Chaotic behavior of an elastoplastic bar in tensile test over a wide range of strain-rate - a numerical investigation

Numerical tensile tests of an elastoplastic cylindrical bar at various high strain-rates are performed by the use of a dynamic explicit FEM code (DYNA3D, a public domain version). The effects of mass (inertia) of the body, strain-rate and strain-rate sensitivity exponent (m-value) on the deformation pattern and the load curve are investigated. As for the material, strain dependentn-th power work hardening property is given by\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\sigma = K\varepsilon ^n (1 + \dot \varepsilon )^m $$ \end{document} where\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\dot \varepsilon $$ \end{document} is strain-rate. The range of the prescribed average strain-rate is 50-1000/s where the tensile tests with constant average strain-rate and with constant tensile velocity are performed. Materials with higher density exert a greater influence on deformation mode at a high strain-rate. Even if the tensile speed is less than that of plastic wave propagation, deformation becomes non-uniform remarkably due to mass effect. It is unexpected that double necking occurs at certain computational conditions. The strain at maximum load point predicted by the numerical simulation does not coincide with the analytically predicted one. Maximum rate of decrease in cross sectional area within the straight portion of the bar is compared with Hart’s instability criterion based on the imperfection in the cross section. The effect of a trivial change in material properties and the prescribed average strain-rate on the deformation pattern is remarkable in high rate tension over\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\dot \varepsilon = 400/s$$ \end{document}.