Nonlinear Solid Mechanics

Overview. Rigorous introduction to nonlinear solid mechanics, especially addressing finite kinematics, material frame indifference, constitutive models within a thermodynamic framework. Analysis of nonlinear material behaviors: hyperelasticity, elastoplasticity, viscosity.

Specific topics:

1. Kinematics of deformations. Transformations, motions, kinematics of local deformation. Finite rotations, the polar decomposition
2. Conservation laws. Conservation of mass. Conservation of linear momentum. Conservation of angular momentum. Conservation of energy. The principle of virtual work. Basic on thermodynamics for constitutive laws.
3. Constitutive theories. Coleman-Noll’s theory of equilibrium constitutive equations. Material frame indifference. Thermodynamic potentials (Helmholtz, Enthalpy, Gibbs energy). Kinetic relations. Material classification.
4. Finite Hyper-elasticity. Elastic symmetry. Internal constraints. Elastic materials: isotropic, transversally isotropic, anisotropic materials.
5. Finite Plasticity. Multiplicative decomposition of the deformation gradient. Exponential and logarithmic mapping. J2 plasticity. Pressure dependent plasticity
6. Special materials: fiber reinforced tissues, liquid crystals.