Contact Mechanics Problems Research Articles

Role of grain-level chemo-mechanics in composite cathode degradation of solid-state lithium batteries

Solid-state Li-ion batteries, based on Ni-rich oxide cathodes and Li-metal anodes, can theoretically reach a high specific energy of 393 Wh kg−1 and hold promise for electrochemical storage. However, Li intercalation-induced dimensional changes can lead to crystal defect formation in these cathodes, and contact mechanics problems between cathode and solid electrolyte. Understanding the interplay between cathode microstructure, operating conditions, micromechanics of battery materials, and capacity decay remains a challenge. Here, we present a microstructure-sensitive chemo-mechanical model to study the impact of grain-level chemo-mechanics on the degradation of composite cathodes. We reveal that crystalline anisotropy, state-of-charge-dependent Li diffusion rates, and lattice dimension changes drive dislocation formation in cathodes and contact loss at the cathode/electrolyte interface. These dislocations induce large lattice strain and trigger oxygen loss and structural degradation preferentially near the surface area of cathode particles. Moreover, contact loss is caused by the micromechanics resulting from the crystalline anisotropy of cathodes and the mechanical properties of solid electrolytes, not just operating conditions. These findings highlight the significance of grain-level cathode microstructures in causing cracking, formation of crystal defects, and chemo-mechanical degradation of solid-state batteries.

Two Nitsche-based mixed finite element discretizations for the seepage problem in Richards’ equation

This paper proposes two algorithms to impose seepage boundary conditions in the context of Richards’ equation for groundwater flows in unsaturated media. Seepage conditions are non-linear boundary conditions, that can be formulated as a set of unilateral constraints on both the pressure head and the water flux at the ground surface, together with a complementarity condition: these conditions in practice require switching between Neumann and Dirichlet boundary conditions on unknown portions on the boundary. Upon realizing the similarities of these conditions with unilateral contact problems in mechanics, we take inspiration from that literature to propose two approaches: the first method relies on a strongly consistent penalization term, whereas the second one is obtained by an hybridization approach, in which the value of the pressure on the surface is treated as a separate set of unknowns. The flow problem is discretized in mixed form with div-conforming elements so that the water mass is preserved. Numerical experiments show the validity of the proposed strategy in handling the seepage boundary conditions on geometries with increasing complexity.

A continuum mechanics framework for wear simulations of sliding surfaces

Wear resulting from sliding motion is a complex physics problem with multiple spatial and temporal scales of interest. The novel model involves solving contact mechanics problems in multiple positions concurrently, followed by an averaging process to calculate the average wear of all asperities in the domain, which effectively mimics the physics of sliding. The model accounts for anisotropic surfaces, including arbitrarily rough surfaces. The novel sliding solution method enables good accuracy, while maintaining computational time at a reasonable level. Results of the model are presented and discussed, with a focus on the further usage of the model.

Minimization principle for hemivariational–variational inequality driven by uniformly monotone operators with application to problems in contact mechanics

In this paper, we consider hemivariational–variational inequalities driven by uniformly monotone or d-monotone operators in Banach spaces. We establish related minimization principles leading to the existence and uniqueness of solutions to the inequality considered as well as we suggest the Ritz type numerical approximations. The theoretical results obtained are next applied to some problems inspired by models from contact mechanics.

Solving forward and inverse problems of contact mechanics using physics-informed neural networks

This paper explores the ability of physics-informed neural networks (PINNs) to solve forward and inverse problems of contact mechanics for small deformation elasticity. We deploy PINNs in a mixed-variable formulation enhanced by output transformation to enforce Dirichlet and Neumann boundary conditions as hard constraints. Inequality constraints of contact problems, namely Karush–Kuhn–Tucker (KKT) type conditions, are enforced as soft constraints by incorporating them into the loss function during network training. To formulate the loss function contribution of KKT constraints, existing approaches applied to elastoplasticity problems are investigated and we explore a nonlinear complementarity problem (NCP) function, namely Fischer–Burmeister, which possesses advantageous characteristics in terms of optimization. Based on the Hertzian contact problem, we show that PINNs can serve as pure partial differential equation (PDE) solver, as data-enhanced forward model, as inverse solver for parameter identification, and as fast-to-evaluate surrogate model. Furthermore, we demonstrate the importance of choosing proper hyperparameters, e.g. loss weights, and a combination of Adam and L-BFGS-B optimizers aiming for better results in terms of accuracy and training time.

