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Constitutive modelling is the mathematical description of how materials respond to various loadings. This is the most intensely researched field within solid mechanics because of its complexity and the importance of accurate constitutive models for practical engineering problems. Topics covered include:Elasticity - Plasticity theory - Creep theory - The nonlinear finite element method - Solution of nonlinear equilibrium equations - Integration of elastoplastic constitutive equations - The thermodynamic framework for constitutive modelling - Thermoplasticity - Uniqueness and discont

Mathematical models. --- Mechanics, Applied. --- Mechanics, Applied - Mathematical models. --- Mechanics, Applied--Mathematical models. --- Mechanics, Applied --- Civil Engineering --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Mathematical models --- Mathematics. --- Math --- Science

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Generalized convexity conditions play a major role in many modern mechanical applications. They serve as the basis for existence proofs and allow for the design of advanced algorithms. Moreover, understanding these convexity conditions helps in deriving reliable mechanical models. The book summarizes the well established as well as the newest results in the field of poly-, quasi and rank-one convexity. Special emphasis is put on the construction of anisotropic polyconvex energy functions with applications to biomechanics and thin shells. In addition, phase transitions with interfacial energy and the relaxation of nematic elastomers are discussed.

Convex domains. --- Mechanics, Applied -- Mathematical models. --- Mechanics, Applied --- Convex domains --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Civil Engineering --- Mathematical models --- Mathematical models. --- Convex regions --- Convexity --- Engineering. --- Mechanics. --- Mechanics, Applied. --- Theoretical and Applied Mechanics. --- Calculus of variations --- Convex geometry --- Point set theory --- Mechanics, applied. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Rank-one convexity