Unilateral contact with adhesion and friction between two hyperelastic bodies

In the present paper, we consider a thermodynamic model using the contact kinematics developed by A. Curnier, Q.C. He and J.J. Téléga [C. R. Acad. Sci. Paris Sér. II 314 (1992) 1] involving unilateral contact, adhesion and Coulomb friction between two homogeneous, isotropic and hyperelastic bodies. Adhesion is described by an internal state variable β introduced by M. Frémond [C. R. Acad. Sci. Paris Sér. II 295 (1982) 913; J. Theor. Appl. Mech. 6 (1987) 383]. Taking the case of contact between a hyperelastic solid and a plane support, we formulate the associated boundary value problem as a minimization problem when no friction is involved. When the intensity of the adhesion obeys a ‘static' law, we obtain an existence result for this problem.     

Thermal relaxation effects in rapid sliding contact with friction

Summary. A rigid die slides at constant sub-critical speed on a homogeneous, isotropic linear coupled thermoelastic half-space. Friction exists, and a dynamic steady state of plane strain is considered. An exact integral transform solution for the related problem of moving surface traction is obtained, and asymptotic expressions valid when thermal relaxation is prominent are extracted.These are used to derive an analytic solution for the sliding problem, and formulas for contact zone size and location, and unilateral constraints imposed by non-tensile contact and non-positive frictional work rate. Expressions for three body wave speeds and a Rayleigh wave speed show, save for the rotational wave case, clear dependence on thermoelastic coupling and thermal relaxation.Calculations for 4340 steel show that the problem eigenvalue is similar to its isothermal counterpart for high sliding speeds, but that the average contact zone temperature increase is less pronounced than when classical Fourier heat conduction effects dominate. Calculations for a hypothetical material similar to steel show that increasing the thermal relaxation time can in effect suppress both the Rayleigh wave and second sound body wave.     

Guided thermoelastic waves in functionally graded plates with two relaxation times

Functionally graded material (FGM) is a promising heat insulation material. Wave propagation in FGM structures has received much attention for the purpose of non-destructive testing and evaluation. Few literatures dealt with the thermoelastic wave in FGM structures although the thermal effect would cause attenuations of elastic waves. In this paper, guided thermoelastic waves in FGM plates subjected to stress-free, isothermal boundary conditions are investigated in the context of the Green–Lindsay (GL) generalized thermoelastic theories (with two relaxation times). Coupled wave equations and heat conduction equation are solved by the Legendre polynomial approach. Dispersion curves for a pure elastic graded plate are calculated to make a comparison with the published data. For the thermoelastic graded plate, dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Attenuation curves for graded plates with different relaxation times are compared. The influences of different material gradient shapes are discussed. Two homogeneous thermoelastic plates with different volume fractions are obtained to show their differences from graded plates. Finally, thermoelastic wave dispersion curves for a homogeneous plate and a graded plate are calculated in the context of the classical coupled thermoelastic theory (CT) to show its differences and similarities to the generalized theory.     

Bending behavior of delaminated composite plates with contact effects

Laminated plates with strip-type delamination under pure bending were investigated analytically and experimentally. In the analysis, a two-dimensional nonlinear finite element code based on updated Lagrangian formulation was developed to analyze the bending behavior of the laminated plates and the local buckling phenomenon of the sublaminates in the delaminated region. The formulation includes large displacements and large rotations needed to describe the local buckling phenomenon of the delaminated region. The transformation matrix method, which satisfies the compatibility of displacements between the upper and lower delaminated surfaces, can reduce the number of system unknowns and was used to cope with this contact problem. The modified Newton-Raphson method was used to solve the resulting nonlinear system equation and a load-controlled scheme used in the incremental solution procedure. In each increment, the iteration process was performed until the contact condition was satisfied. In the experiment, a tensile-test machine equipped with a set of four-point bending device was used to record the load-displacement response of the delaminated plates; the bending moment-curvature relation was calculated therefrom. The analytical results are improved by contact analysis. The results shows that the size of delaminated region had no significant influence on the bending strength of laminated plates, no matter whether the local buckling occurred or not. The normal contact force on the surface of the delaminated region kept constant along the delaminated length.     

On the contact of two heated bodies

The axially symmetric Hertz thermoelastic contact problem is solved under the assumption that the contact heat resistance is inversely proportional to pressure. We consider heat flows directed both inside the body whose coefficient of thermal distortion is smaller and in the opposite direction.Warsaw University, Warsaw, Poland. Franko L'viv State University, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 5, pp. 32–39, September – October, 1995.     

