The special-linear update: An application of differential manifold theory to the update of isochoric plasticity flow rules

Abstract

The evolution of plastic deformations in metals, governed by incompressible flow rules, has been traditionally solved using the exponential mapping. However, the accurate calculation of the exponential mapping and its tangents may result in computationally demanding schemes in some cases, while common low-order approximations may lead to poor behavior of the constitutive update because of violation of the incompressibility condition. Here, we introduce the special-linear (SL) update for isochoric plasticity, a flow-rule integration scheme based on differential manifolds concepts. The proposed update exactly enforces the plastic incompressibility condition while being first-order accurate and consistent with the flow rule, thus bearing all the desirable properties of the now standard exponential mapping update. In contrast to the exponential-mapping update, we demonstrate that the SL update can drastically reduce the computing time, reaching one order of magnitude speed-ups in the calculation of the update tangents. We demonstrate the applicability of the update by way of simulation of single-crystal plasticity uniaxial loading tests. We anticipate that the SL update will open the way to efficient constitutive updates for the solution of complex multiscale material models, thus making it a very promising tool for large-scale simulations