Contact Interface Conditions Research Articles

Layerwise mixed element with sublaminates approximation and 3D zig‐zag field, for analysis of local effects in laminated and sandwich composites

AbstractThe analysis of damaged sandwich composites and thick laminates remains a still challenging task, owing to their intricate distributions of displacements and stresses across the thickness. The arduous task is capturing these distributions with an affordable computational effort. The use of sublaminate zig‐zag models appears promising since they allow to group several physical layers into a sublaminate without violating the continuity of interlaminar stresses. To contribute to research in this field, a mixed, sublaminate element is developed in which displacements and stresses are approximated by two independent zig‐zag models. Like for any zig‐zag model, the interfacial contact conditions are fulfilled a priori suitably choosing the continuity functions and constants. In addition to the contact conditions on interlaminar shears, here those on the transverse normal stress and stress gradient are also fulfilled, as required by the elasticity theory. This uncustomary feature implies the presence of unwise terms which need C2 continuous shape functions. To overcome this drawback, C1 and C2 terms are eliminated from the displacement field, as allowed by the mixed approach, then the interlaminar stresses obtained by the C0‐made displacement model are cast into a separate zig‐zag representation which restores their continuity at the interfaces. As nodal d.o.f. the three displacements and the three interlaminar stresses at the upper and lower faces are assumed, in order to fulfil the contact conditions assembling the sublaminates. Standard, C0, serendipity interpolation polynomials are used to represent both internal displacements and stress fields. As a consequence of this choice, the intra‐element stress equilibria are fulfilled in an approximate integral form. This makes easier the development of the element, but does not compromise its accuracy and convergence rate, as shown by former applications. A postprocessing procedure is developed which improves the estimation of interlaminar stresses and helps to reduce the number of sublaminates. The result is that the analysis can be carried out using a single computational layer across the thickness and a reasonably fine in‐plane discretization, even with distinctly different material properties of layers and in presence of damage. The overall computational time is reduced to an half of that required by a conventional sublaminate model, like present one deprived of zig‐zag terms and postprocessing procedure. The numerical applications concern thermally loaded and piezoelectrically actuated thick laminates and damaged sandwich panels. Copyright © 2006 John Wiley & Sons, Ltd.

Boundary element analysis of 3-D elasto-plastic contact problems with friction

In this paper, a boundary element method for three-dimensional elasto-plastic stress analysis of frictional contact problems in the framework of small strains and small displacements is presented. The contact conditions are used to unite the different system of equations for each body in contact. Several types of contact interface conditions are covered including infinite friction, frictionless and Coulomb friction. In order to include plastic deformation, the initial strain formulation and von Mises yield criterion are employed. The proposed algorithm is applied to the elasto-plastic analysis of the frictionless rigid punch, a large plate with a rigid, circular, cylindrical inclusion under the increasing load and the ceramic femoral head frictional contact problem.

Elasto-plastic static stress analysis of 3D contact problems with friction by using the boundary element method

In this paper, a boundary element method for three-dimensional elasto-plastic stress analysis of frictional contact problems in the framework of small strains and small displacements is presented. The contact conditions are used to unite the different system of equations for each body in contact. Several types of contact interface conditions are covered including infinite friction, frictionless and Coulomb friction. In order to include plastic deformation, the initial strain formulation and von Mises yield criterion are employed. The proposed algorithm is applied to the elasto-plastic analysis of the frictionless rigid punch, a large plate with a rigid, circular, cylindrical inclusion under the increasing load and the ceramic femoral head frictional contact problem.

An effective BE algorithm for 3D elastoplastic frictional contact problems

This paper is concerned with an effective boundary element algorithm for the elasto-plastic analysis of three-dimensional frictional contact problems using a quadratic boundary element formulation in the framework of small strains and small displacements. The contact conditions are used to unite the different system of equations for each body in contact. Several types of contact interface conditions are covered including infinite friction, frictionless and Coulomb friction. In order to include plastic deformation, the initial stain formulation and von Mises yield criterion are employed. The proposed algorithm is applied to the elasto-plastic analysis of the frictionless rigid punch, a large plate with a rigid, circular, cylindrical inclusion under the increasing load and the frictional punch contact problem.

