1. Strain energy. Hydrostatic and deviatoric components of strain energy. Complementary strain energy. 2. Principle of virtual work. Principles of minimum potential energy and minimum of complementary potential energy. 3. Constitutive relations - Axioms of constitutive theory (causality, determinism and equipresence, objectivity, material invariance, neighborhood, memory and temporal irreversibility and maximum probability). 4. Stress-strain relations for isotropic and anisotropic linear elastic materials, generalized Hooke's law. Orthotropic and transverse isotropic material. 5. Stiffness tensor of anisotropic material. Voigt notation for symmetric tensors. Coordinate transformation. 6. Basic terms of composite mechanics. Materials used for composites. Reinforcement materials and matrix materials. Fibrous composites and particulate composites. 7 Determination of basic mechanical parameters of composite materials reinforced by continuous fibers and textiles. 8. Analysis of laminated composites based on the Kirchhoff theory. Laminate stiffness matrix. Influence of temperature and humidity on stress and deformation of laminate. 9. Particle composites and their properties. Nanocomposites. Biocomposites. Hybrid composites. Intelligent materials. 10. Experimental methods and testing of composites. 11. Composite failure. Directional dependence of strength. Shear strength. Impact. Criteria for failure of complex stress state. Strength of laminates. Fundamentals of fracture mechanics of composite materials. Fatigue damage of composites. 12. Linear viscoelastic materials - time-dependent behavior of polymers and some biological materials in small strains. Viscoelastic constitutive equations in differential form. Overview of one-dimensional models of viscoelastic materials, rheological models. 13. Relaxation and creep, principle of superposition, expression of relaxation modules using Prony series, elastic and viscous part of the strain. 14. Dynamic response of viscoelastic materials, complex dynamic modulus and damping. Equivalence of time and temperature. Experimental determination of rheological parameters. 15. Hyperelastic materials - rubbers and foams. Free energy functions and constitutive relationships, most common material models, neo-Hooke, Mooney-Rivlin, Ogden. Determination of material parameters from experiments. 16. Material models of non-traditional and intelligent materials, shape memory alloys, shape memory polymers, magneto-rheological and electro-rheological composites, geomaterials. 17. Numerical simulation. Material models in finite element software and calculation of their response to loads using FEM materials, rheological models.
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