Mortar Contact Research Articles

Multiscale thermomechanical contact: Computational homogenization with isogeometric analysis

A computational homogenization framework is developed in the context of the thermomechanical contact of two boundary layers with microscopically rough surfaces. The major goal is to accurately capture the temperature jump across the macroscopic interface in the finite deformation regime with finite deviations from the equilibrium temperature. Motivated by the limit of scale separation, a two-phase thermomechanically decoupled methodology is introduced, wherein a purely mechanical contact problem is followed by a purely thermal one. In order to correctly take into account finite size effects that are inherent to the problem, this algorithmically consistent two-phase framework is cast within a self-consistent iterative scheme that acts as a first-order corrector. For a comparison with alternative coupled homogenization frameworks as well as for numerical validation, a mortar-based thermomechanical contact algorithm is introduced. This algorithm is uniformly applicable to all orders of isogeometric discretizations through non-uniform rational B-spline basis functions. Overall, the two-phase approach combined with the mortar contact algorithm delivers a computational framework of optimal efficiency that can accurately represent the geometry of smooth surface textures. Copyright © 2013 John Wiley & Sons, Ltd.

Metal forming analysis using meshfree-enriched finite element method and mortar contact algorithm

In this paper, a meshfree-enriched finite element method (ME-FEM) is introduced for the large deformation analysis of nonlinear path-dependent problems involving contact. In linear ME-FEM, the element formulation is established by introducing a meshfree convex approximation into the linear triangular element in 2D and linear tetrahedron element in 3D along with an enriched meshfree node. In nonlinear formulation, the area-weighted smoothing scheme for deformation gradient is then developed in conjunction with the meshfree-enriched element interpolation functions to yield a discrete divergence-free property at the integration points, which is essential to enhance the stress calculation in the stage of plastic deformation. A modified variational formulation using the smoothed deformation gradient is developed for path-dependent material analysis. In the industrial metal forming problems, the mortar contact algorithm is implemented in the explicit formulation. Since the meshfree-enriched element shape functions are constructed using the meshfree convex approximation, they pose the desired Kronecker-delta property at the element edge thus requires no special treatments in the enforcement of essential boundary condition as well as the contact conditions. As a result, this approach can be easily incorporated into a conventional displacement-based finite element code. Two elasto-plastic problems are studied and the numerical results indicated that ME-FEM is capable of delivering a volumetric locking-free and pressure oscillation-free solutions for the large deformation problems in metal forming analysis.

Three‐dimensional numerical solution for wear prediction using a mortar contact algorithm

SUMMARYA finite element formulation to compute the wear between three‐dimensional flexible bodies that are in contact with each other is presented. The contact pressure and the bodies displacements are calculated using an augmented Lagrangian approach in combination with a mortar method, which defines the contact kinematics. The objective of this study is to characterize the wear rate coefficients for bimetallic pairs and to numerically predict the wear depths in new component designs. The proposed method is first validated with the classical pin‐on‐disc problem. Then, experimental results of wear for the metallic pairs used in internal combustion engine valves and inserts are presented and are taken as a reference solution. An example is provided that shows agreement of the numerical and experimental solution. Finally, the proposed algorithm is used to predict the wear in an application example: the wear in an internal combustion engine valve. Copyright © 2013 John Wiley & Sons, Ltd.

Frictional mortar contact for finite deformation problems with synthetic contact kinematics

In this paper we present a mortar based method, for frictional two dimensional contact problems. It is based on the work by Tur et al. (Comput Methods Appl Mech Eng 198(37---40):2860---2873, 2009) and uses the same concentrated integration scheme as well as a non regularized tangential contact formulation based on Lagrange multipliers only. We abstract the contact kinematics to a rather synthetic formulation. Therefore we are able to use two different methods of defining the normal field on the discretized surface normal: The popular method of averaged non-mortar side normal and the rather simple non continuous mortar side normal field. The problem is solved with a fixed point Newton---Raphson procedure and for both normal fields the full linearizations are derived. With numerical examples we show the performance of the more concise formulation of the non averaged non continuous mortar side normal field.

Consistent treatment of boundaries with mortar contact formulations using dual Lagrange multipliers

Computational modelling of contact problems raises two basic questions: Which method should be used to enforce the contact conditions and how should this method be discretised? The most popular enforcement methods are the Lagrange multiplier method, the penalty method and combinations of these two. A frequently used discretisation method is the so called node-to-segment approach. However, this approach might lead to problems like jumps in contact forces, loss of convergence or failure to pass the patch test. Thus in the last few years, several segment-to-segment contact algorithms based on the mortar method were proposed. Combination of a mortar discretisation with a penalty based enforcement of the contact conditions leads to unphysical penetrations. On the other hand, a Lagrange multiplier mortar method requires additional unknowns. Hence, condensation of the Lagrange multipliers is desirable to preserve the initial size of the system of equations. This can be achieved by interpolating the Lagrange multipliers with so-called dual shape functions. Discretising two contacting bodies leads to opposed contact surface representations of finite element edges, called slave and master elements, respectively. In current versions of dual Lagrange multiplier mortar formulations an inconsistency at the boundary appears when only a part of a slave element (instead of the entire element) belongs to the contact area. We present a modified definition of the dual shape functions in such slave elements. The basic idea is to construct dual shape functions that fulfill the so-called biorthogonality condition within the contact area. This leads to consistent mortar matrices also in the boundary region. To avoid ill-conditioning of the stiffness matrix, the modified mortar matrices are weighted with appropriate weighting factors. In doing so, the corresponding modified Lagrange multiplier nodal values are of the same order as the unmodified ones. Various examples demonstrate the performance of the modified mortar contact algorithm.

