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.
- Kinematics of deformations. Transformations, motions, kinematics of local deformation. Finite rotations, the polar decomposition
- 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.
- Constitutive theories. Coleman-Noll’s theory of equilibrium constitutive equations. Material frame indifference. Thermodynamic potentials (Helmholtz, Enthalpy, Gibbs energy). Kinetic relations. Material classification.
- Finite Hyper-elasticity. Elastic symmetry. Internal constraints. Elastic materials: isotropic, transversally isotropic, anisotropic materials.
- Finite Plasticity. Multiplicative decomposition of the deformation gradient. Exponential and logarithmic mapping. J2 plasticity. Pressure dependent plasticity
- Special materials: fiber reinforced tissues, liquid crystals.