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Bo N. J. Persson

Publications and source records attributed to Bo N. J. Persson.

15 recordsLinked to original sources
arXiv2026

Surface separation in elastoplastic contacts

Understanding the contact between rough surfaces undergoing plastic deformation is crucial in many applications. We study the effect of plastic deformation on the surface separation between two solids with random roughness. Assuming a constant penetration hardness, we propose a procedure within Persson's multiscale contact mechanics theory to obtain the average surface separation by applying the elastic formulation to an effective power spectrum that accounts for plastic smoothing. Deterministic numerical simulations based on the boundary element method are used to validate the procedure and show good agreement with the theoretical predictions. The treatment also provides a route to incorporate plastic stiffening of the roughness as the stress state becomes increasingly hydrostatic at large plastic deformation.

cond-mat.soft↗
arXiv2026

Multiscale contact mechanics for elastoplastic contacts

Understanding contact between rough surfaces undergoing plastic deformation is crucial in many applications. We test Persson's multiscale contact mechanics theory for elastoplastic solids, assuming a constant penetration hardness. Using a numerical model based on the boundary element method, we simulate the contact between a flat rigid surface and an elastic-perfectly plastic half-space with a randomly rough surface. The theory's predictions for elastic, plastic, and total contact area agree quantitatively with the numerical results. The simulations also support the boundary conditions assumed in the theory, namely that the stress probability vanishes at both zero and yield stress. These findings reinforce the validity of the theory for systems with constant hardness.

cond-mat.soft↗
arXiv2021

Crack and pull-off dynamics of adhesive, viscoelastic solids

When quickly detaching an elastomer from a counterface, viscoelasticity dramatically increases the perceived adhesion relative to its adiabatic or equilibrium value. Here, we report simulations on the sticking contact between a rigid cylinder and a viscoelastic half space revealing a maximum in the work of adhesion at intermediate pull-off velocities. Maximum tensile forces yet increase monotonically with the pull-off speed and the crack-tip speed in accordance with the Persson-Brener approach. As predicted theoretically, the fracture mode transitions from interfacial crack propagation to quasi-uniform bond breaking with increasing range of adhesion.

cond-mat.soft↗
arXiv2019

Electroadhesion for soft adhesive pads and robotics: theory and numerical results

Soft adhesive pads are needed for many robotics applications, and one approach is based on electroadhesion. Here we present a general analytic model and numerical results for electroadhesion for soft solids with arbitrary time-dependent applied voltage, and arbitrary dielectric response of the solids, and including surface roughness. We consider the simplest coplanar-plate-capacitor model with a periodic array of conducting strips located close to the surface of the adhesive pad, and discuss the optimum geometrical arrangement to obtain the maximal electroadhesion force. For surfaces with roughness the (non-contact) gap between the solids will strongly influence the electroadhesion, and we show how the electroadhesion force can be calculated using a contact mechanics theory for elastic solids. The theory and models we present can be used to optimize the design of adhesive pads for robotics application.

cond-mat.soft↗
arXiv2015

Fluid contact angle on solid surfaces: role of multiscale surface roughness

We present a simple analytical model and an exact numerical study which explain the role of roughness on different length scales for the fluid contact angle on rough solid surfaces. We show that there is no simple relation between the distribution of surface slopes and the fluid contact angle. In particular, surfaces with the same distribution of slopes may exhibit very different contact angles depending on the range of length-scales over which the surfaces have roughness.

cond-mat.soft↗
arXiv2015

General contact mechanics theory for randomly rough surfaces with application to rubber friction

We generalize the Persson contact mechanics and rubber friction theory to the case where both surfaces have surface roughness. The solids can be rigid, elastic or viscoelastic, and can be homogeneous or layered. We calculate the contact area, the viscoelastic contribution to the friction force, and the average interfacial separation as a function of the sliding speed and the nominal contact pressure. We illustrate the theory with numerical results for a rubber block sliding on a road surface. We find that with increasing sliding speed, the influence of the roughness on the rubber block decreases, and for typical sliding speeds involved in tire dynamics it can be neglected.

cond-mat.soft↗
arXiv2014

Viscoelastic contact mechanics between randomly rough surfaces

We present exact numerical results for the friction force and the contact area for a viscoelastic solid (rubber) in sliding contact with hard, randomly rough substrates. The rough surfaces are self-affine fractal with roughness over several decades in length scales. We calculate the contribution to the friction from the pulsating deformations induced by the substrate asperities. We also calculate how the area of real contact, $A(v,p) $, depends on the sliding speed $v$ and on the nominal contact pressure $p$, and we show how the contact area for any sliding speed can be obtained from a universal master curve $A(p)$. The numerical results are found to be in good agreement with the predictions of an analytical contact mechanics theory.

cond-mat.soft↗
arXiv2014

Theory of adhesion: role of surface roughness

We discuss how surface roughness influence the adhesion between elastic solids. We introduce a Tabor number which depends on the length scale or magnification, and which gives information about the nature of the adhesion at different length scales. We consider two limiting cases relevant for (a) elastically hard solids with weak adhesive interaction (DMT-limit) and (b) elastically soft solids or strong adhesive interaction (JKR-limit). For the former cases we study the nature of the adhesion using different adhesive force laws ($F\sim u^{-n}$, $n=1.5-4$, where $u$ is the wall-wall separation). In general, adhesion may switch from DMT-like at short length scales to JKR-like at large (macroscopic) length scale. We compare the theory predictions to the results of exact numerical simulations and find good agreement between theory and the simulation results.

