A Virtual Element Method for transversely isotropic elasticity
For computational mechanics researchers, this provides a locking-free VEM approach for challenging transversely isotropic elasticity problems, though it is an incremental extension of existing VEM techniques.
This work develops a low-order Virtual Element Method for transversely isotropic elasticity that is robust and locking-free for near-incompressible and near-inextensible materials, handling both homogeneous and non-homogeneous fiber directions. Numerical examples demonstrate the method's effectiveness across various element geometries and fiber direction variations.
This work studies the approximation of plane problems concerning transversely isotropic elasticity, using a low-order Virtual Element Method (VEM), with a focus on near-incompressibility and near-inextensibility. Additionally, both homogeneous problems, in which the plane of isotropy is fixed; and non-homogeneous problems, in which the fibre direction defining the isotropy plane varies with position, are explored. In the latter case various options are considered for approximating the non-homogeneous fibre directions at element level. Through a range of numerical examples the VEM approximations are shown to be robust and locking-free for several element geometries and for fibre directions that correspond to mild and strong non-homogeneity.