Biomechanical investigation of pedicle screw–vertebrae complex: a finite element approach using bonded and contact interface conditions

This study used finite element simulation to investigate the load transfer mechanisms within the screw/vertebra complex under different interface conditions, and under varying screw lengths. Both bonded and contact conditions were employed to demonstrate the interface between the screw and vertebra. Loadings were applied at the superior surface of the vertebra and screw unthreaded end, respectively, to represent two modes of flexion loads. The results indicated that the screw within the vertebra underwent a series of discontinuities of loading, identified by the localized high contact pressures, thus creating localized bending moments. The peak stress of screw was located at the junction of the screw’s hub and thread, which is consistent with the location of screw failure observed in a clinical setting and the values of peak stress in the screw were proportional to the amount of moments generated by the two loading modes. The interface condition plays an important role in transferring the force within the screw/vertebra complex. A contact interface condition induces significantly higher stress in the screw than the bonded condition. Therefore providing a binding surface (with HA, or porosity coating on the screw surface) between the screw and the vertebra might be the most effective way to prevent screw failure. The influences of screw length on the peak stress in the screw become negligible when the screw is of sufficient length to extend fully into the vertebral body.

Computational methods for predicting impact damage in composite structures

This paper describes recent progress in materials modelling and numerical simulation of the impact response of fibre-reinforced composite structures. A continuum damage-mechanics (CDM) model for fabric-reinforced composites is developed as a framework within which both in-ply and delamination failure may be modelled during impact loading. Damage-development equations are derived and appropriate materials parameters determined from experiments. The CDM model for in-plane failure has been implemented in a commercial explicit finite element (FE) code, and new techniques are used to model the laminate as a stack of shell elements tied by contact interface conditions. This approach allows the interlaminar layers to be modelled and strength reduction due to delamination to be represented; it also provides a computationally efficient method for the analysis of large-scale structural parts. The code is applied to predict the response of carbon-fabric-reinforced epoxy plates impacted at different velocities by a steel impactor. A comparison of structural response and failure modes from numerical simulations and impact tests is given which shows a good agreement for the prediction of delamination damage at low impact energies and fracture and penetration at higher impact energies.

Development of a model for the prediction of the fretting fatigue regimes

parameters that govern the life of metallic materials under conditions of fretting fatigue may be divided into two broad categories. The first category concerns the material properties (e.g., yield strength, elastic modulus, and surface roughness) while the second concerns the externally imposed loading conditions and contact geometry. The two in-contact materials may either stick, slip, or stick-slip (i.e., there is a slip and a stick region on their interface) against each other. It has been shown that the fatigue life reduction is highest under partial slip. The objective of the present research effort is to develop a model that enables the prediction of the particular fretting fatigue regime (i.e., slip, stick, or mixed). The parameters that affect the fretting fatigue life of metallic components were identified and integrated into a model, which allows the prediction of the interfacial contact conditions. The model was first used to identify the sensitivity of the fretting fatigue regimes upon the materials and external, and geometrical parameters. Experimental results concerned with the fatigue life were plotted on the fretting maps; the fretting fatigue regimes indicated by the latter enabled the interpretation of the experimental data.

Numerical modelling of composite structures under impact loads

This paper describes recent progress on the materials modelling and numerical simulation of the impact response of fibre reinforced composite structures. A continuum damage mechanics (CDM) model for fabric reinforced composites is developed as a framework within which both in-ply and delamination failure may be modelled during impact loads. Damage evolution equations are derived and appropriate materials parameters determined from experiment. The CDM model for in-plane failure has been implemented in a commercial explicit FE code, and new techniques are used to model the laminate as a stack of shell elements tied via contact interface conditions. This approach allows the interlaminar layers and strength reduction due to delamination to be correctly modelled. The code is applied to predict the response of a composite shell impacted at low velocity by a steel impactor, and comparison between predicted structural response and failure modes with observed test results is given.

The Boundary Integral Equation Method for Elastoplastic Stres Analysis of Frictional Contact Problems

For two-dimensional elastoplastic stress analysis of frictional contact problems an isoparametric quadratic formulation of the boundary integral equation (BIE) method is presented with emphasis on clarity at the expense of efficiency. The overall system of equation is obtained by using multi-domain approach in which the contact conditions are taken into account to couple the different system of equation for each body in contact, Several types of contact interface conditions are covered including Infinite friction (stick), frictionless and Coulomb friction slip. In order to include plastic deformation in the analysis, the initial strain formulation and von Mises yield criterion are used. In order to evaluate internal stress and strain rates the differentiation of the displacement in elementwise manner is adopted with its compulsory modeling of partial (where plastic deformation is expected) domain. Elastic-perfectly plastic, work-hardening or mixed hardening material behaviour can be assumed. An efficient and robust incremental-iterative process is proposed to find the proper contact conditions. For the numerical implementation, isoparametric three-noded line elements are used to represent the boundary and eight-noded quadrilateral domain cell are used for partially modelling interior domain. The proposed algorithm is applied to the heftz-like indentation problem and the results are, where appropriate, compared with the presented results in the literature to confirm its correctness and robustness.

