Program

Kinematics

Motion of a body. The deformation gradient. Rigid deformations. Polar decomposizion. Deformation of volume and area. Motion velocity, velocity gradient, stretching, and spin

Basic Mechanical Principles

Balance of mass. Force and Moments. Balance laws for linear and angular momentum. Frame of reference. Frame-indifferent principle. Referential forms for the mechanical law: Piola stress, expended power, second Piola stress. Inertia and invariance.

Basic Thermodynamical Principles

The first law: balance of energy. The second law: non-negative production of entropy.  Basic hypotheses for developing physically meaningful constitutive theories: constitutive response functions, frame indifference and compatibility with thermodynamics, Coleman-Noll procedure.

Constitutive theory

Dissipative phenomena: rigid heat conductors, thermoelasticity; phase segregation and diffusion; diffusion coupled to elasticity; rate-independent, finite-strain plasticity.

References

M.E. Gurtin, An Introduction to Continuum Mechanics, Academic Press, 1982.

M.E. Gurtin, E. Fried, L. Anand, The Mechanics and Thermodynamics of Continua, Cambridge University Press, 2010.

 C. Truesdell, A First Course in Rational Continuum Mechanics, Academic Press, 1977.