# A THEORY OF VISCOPLASTICITY BASED ON INFINITESIMAL TOTAL STRAIN

A viscoplasticity theory based upon a nonlinear viscoelastic solid, linear in the rates of the strain and stress tensors but nonlinear in the stress tensor and the infinitesimal strain tensor, is being investigated for isothermal, homogeneous motions. A general anistropic form and a specific isotropic formulation are proposed. A yield condition is not part of the theory and the transition from linear (elastic) to nonlinear (inelastic) behavior is continuous. Only total strains are used and the constant volume hypothesis is not employed. In this paper Poisson's ratio is assumed to be constant. The proposed equation can represent: initial linear elastic behavior; initial elastic response in torsion (tension) after arbitrary prestrain (prestress) in tension (torsion); linear elastic behavior for pure hydrostatic loading; initial elastic slope upon large instantaneous changes in strain rate; stress (strain)-rate sensitivity; creep and relaxation; defined behavior in the limit of very slow and very fast loading. Stress-strain curves obtained at different loading rates will utilimately have the same "slope" and their spacing is nonlinearly related to the loading rate. The above properties of the equation are obtained by qualitative arguments based on the characteristics of the solutions of the resulting nonlinear first-order differential equations. In some instance numerical examples are given. For metals and isotropy we propose a simple equation whose coefficient functions can be determined from a tensile test (Eqs. (31), (35), (37), (38)). Specializations suitable for materials other than metals are possible. The paper shows that this nonlinear viscoelastic model can represent essential features of metal deformation behavior and reaffirms over previous assertion that metal deformation is basically rate-dependent and can be represented by piecewise nonlinear viscoelasticity. For cycle loading the proposed model must be modified to account for history dependence in the sense of plasticity.

• Supplemental Notes:
• Controlling Office is the Department of the Navy, Office of Naval Research, Structural Mechanics Program, Arlington, Virginia 22217.
• Corporate Authors:

Rensselaer Polytechnic Institute

Department of Aeronautical Engineering and Astronautics
Troy, NY  United States  12180
• Authors:
• Cernocky, E P
• Krempl, E
• Publication Date: 1978-5

## Media Info

• Pagination: n.p.

## Filing Info

• Accession Number: 00179211
• Record Type: Publication