The Rate-equilibrium Method with
Hyperelastic Based Constitutive Models

Steady state analyses often provide the best approach for the study of forming processes. Because constitutive equations for most materials of interest are nonlinear, iterative procedures must be used to obtain solutions. Usually, the iterations consist of solving the equilibrium equation for velocity (with stress assumed known), and then solving the constitutive equation for stress (with velocity assumed known). Under some circumstances the iterations converge to acceptable solutions; however, when the elastic response becomes significantly more pronounced than the non-elastic response, these algorithms tend to diverge. To overcome this difficulty, the rate-equilibrium equations have been used to calculate the velocity velocity field which has proven successful for constitutive models that incorporate a hypoelastic material. In this research, this same approach is extended to hyperelastic materials that exhibit yield surfaces and consequent plastic flow.

Reference: Cheng, Yuan-Fei and Erik Thompson; The Rate-equilibrium Method with Hyperelastic Based Constitutive Models; Simulation of Materials Processing: Theory, Methods and Applications, NUMIFORM`98; Ed: Huetink and Baaijens; Balkema, 1998

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