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We consider a viscoelastic body occupying a smooth bounded domain of $R^3$ under the effects of volumic traction forces. Inertial effects are considered: hence, the equation describing the evolution of displacements is of the second order…

Analysis of PDEs · Mathematics 2015-07-22 Riccardo Scala , Giulio Schimperna

We study the adhesive contact between elastic solids with randomly rough, self affine fractal surfaces. We present molecular dynamics (MD) simulation results for the interfacial stress distribution and the wall-wall separation. We compare…

Soft Condensed Matter · Physics 2009-11-13 C. Yang , B. N. J. Persson , J. Israelachvili , K. Rosenberg

An adhesive unilateral contact between visco-elastic heat-conductive bodies in linear Kelvin-Voigt rheology is scrutinised. The flow-rule for debonding the adhesive is considered rate independent, unidirectional, and non-associative due to…

Analysis of PDEs · Mathematics 2011-10-14 Riccarda Rossi , Tomas Roubicek

We prove the existence of large-data global-in-time weak solutions to an evolutionary PDE system describing flows of incompressible \emph{heat-conducting} viscoelastic rate-type fluids with stress-diffusion, subject to a stick-slip boundary…

Analysis of PDEs · Mathematics 2020-07-14 Miroslav Bulíček , Josef Málek , Vít Průša , Endre Süli

Many seemingly different macroscopic systems (magnets, ferroelectrics, CDW, vortices,..) can be described as generic disordered elastic systems. Understanding their static and dynamics thus poses challenging problems both from the point of…

Disordered Systems and Neural Networks · Physics 2009-11-13 S. Bustingorry , A. B. Kolton , A. Rosso , W. Krauth , T. Giamarchi

Application of the principle of energy balance to a rigid indenter in contact with elastic layer on a flat rigid substrate provides a very simple derivation of the detachment criterion which earlier has been obtained by much more…

Soft Condensed Matter · Physics 2018-05-23 Valentin L. Popov

This paper presents an analytical model of punctual elastic contact between a rigid body of arbitrary geometry and a plane surface. A simple analytical model is developed in order to evaluate the contact force knowing the volume of…

Classical Physics · Physics 2008-02-05 Abdelaziz Sameur , Honoré Yin , Denis Duhamel , Vladimir Vilke

In this paper, we propose a numerical model to describe the adhesive normal contact between a "rigid" spherical indenter and a viscoelastic rough substrate. The model accounts for dissipative process under the assumption that viscoelastic…

Soft Condensed Matter · Physics 2020-12-15 Guido Violano , Antoine Chateauminois , Luciano Afferrante

This paper deals with the study of a three-dimensional model of thermomechanical coupling for viscous solids exhibiting hysteresis effects. This model is written in accordance with the formalism of generalized standard materials and it is…

Analysis of PDEs · Mathematics 2011-11-11 Laetitia Paoli , Adrien Petrov

When a gas in an externally imposed potential field is compressed, temperature gradients appear. This has been called the piezothermal effect. It is possible to analytically calculate the time-dependent behavior of the piezothermal effect…

Fluid Dynamics · Physics 2020-07-15 E. J. Kolmes , V. I. Geyko , N. J. Fisch

Surface roughness is known to easily suppress the adhesion of elastic surfaces. Here a simple model for the contact of \emph{viscoelastic} rough surfaces with significant levels of adhesion is presented. This approach is derived from our…

Soft Condensed Matter · Physics 2008-02-27 Guillaume Haiat , Etienne Barthel

In this paper we prove the existence and uniqueness of the weak solution for a dynamic thermoviscoelastic problem which describes frictional contact between a body and a foundation. We employ the nonlinear constitutive viscoelastic law with…

Mathematical Physics · Physics 2019-01-28 Stanisław Migórski , Paweł Szafraniec

In the paper a study of a model magnetoelastic solid system is presented. The system of interest is a mean-field magnet with nearest-neighbour ferromagnetic interactions and the underlying s.c. crystalline lattice with the long-range Morse…

Statistical Mechanics · Physics 2017-09-15 K. Szałowski , T. Balcerzak , M. Jaščur

In this paper, we study, from both variational and numerical points of view, a dynamic contact problem between a viscoelastic-viscoplastic piezoelectric body and a deformable obstacle. The contact is modelled using the classical normal…

Analysis of PDEs · Mathematics 2017-03-14 M. Campo , J. R. Fernández , Á. Rodríguez-Arós , J. M. Rodríguez

We study the mechanical contact between a deformable body with a wavy surface and a rigid flat taking into account pressurized fluid trapped in the interface. A finite element model is formulated for a general problem of trapped fluid for…

Fluid Dynamics · Physics 2021-03-23 Andrei G. Shvarts , Vladislav A. Yastrebov

We present a general energy approach to study the unsteady adhesive contact of viscoelastic materials. Under the assumption of infinitely short-range adhesive interactions, we exploit the principle of virtual work to generalize Griffith…

Soft Condensed Matter · Physics 2024-08-30 Cosimo Mandriota , Nicola Menga , Giuseppe Carbone

This work presents a self-contained continuum formulation for coupled chemical, mechanical and thermal contact interactions. The formulation is very general and hence admits arbitrary geometry, deformation and material behavior. All model…

Classical Physics · Physics 2021-08-12 Roger A. Sauer , Thang X. Duong , Kranthi K. Mandadapu

Viscoelastic rate-type fluid models are essential for describing the behavior of a wide range of complex materials, with applications in fields such as engineering, biomaterials, and medicine. These models are particularly useful for…

Analysis of PDEs · Mathematics 2025-05-01 Miroslav Bulìček , Jakub Woźnicki

We propose a hysteretic model for electromechanical coupling in piezoelectric materials, with the strain and the electric field as inputs and the stress and the polarization as outputs. This constitutive law satisfies the thermodynamic…

Analysis of PDEs · Mathematics 2014-12-16 Barbara Kaltenbacher , Pavel Krejci

This study proposes and explores a linear hydrodynamic thermo-elasticity system within mixture models, comprising fluid and solid phases, with a focus on biological tissues, particularly tumor-related phenomena. Although tumor growth is not…

Analysis of PDEs · Mathematics 2025-02-11 Michael Eden , Meraj Alam , Prakash Kumar , G P Raja Sekhar