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Abstract: In this paper we consider numerical methods for integro-differential problems based on time discretization via Laplace transformation. We focus our attention in models arising in the context of non Fickian solute transport phenomena in porous media. The mathematical models which describe the evolution of the solute concentrations are characterized by Volterra equations. We present and analyze an hybrid method which combines the Laplace transformation with respect to the time variable with the finite element discretization in the spatial variables. Numerical results illustrate the performance of the method. [Copyright &y& Elsevier]

Abstract: This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method. [Copyright &y& Elsevier]

Abstract: Thin layers with material properties which differ significantly from those of the adjacent media appear in a variety of applications, as in the form of fiber coatings in composite materials. Fully modeling of such thin layers by standard finite element (FE) analysis is often associated with difficult meshing and high computational cost. Asymptotic procedures which model such thin domains by an interface of no thickness on which appropriate interface conditions are devised have been known in the literature for some time. The present paper shows how the first-order asymptotic interface model proposed by Bövik in 1994, and later generalized by Benveniste, can be incorporated in a FE formulation, to yield an accurate and efficient computational scheme for problems involving thin layers. This is done here for linear scalar elliptic problems in two dimensions, prototyped by steady-state heat conduction. Moreover, it is shown that by somewhat modifying the formulation of the Bövik–Benveniste asymptotic model, the proposed formulation is made to preserve the self-adjointness of the original three-phase problem, thus leading to a symmetric FE stiffness matrix. Numerical examples are presented that demonstrate the performance of the method, and show that the proposed scheme is more cost-effective than the full standard FE modeling of the layer. [Copyright &y& Elsevier]

Abstract: In this paper, a three-dimensional (3D), nonisothermal, multiphysics, two-phase steady state transport model and its efficient numerical methods are systematically studied for a full proton exchange membrane fuel cell (PEMFC) in the sense of efficiency and accuracy. The conservation equations of mass, momentum, species, charge and energy are fully addressed in view of nonisothermality and multiphase characteristics. In addition, from an accurate numerical discretization’s point of view, we present some new formulations for species equations by investigating the interactions among the species. In a framework of the combined finite element-upwind finite volume method, some efficient numerical methods are developed in terms of Kirchhoff transformation for the sake of a fast and convergent numerical simulation. The 3D simulations demonstrate that the convergent solutions can be attained within 80 nonlinear iterations, in contrast to the oscillating and nonconvergent iterations conducted by commercial flow solvers or in-house code with standard finite element/volume methods. Numerical convergence tests are carried out to verify the efficiency and accuracy of our numerical algorithms and techniques. [Copyright &y& Elsevier]

Abstract: This article presents a generalization of the recently proposed Finite Cell Method to thin-walled structures. This approach uses a combination of well known Fictitious Domain Methods with high order hierarchical Ansatz spaces known from the p-version of the Finite Element Method. Whereas the original concept embeds a three-dimensional structure in a simple domain being meshed into a grid of cube shaped cells, the extension presented in this paper applies the fictitious domain approach to a two-dimensional master domain defined in the parameter plane of the geometric model. Implementation details are discussed and numerical benchmark problems show the high accuracy and computational efficiency of the new approach. It is also remarked, that the present approach can easily be carried over to isogeometric analysis, opening an attractive possibility to simulate trimmed NURBS-surfaces. [Copyright &y& Elsevier]

Abstract: Wave propagation features in random guided elastic media are considered in this paper. A formulation named stochastic wave finite element (SWFE) is offered. This formulation allows wave characteristics definition by means of a stochastic finite element model. The case of spatially homogeneous random properties is dealt with, through a parametric probabilistic technique. Numerical experiments show the effectiveness of the proposed approach to predict the statistics of guided wave propagation characteristics (means and standard deviations) when compared to Monte Carlo calculations. [Copyright &y& Elsevier]

Abstract: This paper introduces and analyzes two mathematical models for coupling the incompressible Navier–Stokes equations with the porous media flow equations. A numerical method that uses continuous finite elements in the incompressible flow region and discontinuous finite elements in the porous medium, is proposed. Existence and uniqueness results under small data condition of the numerical solution are proved. Optimal a priori error estimates are derived. Numerical examples comparing the two models under varying physical parameters are provided. [Copyright &y& Elsevier]

