| Part I of this dissertation presents a study of the constitutive behavior of engineering materials such as concrete and steel, while Part II is devoted to studying the mathematical properties of the initial value problems posed by such materials.;To conclude Part I, the plasticity and viscoplasticity of polycristalline materials are studied in terms of lattice dislocations. Non-equilibrium statistical mechanics is used to describe the evolution of the dislocation structures during loading and unloading processes. In the light of this model, metals appear as materials with fading memory.;In Part II, the elastoplastic dynamic problem is formulated in a functional form that facilitates the application of the techniques of nonlinear semigroup theory. Existence and uniqueness of the solution is proved by showing that the equations of motion define a contraction semigroup in an adequate Hilbert space. A number of approximation techniques are discussed within the framework of nonlinear semigroup theory that provide a formal background for such numerical techniques as the "return mapping" algorithms and the penalty method.;Finally, the theory of nonlinear semigroups is applied to the problem of existence and uniqueness for evolutionary equations arising in connection with elastoplastic materials with memory effects. The fading memory property is formulated in terms of an obliviating measure. Suitable restrictions on this measure and on the hereditary constitutive mapping are discussed that result in well-posed initial value problems.;In Part I a model for the inelasticity of concrete is developed based on the theory of interacting continua, fracture mechanics and some recently advanced thermodynamic theories of plasticity. The main causes for the inelasticity of concrete are attributed to microcracking, plasticity and a softening elastoplastic coupling. The existence of an interaction between the process of elastic degradation due to microcracking and the plasticity of the material is seen to provide a plausible explanation for a number of experimentally observed phenomena such as plastic anisotropy, lack of isochoricity and normality and unstable plastic behavior. |
