Fundamental knowledge of nonlinear continuum thermodynamics is a crucial prerequisite for the description of large deformations of arbitrary materials with nonlinear constitutive laws. The lecture provides a systematic representation of nonlinear continuum mechanics and the basics of thermodynamics (energy balance, entropy inequality). Proceeding from the fundamental principles of constitutive theory and the 2nd law of thermodynamics, the procedure for the derivation of thermodynamic consistent and admissible material models is described. All methods are exemplarily applied for the description of a nonlinear deformable, thermoelastic solid. Moreover, some aspects of the numerical treatment of nonlinear processes in space and time are discussed. In particular, the lecture comprises the following topics:

• Motivation and introduction of the problem
• Nonlinear continuum mechanics: kinematics, transport theorems, nonlinear deformation and strain measures in absolute and convective notation
• Stress tensors of Cauchy, Kirchhoff, Piola-Kirchhoff, Biot, Mandel and Green-Naghdi
• Mechanical balance relations: balances of mass, linear momentum and angular momentum
• Thermodynamic balance relations: energy balance and entropy inequality (1st and 2nd law of thermodynamics)
• Elements of classical thermodynamics: internal energy and caloric state variables, thermodynamic potentials, Legendre transformations
• Thermodynamic materials theory: thermodynamic principles and process variables, material symmetry
• Thermoelastic solid: evaluation of the entropy principle, isotropy, the coupled problem of thermomechanics, thermoelasticity in nominal form, energy and entropy elasticity
• Numerical aspects: weak form of the boundary-value problem, time integration of coupled problems, linearization of the field equations, stability criteria