Key Engineering Materials Vol. 681

Abstract: A finite element framework based on dual mortar methods is presented for simulating fretting wear effects in the finite deformation regime. The mortar finite element discretization is realized with Lagrangean shape functions as well as isogeometric elements based on non-uniform rational B-splines (NURBS) in two and three dimensions. Fretting wear effects are modeled in an incremental scheme with the help of Archard’s law and the worn material is considered as additional contribution to the gap function. Numerical examples demonstrate the robustness and accuracy of the presented algorithm.

Abstract: This paper extends the frictionless penalty-based node to contact formulation with area regularization to a 3D framework. Based on our previous work [1] focused on axisymmetric modeling, two computational methods are also considered for the determination of the slave node area. The first method, named as the geometrical approach, is based on a force equivalence system, while the second one, named as the consistent approach, is derived from a more sophisticated scheme elaborated upon the virtual work principle. Then, the extended contact elements are derived for the contact formulations with geometrical and consistent area regularization and a consistent linearization is provided accordingly, which guarantees a quadratic rate of convergence of the global Newton Raphson iterative procedure. Finally, two numerical examples assess the performance of both contact formulations with area regularization and demonstrates the robustness and the efficiency of the node to surface contact formulation with consistent area regularization in reproducing a constant contact pressure distribution across the interface between a deformable body and a analytically-defined rigid body, irrespective of the mesh. Our findings will certainly encourage further developments towards the design of a penaltybased node to surface contact algorithm passing the contact patch test, as was already done successfully in 2D contact problems [2].

Abstract: For the two dimensional contact modeling, the standard node-to-segment quadratic contact elements are known to exhibit oscillations of the contact pressure. This situation is particularly critical when using the penalty method with a high penalty parameter because the amplitude of the oscillations increase with increasing penalty parameter. The aim of this article is to present a method for removing the oscillations of contact pressure observed while using quadratic contact element. For this purpose, the nodal forces at the slave and at the master nodes need to be evaluated appropriately. One possibility is to develop a suitable procedure for computing the nodal forces. In that sake, we selected the approach first proposed in [35] in an appropriate manner. After presenting the improved quadratic contact element, some numerical examples are illustrated in this paper to comparethe standard quadratic node-to-segment element with the proposed element. The examples show that the proposed element can strongly reduce the oscillating contact pressure for both plane and curved contact surfaces.

Abstract: In the present study contact between elastic-plastic dissimilar spherical particles are investigated. The investigation is based on analytical and numerical methods and in the latter case in particular the finite element method. The results presented are pertinent to force-displacement relations at contact when elastic and plastic deformations are of equal magnitude. Especially, hard metal particles are considered with a typical application area being analysis of powder compaction.

Abstract: The design of novel mechanical microstructures having auxetic behaviour is proposed in this paper using techniques of topology optimization for compliant mechanisms. The resulting microstructure can be modified in order to cover additional needs, not included in the topology optimization formulation. Classical structural optimization, contact mechanics, homogenization and nonlinear finite element analysis are used for this step. Thus, the modified microstructure or composite is studied with numerical homogenization in order to verify that it still has the wished auxetic behaviour. Finally, nonlinear finite element analysis shows how the auxetic behaviour is influenced by unilateral contact between the constituent materials, large displacements and elastoplasticity.

Abstract: In the paper a class of wear problems is considered, for which the contact zone is fixed on one of contacting bodies and translates on the surface of another body, like in the case of punch in relative translation on a substrate. In the case of constant normal loads interacting with the induced monotonic sliding, the steady state wear process is reached. In the case of fixed normal load and the reciprocal sliding condition the wear process tends to its steady periodic state. Similarly, for periodically varying normal load, a steady periodic state is reached for the case of monotonic sliding. A most general case occurs for in-phase or out-of-phase periodic variation of normal load interacting with the reciprocal sliding. The paper is aimed to provide further study of steady wear states by considering periodically varying normal load combined with monotonic or alternating sliding conditions. The illustrative examples demonstrate the contact pressure and wear distribution in steady states with application to brake wear analysis.

Abstract: An experimental investigation on the friction coefficient in line contacts under mixed and boundary lubrication regimes is described. Rectangular contacts between cylindrical specimens and the flat surface of discs of different material and surface roughness combinations were analyzed. Very low Stribeck numbers have been considered, resulting also in low dimensionless film thickness, so that the morphology of the surfaces and the material had a remarking role. In this work, the theoretical procedure for assessing the friction coefficient in the tested cases is described and compared to experimental results. Additionally, wear effects obtained in boundary lubrication conditions are shown. The surface conditions are put in relation with some particular trends of the friction coefficient obtained for certain combinations of materials and roughness.

Abstract: In this study, the contact problem for a graded elastic half-plane in frictional contact with a rigid stamp is considered. The plane contact problem is assumed to be linear elastic and the Poisson's ratio is assumed to be constant. Analytical formulation of the study includes Fourier transforms of the governing equations and boundary conditions. The resulting integral equation is solved numerically. Contact pressure, in-plane stress and the stress intensity factor at the sharp edges of the contact are evaluated and demonstrated for various stamp profiles. The results are compared with a closed form solution for homogeneous isotropic half-plane indented by rigid stamps. The effects of the nonhomogeneity parameter, coefficient of friction and stamp profiles on the contact and in-plane stresses are analyzed in detail.

Abstract: The contact problem with Coulomb friction together with a simple Kelvin-Voigt viscoelastic model is studied. The numerical solution is obtained using a time discretization by a semi-implicit formula, the visco-elastic solids in contact being discretized by Symmetric Galerkin Boundary Element Method (SGBEM). The resulting minimization problem with a nonsmooth cost functional is suitably transformed in several ways. Firstly, a transformation is performed to apply SGBEM without any viscoelastic fundamental solution. Secondly, a transformation of contact quantities leads to a minimimization with a quadratic programming structure. Numerical examples show the applicability of the proposed approach to solve rather intricate frictional contact problems.