Smooth Yield Surface Constitutive Modeling for Granular Materials
Hammi, Y., Stone, T.W., Paliwal, B., Allison, P. G., & Horstemeyer, M. (2016). Smooth Yield Surface Constitutive Modeling for Granular Materials. Journal of Engineering Materials and Technology. American Society of Mechanical Engineers. 139(1), 011010. DOI:10.1115/1.4034987.
In this paper, the authors present an internal state variable (ISV) cap plasticity model to
provide a physical representation of inelastic mechanical behaviors of granular materials
under pressure and shear conditions. The formulation is dependent on several factors:
nonlinear elasticity, yield limit, stress invariants, plastic flow, and ISV hardening laws to
represent various mechanical states. Constitutive equations are established based on a
modified Drucker–Prager cap plasticity model to describe the mechanical densification
process. To avoid potential numerical difficulties, a transition yield surface function is
introduced to smooth the intersection between the failure and cap surfaces for different
shapes and octahedral profiles of the shear failure yield surface. The ISV model for the
test case of a linear-shaped shear failure surface with Mises octahedral profile is implemented
into a finite element code. Numerical simulations using a steel metal powder are
presented to demonstrate the capabilities of the ISV cap plasticity model to represent
densification of a steel powder during compaction. The formulation is general enough to
also apply to other powder metals and geomaterials.