Analysis of a contact adhesive problem with normal compliance and nonlocal friction

Abstract The aim of this paper is to study a quasistatic contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The contact is modelled with an electrical condition, normal compliance and the associated version of Coulomb’s law of dry friction in which slip dependent friction is included. We derive a variational formulation for the model and, under a smallness assumption, we prove the existence and uniqueness of a weak solution.

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Dynamic frictional thermoviscoelastic contact problem with normal compliance and damage

Bulletin of the Belgian Mathematical Society - Simon Stevin ◽

10.36045/j.bbms.191105 ◽

2021 ◽

Vol 28 (2) ◽

Author(s):

Khelifa Chadi ◽

Mohamed Selmani

Keyword(s):

Contact Problem ◽

Normal Compliance

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Extracting real-crack properties from non-linear elastic behaviour of rocks: abundance of cracks with dominating normal compliance and rocks with negative Poisson ratios

Nonlinear Processes in Geophysics ◽

10.5194/npg-24-543-2017 ◽

2017 ◽

Vol 24 (3) ◽

pp. 543-551 ◽

Cited By ~ 9

Author(s):

Vladimir Y. Zaitsev ◽

Andrey V. Radostin ◽

Elena Pasternak ◽

Arcady Dyskin

Keyword(s):

Experimental Data ◽

Poisson Ratio ◽

A Priori ◽

Elastic Behaviour ◽

Crack Model ◽

Normal Compliance ◽

S Wave ◽

Linear Elastic ◽

Non Linear ◽

Linear Elastic Behaviour

Abstract. Results of examination of experimental data on non-linear elasticity of rocks using experimentally determined pressure dependences of P- and S-wave velocities from various literature sources are presented. Overall, over 90 rock samples are considered. Interpretation of the data is performed using an effective-medium description in which cracks are considered as compliant defects with explicitly introduced shear and normal compliances without specifying a particular crack model with an a priori given ratio of the compliances. Comparison with the experimental data indicated abundance (∼ 80 %) of cracks with the normal-to-shear compliance ratios that significantly exceed the values typical of conventionally used crack models (such as penny-shaped cuts or thin ellipsoidal cracks). Correspondingly, rocks with such cracks demonstrate a strongly decreased Poisson ratio including a significant (∼ 45 %) portion of rocks exhibiting negative Poisson ratios at lower pressures, for which the concentration of not yet closed cracks is maximal. The obtained results indicate the necessity for further development of crack models to account for the revealed numerous examples of cracks with strong domination of normal compliance. Discovering such a significant number of naturally auxetic rocks is in contrast to the conventional viewpoint that occurrence of a negative Poisson ratio is an exotic fact that is mostly discussed for artificial structures.

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Analysis of Ultralong Friction Pile Based on Gradient Dependent Nonlocal Friction Model

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.638-640.380 ◽

2014 ◽

Vol 638-640 ◽

pp. 380-383

Author(s):

Xiao Yan Luo ◽

Wei Ping Liu

Keyword(s):

Frictional Resistance ◽

Friction Model ◽

Gradient Theory ◽

Friction Mechanism ◽

New Model ◽

Friction Law ◽

Nonlocal Friction ◽

Set Up ◽

Friction Pile ◽

Geotechnical Problems

Based on the gradient theory, the gradient dependent nonlocal friction model is established. It is a new model which can describe the nonlocal friction effect. Based on Mindlin’s solution of displacement, an elastic solution of the lateral frictional resistance for ultralong friction pile is derived. The ultralong friction pile is analyzed by using the gradient dependent nonlocal friction model. Compared with the solution to the local friction law, the results shows that nonlocal friction law is feasible and reliable. The study is helpful for understanding the friction mechanism in geotechnical problems. It is a good attempt to set up the more actual and more accurate friction model.

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