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For the finite element simulation of thin soft biological tissues indynamics, shell elements, compared to volume elements, can capture the wholetissue thickness at once, and feature larger critical time steps. However, thecapabilities of existing shell elements to account for irregular geometries,and hyperelastic, anisotropic 3D deformations characteristic of soft tissuesare still limited. As improvement, we developed a new general nonlinear thickcontinuum-based (CB) shell finite element (FE) based on the Mindlin-Reissnershell theory, with large bending, large distortion and large straincapabilities, embedded in the updated Lagrangian formulation and explicit timeintegration. We performed numerical benchmark experiments available from theliterature that focus on engineering linear elastic materials, which, verifiedand proved the new thick CB shell FE to: 1) be accurate an efficient 2) bepowerful in handling large 3D deformations, curved geometries, 3) accommodatecoarse distorted meshes, and 4) achieve comparatively fast computational times.The new element was also insensitive to three types of locking (shear, membraneand volumetric), and warping effects. The capabilities of the present thick CBshell FE in the biomedical realm are illustrated in a companion article (Part2), in which anisotropic incompressible hyperelastic constitutive relations areimplemented and verified.

A New Continuum-Based Thick Shell Finite Element for Soft Biological  Tissues in Dynamics: Part 1 - Preliminary Benchmarking Using Classic  Verification Experiments