A Rheological Model of Nonlinear Viscoplastic Solids

A general rheological model of a nonlinear viscoplastic solid is developed, affording better quantitative prediction of behavior of viscoplastic materials. Rheological properties are quantified in terms of three types of curves obtained by tests, commonly used for description of mechanical material properties: constant rate, force deformation, creep, and relaxation curves. The mathematical model is based on a characteristic nonlinear differential equation describing the mechanical properties of a material. This equation defines the force F acting on a test specimen as composed of a cubic elasticity force K0x+rx3, viscous damping force Cẋ, and internal friction force Ff (sgn ẋ). The elastic parameter K0 quantifies linear elasticity while the strain hardening (or softening when negative) parameter r affords prediction of nonlinear behavior of the material. The viscous and Coulomb damping forces properly account for both rate‐dependent and rate‐independent energy dissipative properties of the material. Local...