Nearly-constrained transversely isotropic linear elasticity: energetically consistent anisotropic deformation modes for mixed finite element formulations

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 nonenergetically decoupled formulations is more sensitive. (C) 2020 Elsevier Ltd. All rights reserved.