An Updated Lagrangian framework for large deformation analysis of thin elastomeric materials

Elastomeric materials are widely used in several engineering disciplines. Due to importance of these materials in vast variety of industries, in this paper, a nonlinear finite element formula for large deformation analysis of hyperelastic elastomeric materials is developed. Both Total Lagrangian (TL) and Updated Lagrangian (UL) frameworks are adopted for developing the FE relations. Firstly, the Total Lagrangian formulation is derived, and then, the Updated Lagrangian framework is achieved after some manipulations the TL relations. This method is derived for the first time which bridges Total Lagrangian framework to the Updated Lagrangian framework. The formulation accounts for isotropic as well as anisotropic hyperelastic materials. Moreover, both compressible and incompressible cases are considered. Eventually, diverse applications of FEM in analyzing large deformation hyperelasticity across various engineering domains are explored. The various approaches and applications showcase the extensive capabilities of both Total and Updated Lagrangian frameworks in this domain.