Formulating and heuristic solving of contact problems in hybrid data-driven computational mechanics

In this work we consider the hybrid Data-Driven Computational Mechanics (DDCM) approach, in which a smooth constitutive manifold is reconstructed to obtain a well-behaved nonlinear optimization problem (NLP) rather than the much harder discrete-continuous NLP (DCNLP) of the direct DDCM approach. The key focus is on the addition of geometric inequality constraints to the hybrid DDCM formulation. Therein, the required constraint force leads to a contact problem in the form of a mathematical program with complementarity constraints (MPCC), a problem class that is still less complex than the DCNLP. For this MPCC we propose a heuristic quick-shot solution approach, which can produce verifiable solutions by solving up to four NLPs. We perform various numerical experiments on three different contact problems of increasing difficulty to demonstrate the potential and limitations of this approach.

Modeling the wear of the "diamond-containing mineral ceramics — ceramics" friction pair

Based on the solution of the contact mechanics problem, a model of wear of the "diamond-containing mineral ceramics — ceramics" friction pair is constructed, in which diamond grains in the ceramic matrix are represented as spherical segments of the same radius. The law of distribution of diamond grains in a ceramic matrix is power law. The dependences of grinding productivity and wear rate of diamond-containing tools on the physical and mechanical properties of contacting materials, roughness parameters of friction surfaces and loading conditions are obtained. Keywords:abrasive diamond tools, mineral ceramics, ceramics, contact interaction model, productivity, grinding, wear onvk@mail.ru, alnikbltov@rambler.ru, vnvkv@yandex.ru

Analysis of stress and deformation of an exponentially graded viscoelastic coated half plane under indentation by a rigid flat punch indenter tip

This paper solves the dynamic contact problem when a rigid flat punch indents into an exponentially graded (FG) viscoelastic coated homogeneous half-plane. A harmonic vertical force is applied to the FG coating, and the solution is obtained for the stress and displacement for both the FG viscoelastic coating and the half-plane using the Helmholtz functions and the Fourier integral transform technique. By applying specific boundary conditions, the contact mechanics problem is converted into a singular integral equation of the first kind. This equation is then solved numerically using the Gauss-Chebyshev integration formulas. The analysis provides detailed insights into how various parameters—such as external excitation frequency, loss factor ratio, Young’s modulus ratio, density ratio, Poisson’s ratio, indentation load, and punch length—affect the dynamic contact stress and dynamic in-plane stress.

Three-dimensional Wiener-Hopf integral equation in mixed problems of anisotropic media

For the first time, an exact solution of the three-dimensional Wiener-Hopf integral equation is given, one-dimensional and two-dimensional versions of which are widely used in mixed, including contact problems. The equation in question can be abstractly represented as the action of a three-dimensional stamp on a four-dimensional half-space or layer. In the work, in relation to contact problems of mechanics, as well as seismology, an application of this method was found. It consists in the fact that along with two geometric coordinates, the time coordinate extending along the entire axis is taken as the third. It allows you to introduce a change of condition at zero for stresses, moving in the contact zone from their values to their velocities. Attempts at an analytical or numerical solution of this problem are not known to the authors. The results may be useful in the fields of using the Wiener-Hopf equation in probability theory and statistics, where one-dimensional variants are used, as well as in seismology. Just as in the two-dimensional case, a universal modeling method based on block elements is used in the study.

Developing Single‐Ion Conductive Polymer Electrolytes for High‐Energy‐Density Solid State Batteries

AbstractSingle‐ion conductive polymer electrolytes (SICPEs) with a cationic transference number (tLi+) close to unity exhibit specific advantages in solid‐state batteries (SSBs), including mitigating the ion concentration gradient and derived problems, suppressing the growth of lithium dendrites, and improving the utilization of cathode materials and the rate performance of SSBs. However, the application of SICPEs remains major challenges, i.e., the ionic conductivity is inferior at room temperature. Therefore, the recent accomplishments in improving the ambient ionic conductivity to be compatible SICPEs with a high transference number are discussed in this review. In particular, some strategies of delocalizing charges in polyanions, designing a highly conductive polymer matrix, and utilizing synergistic effects in SICPEs are focused to shed light on the further development of solid polymer electrolytes for SSBs. Finally, multifunctional species of SICPEs are discussed in view of the mechanical contact and/or charge transfer problems at the solid–solid interface in SSBs.

