Non-Smooth Thermomechanics

1. The Description of a Material.- 3. The Constitutive Laws. Case of No Constraint on the State Quantities or Their Velocities.- 5. The Constitutive Laws on a Discontinuity Surface.- 6. Deformable Solids with Interactions at a Distance.- 7. Deformable Solids Without Interaction at a Distance.- 8. Collision of Rigid Bodies. Multiple Collisions.- 9. Evolution of Two Deformable Solids with Collisions.- 10. Material with Volume Interactions at a Distance. Fibre Reinforced Material.- 11. Solid—Liquid Phase Change. Supercooling. Soil Freezing.- 12. Damage. Gradient of Damage.- 13. Shape Memory Alloys.- 14. Unilateral Contact. Contact with Adhesion.- A.1 Convex Functions.- A.1.1 Subgradient of a Convex Function. Subdifferential Set.- A.1.2 Indicator Function of a Set.- A.1.5 Indicator Function of the Segment [0, 1].- A.1.7 Indicator Function of a Triangle.- A.1.9 A Property of the Subdifferential Set.- A.1.10The Dual Function of a Convex Function.- A.2 Material Derivatives.- A.2.1 Material Derivative of a Function.- A.2.2 Material Derivative of a Surface Integral.- A.2.3 Material Derivative of a Double Surface Integral.- A.2.4 Mass Balance on a Surface.- A.2.5 Material Derivatives of Integrals of Mass Densities.- References.