Mortar contact formulations for deformable–deformable contact: Past contributions and new extensions for enriched and embedded interface formulations

The past 10–15 years have seen important extensions of the mortar method, a technique for joining dissimilar grids popularized by the domain decomposition community, to the more general problem of contact and impact interactions in finite element analysis. This development has taken place largely in response to several long-standing problems in computational contact mechanics: lack of robustness in solution of the nonlinear and nonsmooth equations of evolution; degradation of spatial convergence rates in problems involving nonconforming meshes on interfaces; lack of a variationally consistent technique for stress recovery on interfaces; and so on. This survey paper summarizes some of the major steps in development of mortar contact formulations. It begins with a basic summary of the mortaring idea in the context of tied contact, it discusses key concepts required for the extension of these methods to large deformation, large sliding formulations of contact-impact, and it previews new results where lessons learned from mortar contact formulations can be extended to a much broader class of interface mechanics applications, considering in particular enriched interface formulations and embedded interface approaches to fluid–structure interaction.

Finite deformation frictional mortar contact using a semi‐smooth Newton method with consistent linearization

AbstractA two‐dimensional, finite deformation frictional contact formulation with Coulomb's law is presented. The approach considers multibody contact and is based on a mortar formulation. The enforcement of contact constraints is realized with dual Lagrange multipliers. These alternative multiplier spaces are constructed in a way that the multipliers can easily be eliminated from the global system of equations by static condensation such that the system size does not increase. Friction kinematic variables are formulated in an objective way and enter non‐smooth complementarity functions for expressing the contact constraints. An active set strategy is derived by applying a semi‐smooth Newton method, which treats contact nonlinearities, material and geometrical nonlinearities in one single iterative scheme. By further carrying out a consistent linearization for both normal and frictional contact forces and constraints, a robust and highly efficient algorithm for linear and higher‐order (quadratic) interpolation is achieved. Efficiency of the proposed method and quality of results are demonstrated in several examples. Copyright © 2010 John Wiley & Sons, Ltd.

3D fluid–structure-contact interaction based on a combined XFEM FSI and dual mortar contact approach

Finite deformation contact of flexible solids embedded in fluid flows occurs in a wide range of engineering scenarios. We propose a novel three-dimensional finite element approach in order to tackle this problem class. The proposed method consists of a dual mortar contact formulation, which is algorithmically integrated into an eXtended finite element method (XFEM) fluid–structure interaction approach. The combined XFEM fluid–structure-contact interaction method (FSCI) allows to compute contact of arbitrarily moving and deforming structures embedded in an arbitrary flow field. In this paper, the fluid is described by instationary incompressible Navier–Stokes equations. An exact fluid–structure interface representation permits to capture flow patterns around contacting structures very accurately as well as to simulate dry contact between structures. No restrictions arise for the structural and the contact formulation. We derive a linearized monolithic system of equations, which contains the fluid formulation, the structural formulation, the contact formulation as well as the coupling conditions at the fluid–structure interface. The linearized system may be solved either by partitioned or by monolithic fluid–structure coupling algorithms. Two numerical examples are presented to illustrate the capability of the proposed fluid–structure-contact interaction approach.

A mortar method for energy‐momentum conserving schemes in frictionless dynamic contact problems

AbstractIn the present work the mortar method is applied to planar large deformation contact problems without friction. In particular, the proposed form of the mortar contact constraints is invariant under translations and rotations. These invariance properties lay the foundation for the design of energy‐momentum time‐stepping schemes for contact–impact problems. The iterative solution procedure is embedded into an active set algorithm. Lagrange multipliers are used to enforce the mortar contact constraints. The solution of generalized saddle point systems is circumvented by applying the discrete null space method. Numerical examples demonstrate the robustness and enhanced numerical stability of the newly developed energy‐momentum scheme. Copyright © 2008 John Wiley & Sons, Ltd.

