The tribological aspects of contact systems are greatly affected by the friction and contact pressure distribution throughout the surface of the contact interface. Generally the contact of deformable bodies is a nonlinear problem and for the viscoelastic bodies it has a time-dependent response, since their viscous characteristics depends on time. The introduction of friction with its irreversible characteristic in contact surface makes the contact problem more difficult. The objective of this study is to develop a general augmented Lagrangian finite element formulation associated with an incremental adaptive procedure which established for analysis of frictional contact problems in viscoelastic systems. The contact behavior has been studied through an improved augmented Lagrangian approach. A generalized Maxwell model has been used to model the viscoelastic constitutive equations in which bulk and shear relaxation functions are represented by the sum of a series of decaying exponential functions of time. Based on the principle of virtual work, an effective finite element formulation associated with an incremental relaxation procedure has been developed. As an application of formulation, the numerical example has been presented to evaluate the numerical approach.

Boundary value problems involving contact are great importance in industries related to mechanical and civil engineering، also in environmental، medical، military and aerospace applications. In this paper، the nanoindentation contact problem between a rigid spherical indenter and surface of a viscoelastic half-space of arbitrary shape is considered under assumption of interfacial surfaces are frictionless. Deriving of the relations between the contact pressure distribution، the resultant force on the indenter and the penetration on viscoelastic surface is the main scope of presented study. By appropriate formulation of the viscoelastic constitutive equations، the problem can be solved numerically using the Matrix Inversion Method (MIM)، extended to viscoelastic indentation case and with exactly satisfying the boundary conditions. Comparison of the numerical results with analytical ones for loading-unloading procedure of spherical indenters، shows the efficiency of the method in case of a prescribed penetration as well as given load history.

By increasing use of very small structures, thin films, functionally graded materials, nanocomposites, and heterogeneous surfaces in various engineering areas the conventional tensile and compression tests cannot be readily used for measurement of the viscoelastic relaxation modulus and creep compliance of such materials. Recent developments in the indentation contact analysis for viscoelastic bodies, an exact evaluation of relaxation and creep characteristics of viscoelastic solids has been prepared to use the nanoindentation. In this paper, after representing the measurement methods of elastic properties for the polymeric films and layers, a powerful mathematical approach, based on contact mechanics, was developed to describe viscoelastic characteristics directly by using the novel nanoindentation technique. Independently, a constant-rate displacement and a constant-rate loading histories were used to measure the creep compliance and relaxation modulus from nanoindentation tests, respectively. The viscoelastic moduli, using the viscoelastic contact theories, have been extracted to the nanoindentation load-displacement data. A generalized Maxwell model and a generalized Kelvin model were used to describe the creep and the relaxation constitutive behaviors of viscoelastic layers, respectively.

In this paper، the procedure of a novel computational solution for the formulation and analysis of nano-indentation contact problems between a viscoelastic half-space and a rigid indenter of any arbitrary geometry is presented. The main objective of this paper is to develop the relations which link the contact pressure distribution، the load on the indenter، and the indentation depth with assumption that the surfaces are frictionless. The viscoelastic indentation problem has been solved numerically employing a proper formulation in constitutive equations and applying a new matrix inversion approach satisfying the boundary conditions. The computational approach has been validated by comparing the numerical results to the analytic ones for loading and unloading process of a spherical nano-indenter.

In the present paper, dynamic behavior of a multilayer composite plate with viscoelastic structural damping is investigated against a low-velocity impact by a spherical indenter. Hertz contact law is refined to include effect of the lower layers on the stiffness of the contact region and used in a non-linear form. Voltra hierarchical integral is employed for modeling the viscoelastic material and the layerwise theory and non-linear strain-displacement relations are used to model the plate more accurately. To solve the governing integro-differential equations, a combination of the finite element method, trapezoidal integration method for the Volterra integrals, and the Newmark numerical time integration method is used. In the results section, effects of the various viscoelasticity parameters and the indenter velocity on the time histories of the contact force, indentation, and lateral deflection of the plate are investigated. Results show that due to the damping nature of the viscoelastic materials, the plate rigidity and contact force increase whereas the maximum lateral deflection and the indentation decrease. Furthermore, higher contact forces do not necessarily indicates higher indentations.

