This course aims to provide advanced theoretical and computational foundations for finite element analysis of solid mechanics problems with geometric and material nonlinearities. In particular, the course aims to introduce

• Nonlinear kinematics of deformable solids, including finite strain measures, deformation gradient, and objective stress rates
• Variational principles and weak formulations for linear and nonlinear boundary value problems in solid mechanics
• Finite element formulation of structural elements, including plates and shells, with emphasis on locking phenomena and numerical pathologies
• Incompressible and quasi-incompressible formulations and stabilization techniques such as reduced integration, ANS, and EAS methods
• Consistent linearization of nonlinear weak forms and derivation of material and geometric tangent stiffness matrices
• Constitutive modeling at small and finite strains, including hyperelasticity, viscoelasticity, damage, and finite strain plasticity
• Algorithmic implementation of advanced constitutive models within the finite element framework