Historic adjacent concrete buildings strengthened by cable-ties under seismic pounding effects: A stochastic approach considering uncertain input parameters

Cultural Heritage structures include existing old industrial framed reinforced concrete (RC) buildings. The present study deals with a stochastic numerical treatment for the pounding problem concerning the seismic interaction between historic adjacent framed structures strengthened by cable-ties (tension-only bracings) when the input parameters are uncertain. This problem concerns here the unilateral contact between neighbouring structures during earthquakes and is considered as an inequality problem of dynamic structural contact mechanics. The Monte Carlo method is used for treating the uncertainty concerning input parameters. The purpose here is to estimate numerically and to control actively the influence of the cable-ties on the seismic response of the adjacent structures. Finally, in a practical case of two seismically interacting historic framed reinforced concrete (RC) structures, the effectiveness of the proposed methodology is shown.

A combined SPH-DEM approach for extremely deformed granular packings: validation and compression tests

We present a novel smoothed particle hydrodynamics-discrete element method (SPH-DEM) approach for the simulation of deformable granular media. First, we show how the method converges to the analytical solution in a simple contact mechanics problem, namely the Hertz contact law for elastic spherical grains. Second, we analyze the evolution of a 2D packing of disks under uniaxial compression, displaying the evolution of key metrics of the packing such as the coordination number and the vertical stress. We show that the code produces data in quantitative agreement with what is known from literature. Finally, we demonstrate that our SPH-DEM coupling can be used to study packings of deformable grains from the onset of jamming to extremely compacted states, reaching packing fractions of ϕ≃0.995\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi \\simeq 0.995$$\\end{document}.

ANALYSIS OF NONLINEAR RIGIDITY CHARACTERISTICS OF AIR BLOWER COMPRESSOR ELASTIC SUPPORTS

Vibrations of rotor systems are largely determined by elastic characteristics of supports. In the general case, the dependence of displacements on force for such supports is nonlinear. This applies to bearing supports of various types. In addition to bearings, elastic elements are also used in supports of rotor systems. They are designed to change the overall stiffness of the supports. The paper analyzes the radial stiffness of flexible ring dampers used in rotor supports. For this, two main approaches are proposed. The first is a conventional simulation of this problem of contact mechanics using the finite element method. The second is an analytical method that can be used as an alternative to expensive numerical calculations. This method is based on the principle of minimum additional energy. A special closed-form variational formulation is developed using the Euler-Bernoulli beam approximation for an elastic ring and a simplified model of normal contact on the ring flanges. It was shown that the surface tolerances of parts have a significant effect on the radial response of a flexible ring, which can become nonlinear. Tight fit of the ring on both sides makes it much stiffer, and non-tight fit leads to free movement of the rotor and much weaker damping of its movement. Both methods gave results that are consistent for the considered cases. By varying their design parameters, it is possible to adjust the rotor systems from critical modes of operation. Keywords: rotor system, elastic support, rigidity, finite element analysis, stress-strain state, contact interaction, principle of minimum additional energy

The a posteriori finite element method (APFEM), a framework for efficient parametric study and Bayesian inferences

Stochastic methods have recently been the subject of increased attention in Computational Mechanics for their ability to account for the stochasticity of both material parameters and geometrical features in their predictions. Among them, the Galerkin Stochastic Finite Element Method (GSFEM) was shown to be particularly efficient and able to provide accurate output statistics, although at the cost of intrusive coding and additional theoretical algebraic efforts. In this method, distributions of the stochastic parameters are used as inputs for the solver, which in turn outputs nodal displacement distributions in one simulation. Here, we propose an extension of the GSFEM—termed the A posteriori Finite Element Method or APFEM—where uniform distributions are taken by default to allow for parametric studies of the inputs of interest as a postprocessing step after the simulation. Doing so, APFEM only requires the knowledge of the vertices of the parameter space. In particular, one key advantage of APFEM is its use in the context of Bayesian inferences, where the random evaluations required by the Bayesian setting (usually done through Monte Carlo) can be done exactly without the need for further simulations. Finally, we demonstrate the potential of APFEM by solving forward models with parametric boundary conditions in the context of (i) metamaterial design and (ii) pitchfork bifurcation of the buckling of a slender structure; and demonstrate the flexibility of its use for Bayesian inference by (iii) inferring friction coefficient of a half plane in a contact mechanics problem and (iv) inferring the stiffness of a brain region in the context of cancer surgical planning.

