decomposition of anisotropic deformation modes on the basis of kinematic and energy requirements. Theoretical results exploit the Walpole's formalism. The proposed kinematic split allows to introduce a new class of variational principles, referred to as energetically decoupled, for nearly-constrained transversely isotropic materials in linear elasticity. Low-order mixed finite element models are thus derived for treating near-inextensibility and/or near-incompressibility. Two-dimensional benchmark tests reproducing pure-bending and Cook's membrane problems are conducted. Numerical results show that the accuracy of energetically decoupled formulations is high and robust with respect to variations of material properties, while the accuracy of non-energetically decoupled formulations is more sensitive.

KW - Anisotropic materials

KW - Mixed finite element method

KW - Near-incompressibility

KW - Nearly-inextensible fibers

KW - Variational principles

UR - http://www.scopus.com/inward/record.url?scp=85086995679&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2020.05.011

DO - 10.1016/j.ijsolstr.2020.05.011

M3 - Article

AN - SCOPUS:85086995679

VL - 202

SP - 166

EP - 183

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

ER -