A mathematical model of transition of the material from elastic to elasto-plastic state

The goal of this study is to develop a mathematical model of the transition of the structural material from elastic state to elastoplastic state upon tension. The model is based on a modified three-parameter transition operator from one mathematical function to another. A procedure of the mathematical approximation of the transition and corresponding algorithm, which provides a generalized canonical description of the transition, regardless of the form of the functions that characterize the system behavior before and after the transition are presented. The technique is used to describe the transition of two structural materials from the elastic to elastoplastic state upon tension of the samples. Initial sections of the tension diagram are described using three empirical parameters. The role of each of them — maximum permissible relative deformation, transition rate and asymmetry of the transition — are determined. Statistical interpretation of the elastoplastic transition is developed and substantiated. Mathematical expressions for the integral probability function and probability density functions that provide numerical statistical estimation of the degree of change in the state of the structural elements of the material during loading are derived. Analytical description of the initial part of the tension diagram of the material can be used to rearrange the diagrams when modeling deformation processes in conditions of reversible elastoplastic loading.

An Improved Fractal Contact Model With Special Emphasis on Surface Roughness, Elastoplastic Transition Deformation Zone, and Hardness Effects of Coating Film

In this work, fractal characterization of surface topography is applied to the study of contact mechanics between two coating film rough surfaces. Incorporating with MB model, the occurrence of elastic-plastic transition regime and the hardness effect of coating film are considered in the new contact model. Results show that the real contact areas predicted by this new model are larger than those predicted by MB model. For low fractal roughness parameter and fractal dimension of 1.5, up to 19% of difference can be found between the results from the new model and old model.

Influence of Elasto-Plastic Transition on the Inelastic Response of Beams and Plates

The paper deals with a study of the significance of elastoplastic transition state in the dynamic response of Euler beams and thin plates. The study is based on a comparative evaluation of the responses predicted by two independent approaches that use (i) stress-strain relation and basic plasticity theory and (ii) moment-curvature relation; assuming the shape factor to be unity. Responses are evaluated by way of finite-element idealization followed by numerical integration. It is found that the simplified model, based on moment-curvature relations, underestimates the response by a significant amount for longer durations of the applied load.