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- Vector and Tensor Algebra: Symbols, spaces, products, specific tensors and definitions
- Vector and Tensor Analysis: Functions of scalar, vector- and tensor-valued variables,
divergence and
Stokes' theorem
- Foundations of Continuum Mechanics: Kinematics and deformation, forces and stress concepts:
Cauchy's lemma and theorem,
Cauchy,
Kirchhoff and
Piola-Kirchhoff stress tensors
- Fundamental Balance Laws: Master balance, axiomatic balance relations of mechanics (mass,
momentum and angular momentum), balance of mechanical energy, stress power and the concept of
conjugate variables,
d'Alembert's principle and the principle of virtual work
- Numerical aspects of continuum mechanics : Strong and weak formulation of the boundary-value
problem
- The closure problem of mechanics: Finite elasticity of solid mechanics (as an example),
linearization of the field equations
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