An updated reference configuration formulation for large‐deformation problems

Abstract This paper examines difficulties encountered when using the Green‐Nagdi rate and presents an updated configuration formulation for problems dealing with large deformations. It is shown that a natural link can be established between the updated reference configuration and linearized updated Lagrangian formulations, if Truesdell's objective stress rate is used. Owing to this connection, any limitations associated with the described formulation would be expected to also apply to an updated Lagrangian formulation and vice versa. It is pointed out that, if second‐order effects are induced, the Truesdell rate appears in the rate equation for equilibrium even when strains are infinitesimal. By examining a simple‐shear problem, where hypoelastic material behaviour with ‘Hooke's law’ is assumed, it is shown that the spherical state of stress is coupled with the shear stress when using the Truesdell or Green‐Nagdi stress rate. It is suggested that objective stress rates, introduced in large‐deformation formulations, may contribute to erroneous predictions if a constitutive law is developed independent of the adopted stress rate.