• Coupled systems mechanics
• /
• v.7 no.5
• /
• pp.583-610
• /
• 2018

This paper discusses the issues associated with modeling frictional contact between solid bodies undergoing large deformations. The most common model for friction on contact interfaces in solid mechanics is the Coulomb friction model, in which two distinct responses are possible: stick and slip. Handling the transition between these two phases computationally has been a source of algorithmic instability, lack of convergence and non-unique solutions, particularly in the presence of large deformations. Most computational models for frictional contact have used penalty or updated Lagrangian approaches to enforce frictional contact conditions. These two approaches, however, present some computational challenges due to conditioning issues in penalty-type implementations and the iterative nature of the updated Lagrangian formulation, which, particularly in large simulations, may lead to relatively slow convergence. Alternatively, a plasticity-inspired implementation of frictional contact has been shown to handle the stick-slip conditions in a local, algorithmically efficient manner that substantially reduces computational cost and successfully avoids the issues of instability and lack of convergence often reported with other methods (Laursen and Simo 1993). The formulation of this approach, however, has been limited to the small deformations realm, a fact that severely limited its application to contact problems where large deformations are expected. In this paper, we present an algorithmically consistent formulation of this method that preserves its key advantages, while extending its application to the realm of large-deformation contact problems. We show that the method produces results similar to the augmented Lagrangian formulation at a reduced computational cost.

• Structural Engineering and Mechanics
• /
• v.23 no.4
• /
• pp.431-447
• /
• 2006

A new incremental finite element model is developed to simulate the frictional contact of elastic bodies. The incremental convex programming method is exploited, in the framework of finite element approach, to recast the variational inequality principle of contact problem in a discretized form. The non-classical friction model of Oden and Pires is adopted, however, the friction effect is represented by an equivalent non-linear stiffness rather than additional constraints. Different parametric studies are worked out to address the versatility of the proposed model.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.9
• /
• pp.2242-2251
• /
• 1993

The mesh-based frictional contact model has been developed which does not rely on the spatial derivatives of the tool surface. Only points on the surface are evaluated from the description. which can then be simplified because of the relaxed demands placed on it. The surface tangents, normals, and corresponding derivatives at each finite-element node are evaluated directly from the finite-element mesh, in terms of the connecting nodal positions. The advantages accrue because there is no longer a need for a smooth tool surface to assure reasonable normals and derivatives. Furthermore, it can be shown that the equilibrium equations can only be properly written with a special normal derived from the mesh itself. The validity, accuracy, computation time, and stability of mesh-based contact model were discussed with the numerical examples of rounded flat-top and rough, flat-top rounded punch forming operations. Also, the forming process of a automobile inner panel section was simulated for testing the robustness of new contact model. In the discussion, the superiority of new model was examined, comparing with tool-based contact one.

• Transactions of Materials Processing
• /
• v.12 no.1
• /
• pp.34-42
• /
• 2003

This paper presents a rigid-plastic finite element method to handle the frictional contact problem between two deformable bodies experiencing large deformation. The variational formulation combined with incremental quasi-static model is employed for treating the contact boundary condition. The frictional behavior of the model obeys Coulomb's law of friction. The proposed contact algorithms are classified into two categories, one for searching contacting nodes and the other for calculating contact forces at the contact surface. A slave node and master contact segment are defined using the geometric condition of finite elements on the contact interface. The penalty parameter is used to limit the penetration between contacting bodies, and the finite elements are coupled with contact boundary elements.us gates and cavity thicknesses. Through this study we have observed that the jetting is related to the die swell of material. This means that the jotting is strongly affected by the elastic flow property rather than the viscous flow property in viscoelastic characteristics of molten polymer. Different resins have different elastic properties, and elastic flow behavior depends on the shear rate of flow, i.e. injection speed. Large die swell would eliminate jetting however, the retardation of die swell would stimulate jetting. In the point of mole design, reducing the thickness ratio of cavity to gate can reduce or eliminate jetting regardless of amount of elasticity of polymer melt.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2010.11a
• /
• pp.359-360
• /
• 2010

