SUMMARYThe purpose of this article is to present a general framework for constitutive viscoelastic models in finite strain regime. The approach is qualified as variational since the constitutive updates obey a minimum principle within each load increment. The set of internal variables is strain-based and employs, according to the specific model chosen, a multiplicative decomposition of strain into elastic and viscous components. The present approach shares the same technical procedures used for analogous models of plasticity or viscoplasticity, such as the solution of a minimization problem to identify inelastic updates and the use of exponential mapping for time integration. However, instead of using the classical decomposition of inelastic strains into amplitude and direction, we take advantage of a spectral decomposition that provides additional facilities to accommodate, into simple analytical expressions, a wide set of specific models. Moreover, appropriate choices of the constitutive potentials allow the reproduction of other formulations in the literature. The final part of the paper presents a set of numerical examples in order to explore the characteristics of the formulation as well as its applicability to usual large-scale FEM analyses.

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SUMMARYIn the last few years a number of numerical procedures called as meshless methods have been proposed. Among them, we can mention the di use element method, smooth particle hydrodynamics, element free Galerkin method, reproducing kernel particle method, wavelet Galerkin methods, and the so-called hp-cloud method. The main feature of these methods is the construction of a collection of open sets covering the domain which are used as support of the classical Galerkin approximation functions. The hp-cloud method is focused here because of its advantage of considering from the beginning the h and p enrichment of the approximation space. In this work we present, to our knowledge, the ÿrst results concerning the behaviour of this technique on the solution of Mindlin's moderately thick plate model. It is demonstrated numerically that the behaviour of the method with respect to shear locking is essentially the same as in the p-version of the ÿnite element method, namely, the shear locking can be controlled by using hp cloud approximations of su ciently high polynomial degree. The computational implementation of the method and the issue of numerical integration of the sti ness matrix are also discussed.