Cylindrical Shell Under Axial Impact: Super/Sub-Critical Impact Velocities at Constant Momentum

The dynamic buckling response of a cylindrical shell under axial impact is considered in this study. Specifically, the effects of various combinations of mass and velocity on the response of the cylinder for constant (near critical) momentum. A rigid mass is affixed at one end of the cylinder and is impacted at the other end against an infinitely rigid wall. The boundary conditions are defined by considering the mass rigidly attached to one end, axial velocity towards the right wall, and simply supported contact interface conditions. An explicit finite element code is used (LS-DYNA3D), to determine the response of the shell as variations of mass and velocity are made for a given (near critical) momentum. Specifically, in the neighborhood of critical impact velocities.

Influence of interfacial models on a stress field near a crack terminating at a bimaterial interface

Mode III problem for a semi-infinite crack terminating at bimaterial interface is investigated. The interface is modelled by different interfacial contact conditions. Corresponding boundary value problems are reduced to functional-different equations by the Fourier and Mellin integral transforms, and later to systems of singular integral equations with fixed points singularities. Solutions of the problems for various interfacial contact conditions are found. Particularly, the singularity of stresses near the crack tip is calculated. Numerical results of the singularity exponents, stress intensity factors, and jumps of the displacement near the crack tip are presented.

Neural networks for computing in fracture mechanics. Methods and prospects of applications

A neural network is proposed and studied for the treatment of fracture mechanics problems. Both the cases of classical cracks and of cracks involving Coulomb's friction or detachment (unilateral contact) interface conditions are considered. For the first case, the Hopfield model is appropriately modified, whereas for the second case, a neural model is proposed covering the case of inequalities. For this model, new results generalizing the results of Hopfield and Tank are obtained. Numerical applications illustrate the theory. Finally, the parameter identification problem for fractured bodies is formulated as a supervised learning problem.

Cracks of fractal geometry with unilateral contact and friction interface conditions

Structures involving cracks of fractal geometry are studied here, on the assumption that at the interface unilateral contact and friction boundary conditions hold. Approximating the fractal by a sequence of classical surfaces or curves and combining this procedure with a two-level contact-friction algorithm based on the optimization of the potential and of the complementary energy, we get the solution of the problem after some appropriate transformations relying on the S.V.D.-decomposition of the equilibrium matrix. Numerical examples, using singular elements for the consideration of the crack singularity, illustrate the theory.

Unilateral contact, friction and related interactions in cracks. The direct boundary integral method

The paper presents a theory for the study of cracks having a given geometry by taking into account all types of actions of monotone type like unilateral contact and friction phenomena between the two crack sides. The arising problems are of a non-classical nature, due to the interface conditions expressed in terms of non-differentiable convex superpotentials. The direct B.I.E.M. is extended appropriately in order to treat this type of problem. The developed method is illustrated by a numerical example concerning the calculation of stress intensity factors under the unilateral contact and friction interface conditions.

On the consideration of unilateral contact and friction in cracks. The boundary integral method

AbstractThe scope of the present paper is the study of cracks having a given geometry by taking into account unilateral contact and friction phenomena between the two sides of the crack. The arising problem is highly non‐classical because of the inequality relations describing the unilateral contact and friction interface conditions. The indirect BIEM is extended appropriately in order to treat this problem. Numerical examples concerning the calculation of stress intensity factors under the unilateral contact and friction interface conditions illustrate the developed method.

Contact tractions between orthotropic materials by using the boundary element method

The boundary element formulation and the computer implementation of the 2-D contact problem with small displacements and strains between elastic orthotropic materials are presented in this paper. The computer program includes isoparametric linear, quadratic and quarter-point-traction-singular elements. The contact interface conditions are explicitly imposed. It is possible to include several contact zones with different friction coefficients between the solids. The algorithm minimizes the number of equations to be solved for each load step. Several examples have been included, specially the computation of contact tractions in composite material plates with bolted joints or the influence on the stress intensity factor of the crack closure effects.

Bulk electromigration and contact interface electromigration and conditions for eliminating both mechanisms in SiO 2-covered aluminum lines

Electromigration tests were performed at 200°C with SiO 2-covered, large-grained, narrow Al interconnect lines ending on semiconductor contacts, which were marked by different barrier layers. An overlapping Mo barrier layer produced premature contact failures by interface electromigration. The interface threshold value ( jl) th,i had been reduced by the covering oxide to about 400 A/cm. For Al current densities of 8 × 10 5 A/ cm 2 interface mass flow was avoided by using a short silicide-like barrier layer, which was restricted to the contact area only. The remaining mass flow mechanism was bulk electromigration, resulting in contact openings after extremely long stress periods. Bulk electromigration can be eliminated in oxide covered Al lines, if the positive biased ends are completely covered. The reason is a threshold value for bulk electromigration, which is increased considerably by the covering oxide to a time-dependent value of about 8 × 10 7 Ah/ cm at 200°C.