Oblique impact of similar bodies with circular contact

Summary The general solution for tangential loading histories of similar bodies with circular areas of contact is outlined and applied to the tangential impact. Classical numerical methods use an interpolation function for the stress distribution on a set of points and obtain the stress distribution for given displacements by inversion of a linear equation system. Our solution avoids large systems of simultaneous equations and gives exact solutions for loading histories in form of finite, successive displacement increments. The general equations of motion for the impact are derived and applied to the case, where the normal and the tangential equations of impact are uncoupled. The Nassi-Shneiderman diagrams of the contact algorithm and the impact algorithm are presented. The solution is compared with other results from earlier publications. A tangential coefficient of restitution, which determines the behaviour of the bodies after impact, is plotted as a function of two parameters.     

Frictional contact of flexible and rigid bodies

 This paper is about planar frictional contact problems of both flexible and rigid bodies. For the flexible case a nonlinear finite element formulation is presented, which is based on a modified Coulomb friction law. Stick-slip motion is incorporated into the formulation through a radial return mapping scheme. Linearly interpolating four node elements and three node contact elements are utilized for the finite element discretization. The corresponding tangent stiffness matrices and residual vectors of the equations of motion are presented. In the rigid body case the contact problem is divided into impact and continual contact, which are mathematically described by linear complementarity problems. The impact in normal direction is modeled by a modified Poisson hypothesis, which is adapted to allow multiple impacts. The formulation of the tangential impact is grounded on Coulombs law of friction. The normal contact forces of the continual contact are such that colliding bodies are prevented from penetration and the corresponding tangential forces are expressed by Coulombs law of friction. Examples and comparisions between the different methods are presented. Received: 10 January 2001     

Dynamic contact analysis technique for rapidly sliding elastic bodies with node-to-segment contact and differentiated constraints

For a stabilized Newmark time integration of dynamic contact problems of the rapidly sliding bodies, considering the equality and inequality contact constraints and a high-speed contact point motion sliding on the deforming contact surface, the velocity and acceleration contact constraints are derived. Also, to suppress the numerical oscillations accompanied by the node-to-segment contact of the finite element models, a pseudo-node-to-node contact technique is suggested with the linear shape function elements having the almost equal segment lengths on the contact surface. The numerical simulations are performed with a high-speed punch moving on the beam and the high-speed rotating disks to check the stability and accuracy of the solution.     

Heat conductivity of the adjoining plates with a plane heat source between them

The heat conduction problem in a two-layered plate with a plane heat source between the layers is solved by the introduction of an unknown heat flux determined later from a Volterra integral equation of the second kind by the Bubnov-Galerkin method.     

Failure analysis of steel bearing plates

Steel bearing plates appeared to have failed during service due to wear damage. The subsequent failure analysis revealed that the observed surface damage was the result of widespread plastic deformation and smearing associated with a network of surface crazing, rather than wear. Additionally, the majority of the bearing plates examined met microstructural specifications, although both the carbon and manganese contents were below the specified limits. The deficiencies in carbon and manganese lowered the hardenability of the alloy and may have contributed to the need for an overly severe quench during the heat treatment processing employed during manufacture.     

Dynamic contact of bodies experiencing large deformations

Summary In the paper the statement ad basic features of the large displacement contact problem will be considered. Using the notion and formalism of a material singular surface in continua important physico-chemical phenomena of the contact interface may be described. Our attention is focused on details which follow from the geometrical nonlinearity and from the role of the interfacial layer.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday     

Elastic stresses between curved bodies in rolling contact

An outline of the development of the elastic theory of contact stresses is presented. The literature is discussed in some detail, and equations for the sub-surface stresses are given for several important cases. The effects of surface shear stresses associated with tangential forces and rolling with spin are also considered.     

Failure of axisymmetric bodies with initial crack under plane strain

On the basis of the finite element method (FEM) the authors devised an effective apparatus of numerical investigation of processes of failure of axisymmetric complexly shaped bodies under plane strain, induced by propagation of initial cracks in them. This apparatus was worked out on the basis of the use of special finite elements approximating the existence of a crack from the condition that the stresses normal and tangential to its path are equal to zero. The article suggests new modifications of the method of separate calculation of stress intensity factors and of an algorithm for solving problems of linear fracture mechanics when the path of crack propagation is not known. The reliability of the results obtained with the application of the new method and realizing its complex of programs was confirmed by the solution of control problems. An illustration of the possibilities of the method and of the complex is the calculation of the load bearing capacity of a permanent joint of a cylindrical glass shell with a metallic end cap.Translated from Problemy Prochnosti, No. 7, pp. 24–27, July, 1990.     

The transfer of heat between moving bodies in contact

We present a solution for the problem of the distribution of temperature and that of the intensity of heat flows in bodies that are in contact in the case of steady-state heat transfer and great velocities of motion.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 16, No. 3, pp. 484–488, March, 1969.