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Register a new userFEpX -- Finite Element Polycrystals: Theory, Finite Element Formulation, Numerical Implementation and Illustrative Examples
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FEpX is a modeling framework for computing the elastoplastic deformations of polycrystalline solids. Using the framework, one can simulate the mechanical behavior of aggregates of crystals, referred to as virtual polycrystals, over large strain deformation paths. This article presents the theory, the finite element formulation, and important features of the numerical implementation that collectively define the modeling framework. The article also provides several examples of simulating the elastoplastic behavior of polycrystalline solids to illustrate possible applications of the framework. There is an associated finite element code, also referred to as FEpX, that is based on the framework presented here and was used to perform the simulations presented in the examples. The article serves as a citable reference for the modeling framework for users of that code. Specific information about the formats of the input and output data, the code architecture, and the code archive are contained in other documents.
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In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite element formulation that accurately captures the mechanical behaviour of heterogeneous materials in a computationally efficient manner. The strategy exploits analytical solutions derived by Eshelby for ellipsoidal inclusions in order to determine the mechanical perturbation fields as a result of the underlying heterogeneities. Approximation functions for these perturbation fields are then incorporated into a finite element formulation to augment those of the macroscopic fields. A significant feature of this approach is that the finite element mesh does not explicitly resolve the heterogeneities and that no additional degrees of freedom are introduced. In this paper, hybrid-Trefftz stress finite elements are utilised and performance of the proposed formulation is demonstrated with numerical examples. The method is restricted here to elastic particulate composites with ellipsoidal inclusions but it has been designed to be extensible to a wider class of materials comprising arbitrary shaped inclusions.
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We present experimental results and numerical Finite Element analysis to describe surface swelling due to the creation of buried graphite-like inclusions in diamond substrates subjected to MeV ion implantation. Numerical predictions are compared to experimental data for MeV proton and helium implantations, performed with scanning ion microbeams. Swelling values are measured with white light interferometric profilometry in both cases. Simulations are based on a model which accounts for the through-the-thickness variation of mechanical parameters in the material, as a function of ion type, fluence and energy. Surface deformation profiles and internal stress distributions are analyzed and numerical results are seen to adequately fit experimental data. Results allow us to draw conclusions on structural damage mechanisms in diamond for different MeV ion implantations.
The stochastic partial differential equation approach to Gaussian processes (GPs) represents Matern GP priors in terms of $n$ finite element basis functions and Gaussian coefficients with sparse precision matrix. Such representations enhance the scalability of GP regression and classification to datasets of large size $N$ by setting $napprox N$ and exploiting sparsity. In this paper we reconsider the standard choice $n approx N$ through an analysis of the estimation performance. Our theory implies that, under certain smoothness assumptions, one can reduce the computation and memory cost without hindering the estimation accuracy by setting $n ll N$ in the large $N$ asymptotics. Numerical experiments illustrate the applicability of our theory and the effect of the prior lengthscale in the pre-asymptotic regime.
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