A moment–curvature-based constitutive model for interactive simulation of visco-plastic rods

Abstract

A moment–curvature constitutive model is proposed for the dynamic simulation of visco-plastic rods subject to time-varying loads and constraints at interactive rates. Smooth spline functions are used to discretize the geometry of the rod and its kinematics with the centerline coordinates as degrees of freedom (DOF) and scalar twist as degrees of freedom (DOF). The plastic curvature is defined as a uniformly varying field in contrast to localized lumped plasticity models, suitable for simulation of spatial rods that undergo uniform plastic deformation such as a cable or surgical suture thread. The yield criterion and plastic/visco-plastic flow rule are developed for spatial rods taking advantage of the availability of smooth moment–curvature fields using the spline-based formulation. With the Bishop frame field as a reference, the material curvatures are quantified using the twist degree of freedom, enabling tracking the plastic fields with scalar twist, thereby eliminating slopes as DOF. Taking advantage of the invariant sub-blocks and the sparsity of the dynamic system matrix arising from the numerical discretization, an hierarchical (H-matrix) solution approach is utilized for efficient computation. Uniform curvature bending tests and moment relaxation tests are performed to study the convergence behavior of the model. Several real-world tests involving contact are performed to demonstrate the applicability of the model in interactive simulations.