====== About project ====== <WRAP group> <WRAP column 20%> **Title:** </WRAP> <WRAP column 70%> **Numerical analysis of instabilities of isotropic thermoplastic materials at large deformation** </WRAP> // // <WRAP group> <WRAP column 20%> **Principal Investigator:** **Period:** **Sponsor:** </WRAP> <WRAP column 70%> Jerzy Pamin, PhD, prof. of CUT October 1, 2015 - September 30, 2017 National Science Centre of Poland (NCN) [[https://www.ncn.gov.pl/?language=en|website]] </WRAP> ---- ==== Research project objectives ==== The aim of the project is to investigate the conditions and possible forms of unstable behaviour of isotropic elastic-plastic materials in a thermo-mechanical context (thus treating the isothermal process as a special case). When associative plastic flow is assumed, such instabilities can occur due to geometrical softening, material softening and/or thermal softening. The research is limited to phenomenological continuum modelling. No inertial effects are considered, but stationary and non-stationary heat flow is admitted. When instabilities result in localized deformation modes an important difficulty occurs in mathematical modelling and numerical simulations: the considered boundary value problem (BVP) loses wellposedness and regularization is necessary. In the isothermal case the regularization can be provided for instance by a gradient-type enhancement of the constitutive description (as in the proposed research), in the thermo-mechanical model the coupling and in particular thermal conduction can provide some localization limiting properties. In the project the conditions of loss of well-posedness of the BVP for thermoplastic material undergoing large deformation will be determined, the influence of stress state on instability modes will be investigated and the regularizing effect of heat conduction on instabilities due to thermal, geometrical and material softening will be assessed. ==== Research methodology ==== The research will be carried out using analytical derivations and numerical models implemented within the Finite Element Method (FEM). In the theoretical-computational analysis the necking phenomenon will be treated as the main benchmark, i.e. object of numerical experiments. It involves both diffuse and localized instability modes and has been considered in many papers, although usually only isothermal conditions have been assumed. In the project the results for isothermal, adiabatic and conductive processes will be compared. The numerical simulations will be performed using the symbolic-numerical packages AceGen (code generator) and AceFEM (finite element program) in the Wolfram Mathematica environment. As an alternative finite element engine the ABAQUS finite element package will be used. ABAQUS is an established tool of numerical analysis, although it is not equipped with nonlocal material models or full thermomechanical coupling. The computational model developed to analyze coupled problems of this type will be validated in the research. The proposed research is novel, only few scientists considered the instability and localized deformation problems accounting for thermo-plastic coupling and large strain in the past. The use of gradient-enhanced continuum description should make the results free from pathological discretization sensitivity. ==== Expected impact on the development of science, civilization and society ==== The results of this project will contribute to the understanding of instability phenomena in large strain thermo-plasticity. The outcome of this research can have important implications for mechanical and civil engineering since the established knowledge and understanding of instability phenomena, as well and the formulation of reliable numerical models of failure of thermoplastic materials, will result in safer design of structures in extreme loading conditions (mechanical systems in high temperature service regime, civil engineering structures in fire). The reliability of simulation tools like the one employed in this project and understanding physical processes through numerical simulations are important for the development of new materials designed for advanced applications. In particular such nonlocal models should be used in the description of phenomena having their source in the evolution of microstructures during deformation. Hence, they can be the macroscopic limit of multi-scale analysis which is now in the focus of the international community of materials scientists. {{ :en:pldef.gif?nolink |}} //Elongation of a rectangular plate with imperfection modelled using gradient thermoplasticity with temperature averaging [Wcisło & Pamin, 2017]. Deformed mesh with distribution of plastic strain measure.//