Constitutive equations of elastic/viscoplastic materials based on hypoelasticity.

Rate type constitutive equations of elastic/viscoplastic materials are proposed. The constitutive equations have been obtained by introducing an excess stress term into Tokuoka's constitutive equations of elastic/plastic materials based on hypoelasticity. His equations have two kinds of internal variables (hardening parameters), and they have been proved to describe characteristic properties of elastic/plastic materials, e.g., yielding, unloading, reloading, flow rules, isotropic hardening, Bauschinger effect etc. The proposed constitutive equations reduce to Tokuoka's ones for sufficiently slow deformations, and they can also exhibit several strain rate effects. That is, they can describe rate sensitivity of the yield surface, the stress response for sudden change of the strain rate, creep, relaxation etc. An explicit form of the constitutive equations of von Mises type elastic/viscoplastic materials has been derived from general constitutive equations, by use of the representaion theorem for tensors, symmetry of tension and compression, the principle of material frame indifference etc. As an example, the above strain rate effects in uniaxial tension are analyzed, and significant agreement with the experimental results is shown.