Energy‐momentum schemes for large deformation contact problems

AbstractDynamic contact problems in elasticity are dealt with in the framework of nonlinear finite element methods. A new energymomentum conserving time‐stepping scheme for the mortar contact formulation is presented. The proposed method relies on a reparametrization of the contact constraints in terms of specific invariants. For the time discretisation of the contact forces emanating from the mortar formulation the notion of a discrete gradient is applied. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A segment-to-segment mortar contact method for quadratic elements and large deformations

This paper describes a new extension of mortar based, segment-to-segment algorithms for large deformation contact analysis, permitting their use when quadratic interpolations are used in the underlying finite element method. The work builds upon results previously described by Puso and Laursen [M.A. Puso, T.A. Laursen, A mortar segment-to-segment contact method for large deformation solid mechanics, Comput. Methods Appl. Mech. Engrg. 193 (2004) 601–629; M.A. Puso, T.A. Laursen, A mortar segment-to-segment frictional contact method for large deformations, Comput. Methods Appl. Mech. Engrg. 193 (2004) 601–629], where methods were developed for quasistatic and implicit dynamic analysis in the context of linear element interpolations. Here, we see that many algorithmic ideas from the linear case can be adopted for use with quadratic elements along with different alternative interpolations of the mortar (contact) multipliers. The result is a class of methods appropriate for use for either mesh tying, true large sliding simulation (frictionless or frictional) and readily admits mixing of element types. Several numerical examples are given to demonstrate the effectiveness of the approach.

Two dimensional mortar contact methods for large deformation frictional sliding

AbstractThis paper presents a mortar‐based formulation for the solution of two dimensional frictional contact problems involving finite deformation and large sliding. As is widely recognized, traditional node‐to‐surface contact formulations have several drawbacks in solution of deformable‐to‐deformable contact problems, including lack of general patch test passage, degradation of spatial convergence rates, and robustness issues associated with the faceted representation of contacting surfaces. The mortar finite element method, initially proposed as a technique to join dissimilarly meshed domains, has been shown to preserve optimal convergence rates in tied contact problems (see (Discretization Methods and Iterative Solvers Based on Domain Decomposition, Springer‐Verlag, Heidelberg, 2001) for a recent review), and is examined here as an alternative spatial discretization method for large sliding contact. In particular, a novel description for frictional sliding conditions in large deformation mortar formulations is proposed in this work.In recent years, the mortar element method has already been successfully implemented to solve frictional contact problems with linearized kinematics (see (Int. J. Numer. Meth. Engng 1993; 36: 3451)). However, in the presence of large deformations and finite sliding, one must face difficulties associated with the definition and linearization of contact virtual work in the case where the mortar projection has a direct dependence on the tangential relative motion along the interface. In this paper, such a formulation is presented, with particular emphasis on key aspects of the linearization procedure and on the robust description of the friction kinematics. Some novel techniques are proposed to treat the non‐smoothness in the contact geometry and the searching required to define mortar segments. A number of numerical examples illustrate the performance and accuracy of the proposed formulation. Copyright © 2004 John Wiley & Sons, Ltd.

Concrete-concrete pressure contacts under dynamic loading, studied by contact electrical resistance measurement

A mortar–mortar contact was studied under dynamic loading at different compressive stress amplitudes by measuring the contact electrical resistance. Irreversible decrease in the contact resistance upon unloading was observed at a low stress amplitude (5 MPa) due to local plastic deformation at the asperities at the interface. Irreversible increase in the contact resistance at the maximum stress was observed, probably due to debris generation; it was more significant at a higher stress amplitude (15 MPa). At a stress amplitude of 15 MPa, irreversible increase in the contact resistance upon unloading was observed in the first four loading cycles, probably due to severe debris generation.

Adsorption of Carbon-14 on Mortar

AbstractThe sorption experiments of carbon-14 on the mortar grain (grain size : 0.50 – 1.0 mm) focused on the chemical form of the carbon-14 were carried out by the batch method. Three kinds of carbon-14 chemical form were used for the experiments : sodium carbonate (Na214CO3) as the inorganic radiocarbon, and sodium acetate (CH314COONa) and acetaldehyde (14CH314CHO) as the organic radiocarbons. 0.30 gram samples of mortar were soaked in the solution with carbon-14 at 15°C for periods of up to 160 days. At the end of each run, carbon-14 concentrations in the supernatants were determined before and after centrifugation (3,500 rpm., 1 hr.).In the mortar-sodium carbonate system, the retention process of carbon-14 related to reaction on the surface of the mortar was speculated as follows. First, 3CaO-SiO2. and 2CaO-SiO2, of the mortar components contact with water and produce Ca(OH)2. Ca(OH)2 produces Ca2+ and OH− in the solution. Then, calcite forms from Ca2+ and CO32− in the solution. Thus, the sorption ratio of carbon-14 onto mortar will be high until mortar nas been completely carbonated because Ca2+ is rich in the mortar and the solubility of calcite is low.In the mortar-organic carbon system, the soluble organic carbon-14 is hardly sorbed on the surface of the mortar. Therefore, the cementitious materials may not inhibit the release of organic radiocarbons from the low-level radioactive wastes, contrary to the case of inorganic radiocarbon.