In the present paper, responses of a multilayer viscoelastic composite plate against a low-velocity impact by a rigid spherical indenter is investigated. In this regard, a novel energy formulation that is suitable for impact analysis and accounts for the potential energy due to indentation is proposed and employed, for the first time. First, Hertz contact law is refined to include effect of the lower layers on the stiffness of the contact region. Voltra hierarchical integral is employed for modeling the viscoelastic material and a layerwise theory capable of considering the transverse flexibility of the layers is used to accurately model the plate behavior. To solve the governing integro-differential equations, the finite element method, trapezoidal integration method, and Newmark numerical time integration method are used. In the results section, effects of the various viscoelasticity parameters and the indenter velocity on the time histories of the contact force, indentation, and lateral deflection of the plate are investigated. Results show that due to the damping nature of the viscoelastic materials, the plate rigidity and contact force increase whereas the maximum lateral deflection and the indentation decrease. Furthermore, higher contact forces do not necessarily indicates higher indentations.

In the most contact theories such as Hertz, DMT and JKR, which are the most practical contacts models, biological particles are considered as a spherical elastic particle, which is not the best assumption. In this assumption, the history of loadings are not considered in that the history of strains and stresses will not analyzed properly. Therefore, in the first part of this paper, three models of elastic in spherical geometry have been developed to the viscoelastic models. By simulations and comparing the results with the experimental data of MCF-10A (breast-cancer cell), which is derived by Atomic Force Microscopy, it is revealed that viscoelastic models are more accurate than elastic models in the force-indentation curves. Then, according to the fact that most bacteria's geometry is cylindrical, contact theory for a sphere and cylinder have been developed and simulated for three groups of nanobacteria (Epidermidis, SallyVirus, and Aureus). By comparing simulations results with experimental data we observe that elastic models are not reasonable and contacts radius in viscoelastic model are smaller than they were for elastic models.

The objective of this study is to develop a general finite element formulation associated with an incremental adaptive procedure established for the calculation of contact pressure distributions in viscoelastic structures. A generalized Maxwell model has been used to model the viscoelastic constitutive equations in which bulk and shear relaxation functions are represented by sum of a series of decaying exponential functions of time. Based on the principle of virtual work, an effective finite element formulation, associated with an incremental relaxation procedure, has been developed. The viscoelastic contact behavior has been studied through an improved augmented Lagrangian approach, based on kinematical conditions of contact bodies. The proper convergence caused by the numerical examples with those obtained from analytical results shows the applicability of presented finite element formulation.

One of the most important factors that affect tire friction is surface roughness، which determines the size of the real contact area، real pressure distribution on the contact interface، and scales of mechanical engagement between viscoelastic rubber and a rough substrate. The need to predict coefficient of friction (COF) for rubber on rough surfaces for applications such as traction of tires on the road surfaces led to some physical models such as Heinrich-Kluppel’s model. The current study examines the applicability of the Heinrich-Kluppel model، using different viscoelastic representations، in numerical simulations of COF for rubber، and its agreement with the experimental results. For this purpose، roughness characteristics of the surfaces and viscoelastic properties of rubber were measured by fractal analysis and dynamic-mechanical-thermal analysis (DMTA)، respectively. These data were employed in the numerical code to simulate COF for a rubber sample. The model was also modified by replacing the Zener viscoelastic representation in the original model with the generalized Maxwell viscoelastic representation. On the other hand، COF for rubber was measured on the same rough surface (different sand-papers) by an in-house friction tester، and results were compared with the numerical results. It was shown that computer simulation could predict the load and speed dependence of rubber friction very well. The application of the generalized Maxwell model improved agreement between the numerical and experimental results for high sliding speeds where the Zener viscoelastic model failed to predict the right trend in variation of COF with speed. This speed range was matched with the sliding velocities in the footprint of tire under rolling conditions.

This paper presents an experimentally validated finite element analysis of the low-velocity impact on viscoelastic laminates with consideration of large deflection and higher-order shear deformation effects in the time domain. The generalized Maxwell model (Wiechert) is incorporated into the FEM procedure to simulate the viscoelastic feature of the structure. In a geometrically nonlinear analysis, a displacement field considering higher-order shear deformation and large deflection of the laminate is assumed, and the finite element formulation is extracted. To evaluate the contact force, the modified Hertzian contact law is implemented into the finite element program. Numerical results including contact force output histories and deflections are then derived and compared with the experimental data. The obtained results show that the viscoelasticity effect and large deflection have a significant effect on the results, so they must be considered to gain a precise description of the low-velocity impact response. This model achieved good conformance with experimental results.