Modelización numérica del comportamiento estructural cíclico de barras esbeltas de acero con pandeo restringido

This work presents a numerical model of the cyclic structural behavior of dissipative buckling-restrained braces, commonly used as an alternative to classical concentric braces for seismic protection of building frames and other structures. Such devices are usually composed of a slender steel core embedded in a stockiest casing that is intended to prevent its buckling when it is under compression. The casing is made either of mortar or steel, and a sliding interface is interposed between the core and the casing to prevent excessive shear stress transfer. The behavior of the steel core is described by a damage and plasticity model; the behavior of the mortar casing is described by an isotropic damage model and the sliding behavior of the interface is described by a contact penalty model. These 3 models are implemented in the Abaqus software package following an explicit formulation. In a previous article (published in an earthquake engineering journal) the model was briefly described, its ability to reproduce the cyclical behavior of buckling-restrained braces was preliminarily pointed out and their results were satisfactorily compared with those of experimental tests. The aim of this paper is to describe the model thoroughly and to present new judgments about its usefulness.     

Different weak FE‐formulations for 2‐D frictionless Large Deformation Contact based on the Mortar Method

The application of the mortar method in contact mechanics is motivated by the limited use of well known elements, for example the node‐to‐segment (NTS) element, see [1]. The NTS element contains a strong projection of the displacements from one contacting body to the next. Coupling of this element type with higher order shape functions leads to a loss of accuracy of contact stresses. In contrast to this, the mortar element has the advantage of a weak projection. Therefore, consistent coupling with continuum elements of higher order is possible. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Approximation du problème de contact unilatéral par la méthode des éléments finis avec joints

The purpose of this Note is to extend the mortar finite element method to handle the unilateral contact model between two deformable bodies. The corresponding variational inequality is approximated using finite elements with meshes which do not fit on the contact zone. The mortar technique allows us to match (independent) discretizations within each solid and to express the contact conditions in a satisfying way. Then, we carry out a numerical analysis of the algorithm and, using a bootstrap argument, we give an upper bound of the convergence rate similar to that already obtained for compatible grids.     

Un algoritmo de contacto mortar aplicable a problemas tridimensionales

In this paper we propose a mortar algorithm for the study of contact mechanics in three dimensional elasticity problems. The projection surface used for integrating the equations is selected through a local cartesiana base defined in each contact element. In this way, some difficulties in the algorithm implementation as well as in the linearization of the equations are avoided. The proposed examples show that the algorithm satisfies the patch tests. Finally, we use the algorithm in an industrial application, the contact of an internal combustion engine valve with its seat.     

The contact problem with the bulk application of intermolecular interaction forces (a refined formulation)

A refined formulation of the contact problem when there are intermolecular interaction forces between the contacting bodies is considered. Unlike the traditional formulation, it is assumed that these forces are applied to points within the body, rather than to the surface of the deformable body as a contact pressure, and that the body surface is load-free. Solutions of the contact problems for a thin elastic layer attached to an absolutely rigid substrate and for an elastic half-space are analysed. The refined and traditional formulations of the problem when there is intermolecular interaction are compared. ©2013     

Modeling frictional contact in shell structures using variational inequalities

A new variational inequality-based formulation is presented for the large deformation analysis of frictional contact in shell structures. This formulation is based on a seven-parameter continuum shell model which accounts for the normal stress and strain through the shell thickness and accommodates double-sided shell contact. The kinematic contact conditions are expressed accurately in terms of the physical contacting surfaces of the shell. Furthermore, Lagrange multipliers are used to ensure that the kinematic contact constraints are accurately satisfied and that the solution is free from user-defined parameters. Large deformations and rotations are accounted for by invoking the Piola–Kirchhoff stress and the Green–Lagrange strain measures. Three examples involving a strip friction test, ring contact and sheet compression tests are used to verify the developed formulations and algorithms, and test various aspects of the solution technique. Photoelastic analysis of the ring compression example is performed for experimental verification.     

T-splines discretizations for large deformation contact problems

A T-spline-based isogeometric analysis is applied to frictional contact problems between deformable bodies in the context of large deformations. The continuum is discretized with cubic T-splines and cubic NURBS (Non-Uniform Rational B-Splines) for comparison purposes. A Gauss-point-to-surface (GPTS) formulation is combined with the penalty method to treat the normal and friction contact constraints in the discretized setting. It is demonstrated that the proposed formulation combined with analysis-suitable T-spline interpolations, is a computationally accurate and efficient technology for local and global solutions of contact problems. T-spline analysis models are generated using commercially available T-spline modeling software without intermediate mesh generation or geometry clean-up steps. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of large deformation frictional contact in powder compaction processes

In this paper, the computational aspects of large deformation frictional contact are presented in powder forming processes. The influence of powder–tool friction on the mechanical properties of the final product is investigated in pressing metal powders. A general formulation of continuum model is developed for frictional contact and the computational algorithm is presented for analyzing the phenomena. It is particularly concerned with the numerical modeling of frictional contact between a rigid tool and a deformable material. The finite element approach adopted is characterized by the use of penalty approach in which a plasticity theory of friction is incorporated to simulate sliding resistance at the powder–tool interface. The constitutive relations for friction are derived from a Coulomb friction law. The frictional contact formulation is performed within the framework of large FE deformation in order to predict the non-uniform relative density distribution during large deformation of powder die pressing. A double-surface cap plasticity model is employed together with the nonlinear contact friction behavior in numerical simulation of powder material. Finally, the numerical schemes are examined for efficiency and accuracy in modeling of several powder compaction processes.     

