An anisotropic plasticity theory of sheet metals based on a polynomial of Hill’s 1948 yield function

A polynomial consisting of multiple Hill’s well-known 1948 stress functions is proposed as a new yield function in an associated anisotropic plasticity theory for modeling orthotropic sheet metals. The particular non-homogeneous polynomial yield function of the theory investigated here has up to a total of 16 anisotropic material parameters with the specific aim to characterize the yielding and plastic flow of a sheet metal subjected to seven uniaxial and one equibiaxial tensile tests. Least square error minimization with either simple algebraic constraints or heuristic matrix-based constraints imposed on its material parameters was proposed for calibration of the new yield criterion with guaranteed convexity. To demonstrate capabilities of the newly proposed theory, it was applied to model four selected steel sheet materials whose yield stresses and plastic strain ratios from eight tensile tests have already been made available by others in the existing literature. Results of this study show that the new anisotropic plasticity theory is effective in modeling the yielding and plastic flow of these four sheet metals under uniaxial and equibiaxial tension. It may be used as a more capable and yet user-friendly alternative to existing sixth-order Yld2000 (M=6) and Yld20004 (M=6) yield functions in numerical simulations of deep drawing and hole expansion of steel sheets. • Develop a non-homogeneous polynomial yield criterion for orthotropic sheet metals. • Use two convexity-constrained least square minimization methods for its calibration. • Model accurately a steel sheet under seven uniaxial and one equibiaxial tension tests. • The new yield functions with 8, 12 and 16 material parameters are more user-friendly.