Discontinuous Galerkin approximations for near-incompressible and near-inextensible transversely isotropic bodies
For computational mechanics researchers, this paper addresses locking in DG methods for anisotropic materials, but the contribution is incremental as it extends known isotropic techniques to transverse isotropy.
This work studies discontinuous Galerkin approximations for transversely isotropic linear elastic bodies, identifying extensional locking in the inextensible limit and proposing under-integration of extensional edge terms as a remedy, which achieves uniformly convergent, optimal-rate behavior confirmed by numerical tests.
This work studies discontinuous Galerkin (DG) approximations of the boundary value problem for homogeneous transversely isotropic linear elastic bodies. Low-order approximations on triangles are adopted, with the use of three interior penalty DG methods, viz. nonsymmetric, symmetric and incomplete. It is known that these methods are uniformly convergent in the incompressible limit for the isotropic case. This work focuses on behaviour in the inextensible limit for transverse isotropy. An error estimate suggests the possibility of extensional locking, a feature that is confirmed by numerical experiments. Under-integration of the extensional edge terms is proposed as a remedy. This modification is shown to lead to an error estimate that is consistent with locking-free behaviour. Numerical tests confirm the uniformly convergent behaviour, at an optimal rate, of the under-integrated scheme.