An Energy-Based Variational Model of Ferromagnetic Hysteresis for Finite Element Computations

in Journal of Computational & Applied Mathematics (2013), 246

This paper proposes a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic ... [more ▼]

This paper proposes a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic formulation. In particular, the stored magnetic energy and the dissipated energy are known at all times, and not solely after the completion of closed hysteresis loops as is usually the case. The obtained incremental formulation is variationally consistent, i.e., all internal variables follow from the minimization of a thermodynamic potential. [less ▲]

The impact of surface higher order differentiability in two-dimensional contact elements

in Journal of Computational & Applied Mathematics (2013), 246

The aim of this work is to propose new contact elements of higher order of differentiability for analysing two-dimensional frictionless contact problems. Several methods were proposed in the literature to ... [more ▼]

The aim of this work is to propose new contact elements of higher order of differentiability for analysing two-dimensional frictionless contact problems. Several methods were proposed in the literature to solve the problem caused by the lack of continuity resulting from the discretization. Among them are Bézier interpolation, Hermitian interpolation and splines. One of the difficulties in using Hermitian interpolation is to verify the partition of unity. Therefore, new elements that satisfy the C1 and C2 continuity at the interface are presented in this paper. These new contact elements are based on Hermitian polynomials for ensuring a higher order of continuity. The advantage is that this approach can be easily developed not only for linear elements but also for quadratic elements with higher order of differentiability. The performance of different surface representations is assessed through a comparison with a C0 surface discretization. Some numerical examples are used for assessing the accuracy and the convergence behaviour [less ▲]

An exact Riemann Solver and Godunov Scheme for Simulating Highly Transient Mixed Flows

in Journal of Computational & Applied Mathematics (2011), 235

Dam-break flow computation based on an efficient flux-vector splitting

in Journal of Computational & Applied Mathematics (2010), 234

Dam-break flow computation is a task of prime interest in the scope of risk analysis processes related to dams and reservoirs. In this paper, a 2D finite volume multiblock flow solver, able to deal with ... [more ▼]

Dam-break flow computation is a task of prime interest in the scope of risk analysis processes related to dams and reservoirs. In this paper, a 2D finite volume multiblock flow solver, able to deal with natural topography variation, is presented in details. The model is based on an efficient Flux Vector Splitting method developed by the authors. A number of validation examples are comprehensively described. [less ▲]

An improved constitutive model for the numerical simulation of semi-solid thixoforming

in Journal of Computational & Applied Mathematics (2010), 234

In order to model thixoforming processes, previous papers presented a thermomechanical one-phase modelling. This first version of the constitutive model revealed several limitations: the model could not ... [more ▼]

In order to model thixoforming processes, previous papers presented a thermomechanical one-phase modelling. This first version of the constitutive model revealed several limitations: the model could not degenerate properly to pure solid or liquid behavior nor to free solid suspensions. The aim of this paper was to propose solutions to overcome these limitations. [less ▲]

Isotropic continuum damage/repair model for alveolar bone remodelling

in Journal of Computational & Applied Mathematics (2010), 234

Several authors have proposed mechanical models to predict long term tooth movement, considering both the tooth and its surrounding bone tissue as isotropic linear elastic materials coupled to either an ... [more ▼]

Several authors have proposed mechanical models to predict long term tooth movement, considering both the tooth and its surrounding bone tissue as isotropic linear elastic materials coupled to either an adaptative elasticity behavior or an update of the elasticity constants with density evolution. However, tooth movements obtained through orthodontic appliances result from a complex biochemical process of bone structure and density adaptation to its mechanical environment, called bone remodeling. This process is far from linear reversible elasticity. It leads to permanent deformations due to biochemical actions. The proposed biomechanical constitutive law, inspired from Doblaré and García (2002) [30], is based on a elasto-viscoplastic material coupled with Continuum isotropic Damage Mechanics (Doblaré and García (2002) [30] considered only the case of a linear elastic material coupled with damage). The considered damage variable is not actual damage of the tissue but a measure of bone density. The damage evolution law therefore implies a density evolution. It is here formulated as to be used explicitly for alveolar bone, whose remodeling cells are considered to be triggered by the pressure state applied to the bone matrix. A 2D model of a tooth submitted to a tipping movement, is presented. Results show a reliable qualitative prediction of bone density variation around a tooth submitted to orthodontic forces. [less ▲]

A hybrid optimization technique coupling evolutionary and local search algorithms

in Journal of Computational & Applied Mathematics (2008), 215(2), 448-456

Evolutionary Algorithms are robust and powerful global optimization techniques for solving large scale problems that have many local optima. However, they require high CPU times, and they are very poor in ... [more ▼]

Evolutionary Algorithms are robust and powerful global optimization techniques for solving large scale problems that have many local optima. However, they require high CPU times, and they are very poor in terms of convergence performance. On the other hand, local search algorithms can converge in a few iterations but lack a global perspective. The combination of global and local search procedures should offer the advantages of both optimization methods while offsetting their disadvantages. This paper proposes a new hybrid optimization technique that merges a Genetic Algorithm with a local search strategy based on the Interior Point method. The efficiency of this hybrid approach is demonstrated by solving a constrained multi-objective mathematical test-case. [less ▲]

Discrete finite element characterizations of source fields for volume and boundary constraints in electromagnetic problems

in Journal of Computational & Applied Mathematics (2008), 215(2), 438-447

The consideration of electromagnetic field sources in potential formulations necessitates the definition of source fields. Such source fields are first defined for both volume and boundary constraints in ... [more ▼]

The consideration of electromagnetic field sources in potential formulations necessitates the definition of source fields. Such source fields are first defined for both volume and boundary constraints in static electromagnetic models. Then, automatic procedures are proposed to conveniently and efficiently characterize discrete source fields, with regard to their use in finite element formulations, their supports, their direct expression requiring no pre-computation, and their associated constraints. Two application examples are proposed to illustrate the approach. [less ▲]

An O(1) Integration Scheme for Three-Dimensional Surface Scattering Problems

in Journal of Computational & Applied Mathematics (2007), 204

A variational framework for nonlinear viscoelastic models in finite deformation regime

in Journal of Computational & Applied Mathematics (2005), 215(2), 400-408

This work presents a general framework for constitutive viscoelastic models in the finite deformation regime. The approach is qualified as variational since the constitutive updates consist of a ... [more ▼]

This work presents a general framework for constitutive viscoelastic models in the finite deformation regime. The approach is qualified as variational since the constitutive updates consist of a minimization problem within each load increment. The set of internal variables is strain-based and uses a multiplicative decomposition of strain in elastic and viscous components. Spectral decomposition is explored in order to accommodate, into analytically tractable expressions, a wide set of specific models. Moreover, it is shown that, through appropriate choices of the constitutive potentials, the proposed formulation is able to reproduce results obtained elsewhere in the literature. Finally, numerical examples are included to illustrate the characteristics of the present formulation. (C) 2007 Elsevier B.V. All rights reserved. [less ▲]