  For the finite element simulation of thin soft biological tissues in
dynamics, shell elements, compared to volume elements, can capture the whole
tissue thickness at once, and feature larger critical time steps. However, the
capabilities of existing shell elements to account for irregular geometries,
and hyperelastic, anisotropic 3D deformations characteristic of soft tissues
are still limited. As improvement, we developed a new general nonlinear thick
continuum-based (CB) shell finite element (FE) based on the Mindlin-Reissner
shell theory, with large bending, large distortion and large strain
capabilities, embedded in the updated Lagrangian formulation and explicit time
integration. We performed numerical benchmark experiments available from the
literature that focus on engineering linear elastic materials, which, verified
and proved the new thick CB shell FE to: 1) be accurate an efficient 2) be
powerful in handling large 3D deformations, curved geometries, 3) accommodate
coarse distorted meshes, and 4) achieve comparatively fast computational times.
The new element was also insensitive to three types of locking (shear, membrane
and volumetric), and warping effects. The capabilities of the present thick CB
shell FE in the biomedical realm are illustrated in a companion article (Part
2), in which anisotropic incompressible hyperelastic constitutive relations are
implemented and verified.
