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The aim of this paper is to present a streamlined and fully three-dimensional version of the quasicontinuum (QC) theory of Tadmor et al. [18, 19] and to analyze its accuracy and convergence characteristics. Specifically, we assess the effect of the summation rules on accuracy; we determine the rate of convergence of the method in the presence of strong(More)
We develop a new paradigm for thin-shell finite-element analysis based on the use of subdivision surfaces for: i) describing the geometry of the shell in its undeformed configuration , and ii) generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the Kirchhoff-Love theory of thin shells. The particular(More)
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)
SUMMARY We develop a three-dimensional ÿnite-deformation cohesive element and a class of irreversible cohesive laws which enable the accurate and eecient tracking of dynamically growing cracks. The cohesive element governs the separation of the crack anks in accordance with an irreversible cohesive law, eventually leading to the formation of free surfaces,(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)
Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions , and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem. Discretizations of this nonsmooth mechanics(More)
We propose an approximation scheme for a variational theory of brittle fracture. In this scheme, the energy functional is approximated by a family of functionals depending on a small parameter and on two fields: the displacement field and an eigendeformation field that describes the fractures that occur in the body. Specifically, the eigendeformations allow(More)