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SUMMARY The purpose of this paper is to review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering interest. In particular, the conservation properties of both synchronous and asynchronous variational integrators (AVIs) are discussed in detail. We present selected numerical examples which(More)
We describe a new class of asynchronous variational integrators (AVI) for non-linear elastodynamics. The AVIs are distinguished by the following attributes: (i) The algorithms permit the selection of independent time steps in each element, and the local time steps need not bear an integral relation to each other; (ii) the algorithms derive from a spacetime(More)
We present an artificial viscosity scheme tailored to finite-deformation Lagrangian calculations of shocks in materials with or without strength on unstructured tetrahedral meshes of arbitrary order. The artificial vis-cous stresses are deviatoric and satisfy material-frame indifference exactly. We have assessed the performance of the method on selected(More)
The formulation of multiple-time-step integrators can provide substantial computational savings for mechanical systems with multiple time scales. However, the scope of these savings may be severely limited by the range of allowable time step choices. In this paper we have performed an exhaustive study of the linear stability of the fully asynchronous(More)
A method is presented for capturing shock discontinuities appearing in elastic and plastic solids. The approach is based on a Lagrangian finite element formulation for solids undergoing large, possibly plastic, deformations and a formulation of artificial viscosity. The proposed artificial viscosity method is formulated at the constitutive level and,(More)
The ground state crystal structure of Fe, ferromagnetic body-centered cubic (bcc), undergoes a stress-induced martensitic phase transformation to a hexagonally close-packed (hcp) structure. Both bcc and hcp have been observed to coexist over a large range deformations, such that the nonlinearities in the constitutive behavior of each phase need to be(More)
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