cond-mat.soft↗
arXiv2013

Self-Affine Elastic Contacts: Percolation and Leakage

We study fluid flow at the interfaces between elastic solids with randomly rough, self-affine surfaces. We show by numerical simulation that elastic deformation lowers the relative contact area at which contact patches percolate in comparison to traditional approaches to seals. Elastic deformation also suppresses leakage through contacts even far away from the percolation threshold. Reliable estimates for leakage can be obtained by combining Persson's contact mechanics theory with a slightly modified version of Bruggeman's effective-medium solution of the Reynolds equation.

cond-mat.soft↗
arXiv2013

Finite-size scaling in the interfacial stiffness of rough elastic contacts

The total elastic stiffness of two contacting bodies with a microscopically rough interface has an interfacial contribution K that is entirely attributable to surface roughness. A quantitative understanding of K is important because it can dominate the total mechanical response and because it is proportional to the interfacial contributions to electrical and thermal conductivity in continuum theory. Numerical simulations of the dependence of K on the applied squeezing pressure p are presented for nominally flat elastic solids with a range of surface roughnesses. Over a wide range of p, K rises linearly with p. Sublinear power-law scaling is observed at small p, but the simulations reveal that this is a finite-size effect. We derive accurate, analytical expressions for the exponents and prefactors of this low-pressure scaling of K by extending the contact mechanics theory of Persson to systems of finite size. In agreement with our simulations, these expressions show that the onset of the low-pressure scaling regime moves to lower pressure as the system size increases.

cond-mat.soft↗
arXiv2013

On the validity of the method of reduction of dimensionality: area of contact, average interfacial separation and contact stiffness

It has recently been suggested that many contact mechanics problems between solids can be accurately studied by mapping the problem on an effective one dimensional (1D) elastic foundation model. Using this 1D mapping we calculate the contact area and the average interfacial separation between elastic solids with nominally flat but randomly rough surfaces. We show, by comparison to exact numerical results, that the 1D mapping method fails even qualitatively. We also calculate the normal interfacial stiffness $K$ and compare it with the result of an analytical study. We attribute the failure of the elastic foundation model to the neglect of the long-range elastic coupling between the asperity contact regions.

cond-mat.mtrl-sci↗
arXiv2006

Role of surface roughness in superlubricity

We study the sliding of elastic solids in adhesive contact with flat and rough interfaces. We consider the dependence of the sliding friction on the elastic modulus of the solids. For elastically hard solids with planar surfaces with incommensurate surface structures we observe extremely low friction (superlubricity), which very abruptly increases as the elastic modulus decreases. We show that even a relatively small surface roughness may completely kill the superlubricity state.

cond-mat.soft↗
arXiv2006

Contact mechanics for randomly rough surfaces

When two solids are squeezed together they will in general not make atomic contact everywhere within the nominal (or apparent) contact area. This fact has huge practical implications and must be considered in many technological applications. In this paper I briefly review basic theories of contact mechanics. I consider in detail a recently developed contact mechanics theory. I derive boundary conditions for the stress probability distribution function for elastic, elastoplastic and adhesive contact between solids and present numerical results illustrating some aspects of the theory. I analyze contact problems for very smooth polymer (PMMA) and Pyrex glass surfaces prepared by cooling liquids of glassy materials from above the glass transition temperature. I show that the surface roughness which results from the frozen capillary waves can have a large influence on the contact between the solids. The analysis suggest a new explanation for puzzling experimental results [L. Bureau, T. Baumberger and C. Caroli, arXiv:cond-mat/0510232] about the dependence of the frictional shear stress on the load for contact between a glassy polymer lens and flat substrates. I discuss the possibility of testing the theory using numerical methods, e.g., finite element calculations.

cond-mat.soft↗
arXiv2006

Impact of molecular structure on the lubricant squeeze-out between curved surfaces with long range elasticity

The properties of butane (C4H10) lubricants confined between two approaching solids are investigated by a model that accounts for the curvature and elastic properties of the solid surfaces. We consider the linear n-butane and the branched iso-butane. For the linear molecule, well defined molecular layers develop in the lubricant film when the width is of the order of a few atomic diameters. The branched iso-butane forms more disordered structures which permit it to stay liquid-like at smaller surface separations. During squeezing the solvation forces show oscillations corresponding to the width of a molecule. At low speeds (< 0.1 m/s) the last layers of iso-butane are squeezed out before those of n-butane. Since the (interfacial) squeezing velocity in most practical applications is very low when the lubricant layer has molecular thickness, one expects n-butane to be a better boundary lubricant than iso-butane. N-butane possessing a slightly lower viscosity at high pressures, our result refutes the view that squeeze out should be harder for higher viscosities, on the other hand our results are consistent with wear experiments in which n-butane were shown to protect steel surfaces better than iso-butane.

cond-mat.mtrl-sci↗