Multi-Mechanism Models - Theory and Applications

Abstract

Multi-mechanism models (MM models) are used studying various materials and mechanical effects. In this work, a general concept of modeling with MM models of serial type is introduced within the framework of continuum mechanics. Contrary to many authors, the thermoelastic strain is not regarded as a special separated strain. The modular principle of MM models is illustrated by several basic, advanced and generalized mechanisms and MM models. We specify the modeling of linear viscoelasticity with MM models and apply the concept of MM models to the phenomena of transformation-induced plasticity. In the case of viscoelasticity, we present the 3d mathematical problems of a thermoelastic-(N)-coupled-Kelvin-Voigt-element model and an isothermal-(N)-coupled-Kelvin-Voigt-element model. The latter model is mathematically analyzed according to its weak solvability as a mixed boundary value problem by transforming the original problem into an equivalent system of integro-differential equations. Therefore, the presented approach of proving an existence and uniqueness result is nonstandard. In case of a 1d rod, the modeling and the mathematical treatment are provided related to the isothermal-(2)-coupled-Kelvin-Voigt-element model. We conduct numerical simulations of the isothermal-(2)-coupled-Kelvin-Voigt-element model for 3d and 1d situations. The results underline the quality of the introduced viscoelastic model covering material effects like ratcheting without predicting instantaneous elasticity. The phenomena of transformation-induced plasticity can occur for materials which undergo phase transformations when moderate stresses are applied. A detailed test evaluation for experiments characterizing the interaction of classic plasticity and transformation-induced plasticity of the steel 100Cr6 (SAE 52100) is presented. A MM model considering the interaction of classic plasticity and transformation-induced plasticity is verified by these experiments. Therefore, we develop numerical schemes of the model suited for uniaxial situations and perform systematical parameter identifications for some selected experiments.