• Transactions of the Korean Society of Automotive Engineers
• /
• v.9 no.3
• /
• pp.173-180
• /
• 2001

In the case of axisymmetric thermal analysis of drum brakes, the distribution of frictional heat produced on the interface and temperature difference between mating frictional faces are very interesting problems to computational researchers. In the first part, the influence of the s-cam load angles and elastic modulus of the pad on the contact pressure distribution between pad and drum was checked by a three dimensional model. In the second part heat conduction from the interface to the pad and the drum was modeled by using a thin interface element, so artificial division of the generated frictional heat between pad and drum is not necessary. Temperature difference between mating frictional faces is successfully modeled by using the interface element. The influence of some parameters on the thermal distribution is checked. The analysis was performed by ABAQUS/Standard code.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.11 no.6
• /
• pp.93-100
• /
• 2003

This paper describes the thermoelastic instability arising from friction heat generation in braking and proposes the finite element methods to predict the variation of temperature and thermal deformation. In a conventional disc brake analysis, heat generation is only related with wheel speed and friction material and the interface pressure between disc and pad is assumed constant. But under dynamic braking conditions, the frictional heat causes the thermoelastic distortion that leads to more concentrated contact pressure distribution and hence more and more non-uniform temperature. In this paper, to complete the solution of the thermomechanically coupled problem, the linear relation model between pressure and temperature is proposed and demonstrated in examples of a simple two dimensional contact problem. And the two dimensional model has been extended to an annular three dimensional disc model in order to consider more realistic geometry and to provide a more accurate critical speed for automotive brake systems.

• 제어로봇시스템학회:학술대회논문집
• /
• 2004.08a
• /
• pp.1424-1429
• /
• 2004

In this paper a mathematical framework for deriving acceleration bounds from given joint torque limits of multiple cooperating robots are described. Especially when the different frictional contacts for every contact are assumed and the torque limits are given in 2-norm sense, we show that the resultant geometrical configuration for the acceleration is composed of corresponding parts of ellipsoids. Since the frictional forces at the contacts are proportional to the normal squeezing forces, the key points of the work includes how to determine internal forces exerted by each robot in order not to cause slip at the contacts while the object is carried by external forces. A set of examples composed of two robot systems are shown with point-contact-with-friction model and insufficient or proper degree of freedom robots.

• Journal of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.161-185
• /
• 2016

We consider a mathematical model which describes the quasistatic frictional contact between a piezoelectric body and an electrically conductive obstacle, the so-called foundation. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with Signorini's conditions and a version of Coulomb's law of dry friction in which the adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation for the model, in the form of a system for the displacements, the electric potential and the adhesion. Under a smallness assumption which involves only the electrical data of the problem, we prove the existence of a unique weak solution of the model. The proof is based on arguments of time-dependent quasi-variational inequalities, differential equations and Banach's fixed point theorem.

• Journal of the Korea Convergence Society
• /
• v.9 no.1
• /
• pp.283-289
• /
• 2018

In automotive disc brake systems, frictional heat is not uniformly dispersed for reasons such as heat flux and thermal deformation. The thermoelastic deformation due to the frictional heat affects the contact pressure distribution and the contact load may be concentrated on the contact portion on the the disc brake surface, resulting in thermoelastic instability. In this study, thermal analysis and thermal deformation analysis considering the contact between disk and pad occurred during braking through 3D axial symmetry model with reference to the experimental equation and Kao's analysis method of contact pressure of disk and pad. ANSYS is used to analyze the thermal and elastic instability problems occurring at the contact surface between the disk and the pad, considering both the thermal and mechanical loads. A 3D axisymmetric model with direct contact between the disk and the pad was constructed to more accurately observe the thermal behavior of the disk by observing the frictional surface temperature, thermal deformation and contact thermal stress of the disk.