Abstract: In this paper we present a hyperelastic rod model that takes into account self-contact forces. The model is based on Cosserat rod theory that incorporates shear, elongation, flexure and twist deformations. The problem of avoiding self-penetration of parts of the rod is handled by the introduction of a contact distance function and the incorporation of associated contact forces. We present a penalty method for the treatment of the multi-valued and non-differentiable contact law. We also describe an augmented Lagrangian formulation of this problem. We then give the details of the finite-element discretization of the elastic rod self-contact problem as well as some numerical examples. [Copyright &y& Elsevier]

Abstract: This article addresses a new approach for computations of radiative heat transfer in cooling glass. The new solution combines meshfree finite pointset method (FPM) and models of radiative heat transfer in semi-transparent media. This allows to exploit the advantages of particle methods, like their natural capacity to follow changes of deforming geometries, and to reconstruct time evolution of temperature fields due to conduction and radiation effects. Special attention is paid to the radiation as a dominant mechanism of heat transport in high temperatures in semi-transparent materials (e.g. glass). The paper begins with a brief presentation of FPM. It is followed by a discussion of mathematical models of radiation used in computations. The closing part gives a concise review of results of numerical simulations. [Copyright &y& Elsevier]

Just like all constitutive models involving softening, Gurson’s [A.L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: Part I – Yield criteria and flow rules for porous ductile media, ASME J. Engrg. Mater. Technol. 99 (1977) 2–15] model of ductile rupture predicts unlimited localization of strain and damage. Leblond et al.’s [J.B. Leblond, G. Perrin, J. Devaux, Bifurcation effects in ductile metals with nonlocal damage, ASME J. Appl. Mech. 61 (1994) 236–242] have proposed to solve this problem in a heuristic way by using a nonlocal evolution equation for the porosity, which expresses its time-derivative as a spatial convolution integral of some “local porosity rate”. This paper is devoted to the numerical implementation and assessment of this phenomenological variant of Gurson’s model. The numerical implementation proposed bears some resemblance to Aravas’s [N. Aravas, On the numerical integration of a class of pressure-dependent plasticity models, Int. J. Numer. Methods Engrg. 24 (1987) 1395–1416] classical one but departs from it through use of an explicit algorithm with respect to the porosity, if not with respect to other parameters. The main reason for this choice lies in the proof of existence and uniqueness, for such an algorithm, of the solution of the “projection problem” onto Gurson’s yield locus. The assessment of the model is based on two criteria, absence of mesh size effects in finite element computations and agreement of experimental and numerical results for some typical ductile fracture tests. Since the first topic has already been investigated by Tvergaard and Needleman’s [V. Tvergaard, A. Needleman, Effects of nonlocal damage in porous plastic solids, Int. J. Solids Struct. 32 (1995) 1063–1077], we concentrate on the second one. Unfortunately, numerical experience reveals that the modification of Gurson’s model envisaged degrades the agreement between experimental results and model predictions. A theoretical analysis of this phenomenon is presented. Although based on crude simplifying assumptions, this analysis suffices to qualitatively explain the failure of the model and suggest a simple remedy. Numerical experience confirms that this remedy considerably improves numerical predictions. Thus, with this modification, Leblond et al. (1994)’s proposal appears as a viable solution to the problem of unlimited localization of strain and damage in Gurson (1997)’s model. [Copyright &y& Elsevier]

This paper develops and demonstrates a mixed beam finite element that can represent the inelastic three-dimensional stability behavior of frames composed of open-walled cross-section members. The kinematics of deformation of the element include finite rotation and warping of the cross-section due to torsion. The material inelasticity is based on a two-space model that includes the effect of shear stresses due to uniform torsion in addition to normal stresses due to axial force, biaxial bending, and bimoment. Initial geometric imperfections and residual stresses are accommodated. The formulation is based on a two-field (displacement and generalized stress) Hellinger–Reissner (HR) variational principle. The interpolation of the generalized stresses (i.e., cross-section stress resultants) along the element length is based on the geometrically-exact nonlinear governing differential equations of equilibrium. This leads to significant improvements in the accuracy over conventional displacement-based elements in problems involving highly nonlinear variations in the curvature along the member lengths due to geometric nonlinearity and/or distributed plasticity effects. Several numerical examples involving two- and three-dimensional elastic and inelastic stability behavior are presented to illustrate the capabilities of the formulation. [Copyright &y& Elsevier]