Leakage Threshold of a Saddle Point

The threshold condition for leakage inception is of great interest to many engineering applications, and it is essential for seal design. In the current study, the leakage threshold is studied by means of a numerical method for a mechanical contact problem between an elastic bi-sinusoidal surface and a rigid flat surface. The coalesce process of the contact patches is first investigated, and a generalized form of solution for the relation between the contact area ratio and the average applied pressure is acquired. The current study shows that the critical value of the average applied pressure and the corresponding contact area required to close the percolation path can be represented as a power law of a shape parameter, if the effect of the hydrostatic load from the pressurized fluid is ignored. With contact patches merged under a constant applied load, the contact breakup process is investigated with elevated sealed fluid pressure condition, and it is shown that the leakage threshold is a function of the excess pressure, which is defined as a ratio between the average applied pressure and the critical pressure under dry contact conditions.Graphical abstract

Application of the p-version of FEM to hierarchic rod models with reference to mechanical contact problems

The formulation of a system of hierarchic models for the simulation of the mechanical response of slender elastic bodies, such as elastic rods, is considered. The present work is concerned with aspects of implementation and numerical examples. We use a finite element formulation based on the principle of minimum potential energy. The displacement fields are represented by the product of one-dimensional field functions and two-dimensional director functions. The field functions are approximated by the p-version of the finite element method. Our objective is to control both the model form errors and the errors of discretization with a view toward the development of advanced engineering applications equipped with autonomous error control procedures. We present numerical examples that illustrate the performance characteristics of the algorithm.

Recent Advancements in the Tribological Modelling of Rough Interfaces

This paper analyses some effective strategies proposed in the last few years to tackle contact mechanics problems involving rough interfaces. In particular, we present Boundary Element Methods capable of solving the contact with great accuracy and, at the same time, with a marked computational efficiency. Particular attention is paid to non-linearly elastic constitutive relations and, specifically, to a linearly viscoelastic rheology. Possible implications deal with all the tribological mechanical systems, where contact interactions are present, including, e.g., seals, bearings and dampers.

A Mortar Finite Element Formulation for Large Deformation Lubricated Contact Problems with Smooth Transition Between Mixed, Elasto-Hydrodynamic and Full Hydrodynamic Lubrication

This work proposes a novel model and numerical formulation for lubricated contact problems describing the mutual interaction between two deformable 3D solid bodies and an interposed fluid film. The solid bodies are consistently described based on nonlinear continuum mechanics allowing for finite deformations and arbitrary constitutive laws. The fluid film is modelled as a quasi-2D flow problem governed by the (thickness-)averaged Reynolds equation. In contrast to existing approaches, the proposed model accounts for the co-existence of frictional contact tractions and hydrodynamic fluid tractions at every local point on the contact surface of the interacting bodies and covers the entire range of lubrication in one unified modelling framework with smooth transition between these different regimes. From a physical point of view, this approach can be considered as a model for the elastic deformation of asperities on the lubricated contact surfaces. The finite element method is applied for spatial discretization of the 3D solid-mechanical problems and the 2D interface effects, consisting of the averaged Reynolds equation governing the fluid film and the non-penetration constraint of the mechanical contact problem. A consistent and accurate model behavior is demonstrated by studying several challenging benchmark test cases.

The INTERNODES method for applications in contact mechanics and dedicated preconditioning techniques

• The INTERNODES method is applied to problems in contact mechanics. • We propose a highly efficient preconditioner to solve the sequence of linear systems. • An algorithm is suggested to cheaply solve linear systems with the preconditioning matrix. • The quality of the preconditioner is assessed on small to medium size 2D problems. The mortar finite element method is a well-established method for the numerical solution of partial differential equations on domains displaying non-conforming interfaces. The method is known for its application in computational contact mechanics. However, its implementation remains challenging as it relies on geometrical projections and unconventional quadrature rules. The INTERNODES (INTERpolation for NOn-conforming DEcompositionS) method, instead, could overcome the implementation difficulties thanks to flexible interpolation techniques. Moreover, it was shown to be at least as accurate as the mortar method making it a very promising alternative for solving problems in contact mechanics. Unfortunately, in such situations the method requires solving a sequence of ill-conditioned linear systems. In this paper, preconditioning techniques are designed and implemented for the efficient solution of those linear systems.

On the limitations of low‐rank approximations in contact mechanics problems

AbstractTypical strategies for reducing the computational cost of contact mechanics models use low‐rank approximations. The underlying hypothesis is the existence of a low‐dimensional subspace for the displacement field and a non‐negative low‐dimensional subcone for the contact pressure. However, given the local nature of contact, it seems natural to wonder whether low‐rank approximations are a good fit for contact mechanics or not. In this article, we investigate some of their limitations and provide numerical evidence showing that contact pressure is linearly inseparable in many practical cases. To this end, we consider various mechanical problems involving nonadhesive frictionless contacts and analyze the performance of the low‐rank models in terms of three different criteria, namely, compactness, generalization, and specificity.