Coupling between scalar and vector potentials by the mortar element methodCouplage entre potentiels scalaire et vecteur par la méthode des éléments joints

The T–$\text{Ω}$ formulation of the magnetic field is widely used in magnetodynamics. It allows the use of a scalar function in the computational domain and a vector quantity only in the conducting parts. Here we propose to approximate these two quantities on different meshes and to couple them by means of the mortar element method. To cite this article: Y. Maday et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 933–938.     

A scalable FETI-DP algorithm with non-penetration mortar conditions on contact interface

By combining FETI algorithms of dual-primal type with recent results for bound constrained quadratic programming problems, we develop an optimal algorithm for the numerical solution of coercive variational inequalities. The model problem is discretized using non-penetration conditions of mortar type across the potential contact interface, and a FETI-DP algorithm is formulated. The resulting quadratic programming problem with bound constraints is solved by a scalable algorithm with a known rate of convergence given in terms of the spectral condition number of the quadratic problem. Numerical experiments for non-matching meshes across the contact interface confirm the theoretical scalability of the algorithm.     

On a geometrically exact theory for contact interactions

The focus of the contribution is on the development of the unified geometrical formulation of contact algorithms in a covariant form for various geometrical situations of contacting bodies leading to contact pairs: surface-to-surface, line-to-surface, point-to-surface, line-to-line, point-to-line, point-to-point. The computational contact algorithm will be considered in accordance with the geometry of contact bodies in a covariant form. This combination forms a geometrically exact theory of contact interaction, see [1]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Mortar finite element method with Lagrange multipliers

Summary. The present paper deals with a variant of a non conforming domain decomposition technique: the mortar finite element method. In the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices (and the edges in 3D) of subdomains. It is shown that, written under primal hybrid formulation, the approximation problem, issued from a discretization of a second order elliptic equation in 2D, is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms. Finally the parallelization advantages consequence of this variant are also addressed. Received December 1, 1996 / Revised version received November 23, 1998 / Published online September 24, 1999     

The p-version of the FEM for computational contact mechanics

Contact analyses are being performed in various engineering applications. Here, like in most other fields, FE codes are based on low order elements using linear or quadratic shape functions. The intention of this paper is to show that finite elements with shape functions of high polynomial degree (p-FEM) are a very attractive alternative to low order elements, even for computational contact mechanics. One of the advantages is the possibility to enhance the element formulation with the blending function method in order to accurately discretize the given geometry, which leads in combination with high convergence rates to very efficient computations. In order to solve the problem of frictionless contact, a penalty formulation is applied in this work. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A propos d'approximation par elements finis optimale pour les problèmes de contact unilatéral

We consider a interpolation type operator and a projection type operator with values in a finite element function set, defined for continuous functions and keeping positiveness. We prove with a counter-example that the two operators do not verify optimal approximation results with respect to a dual norm. This counter-example yields some predicted results concerning optimality of the mortar element method and finite element analysis for unilateral contact problems.     

A Mathematical Programming Incremental Formulation for Unilateral Frictional Contact Problems of Linear Elasticity

In this article a detailed analytical formulation of the unilateral contact boundary conditions with Coulomb's law of dry friction is first attempted and the quasi-static contact problem between 3-D elastic bodies is studied thereafter. Discretizing the bodies by the Finite Element Method, introducing fictitious contact bonds and using the concept of the equivalent structural system, an incremental Nonlinear Complementarity Problem is finally formulated. Then, using additional simplifying assumptions, this problem can be transformed into an incremental Linear Complementarity Problem.     

Method of nonlinear boundary equations in problems of contact of several elastic bodies

The method of nonlinear boundary equations is applied to develop new formulations of contact problems with unknown contact regions. Our formulation is free from inequality constraints, which enter the method of variational inequalities and the standard formulations of contact problems. Methods of the theory of operator equations are applied to prove that the problems are well-posed.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 62–70, 1987.     

Structural contact problems for large deformations - Comparison of steady and non steady normal field

We will present a comparison between two formulations of the normal vector field for contact algorithms based on the mortar method. First the non steady normal field is discussed. The non steadiness is a result of the C⁰ continuity of the boundary discretization. This is the common result if one discretize the domain with classical finite element methods. Second we will present results for a special normal field distribution. We average the nodal normal vector of two ascending edges and interpolate this nodal normal throughout the edges. We have implemented both methods and present comparisons based on numerical experiments. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)