Michel R. Labrosse

Bahareh Momenan, Michel R. Labrosse

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.

Bahareh Momenan, Michel R. Labrosse

In a companion article (Part 1), we presented the development of a thick continuum-based (CB) shell finite element (FE) based on Mindlin-Reissner theory. We verified the accuracy, efficiency and locking insensitivity of the element in modeling large 3D deformations, using linear elastic material properties. In the present article, we developed and implemented the kinetics description, within the updated Lagrangian (UL) formulation, of anisotropic incompressible hyperelastic constitutive relations that enable the CB shell FE to accurately model very large 3D strains and deformations. Specifically, we developed the measures of deformation in the lamina coordinate system, presented three techniques to model nonlinear hyperelastic strains, and enabled the direct enforcement of incompressibility and of the zero normal stress condition without using a penalty factor or a Lagrange multiplier. Moving towards the application of the present work to the biomedical realm, we performed multiple experiments concerning mechanical behavior of rubber-like materials and soft biological tissues in different geometries and loading conditions. Excellent agreements between the present FE results and the analytical and/or experimental data proved the CB shell FE combined with the present constitutive techniques to be a highly reliable and efficient tool for modeling, analyzing, and predicting mechanical behavior of soft biological tissues.