, Get from previous iteration current value of the displacement vector u and the Lagrange multiplier ? f
, If the gap V g (u) > V f or ? f < 0, the fluid is considered to be in inactive state and the trapped fluid element is excluded from consequent calculations
if V g (u) ? V f and ? f ? 0, the fluid is in active state, then the residual vector and the tangent matrix are ,
Contact and rubbing of flat surfaces, Journal of Applied Physics, vol.24, issue.8, pp.981-988, 1953. ,
Elastic deformation and the laws of friction, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.243, pp.190-205, 1957. ,
The friction and lubrication of solids, vol.1, 2001. ,
Contact of nominally flat surfaces, Proceedings of the Royal Society of London A: Mathematical, vol.295, pp.300-319, 1966. ,
Self-affine elastic contacts: percolation and leakage, Physical review letters, vol.108, issue.24, p.244301, 2012. ,
Evolution of the free volume between rough surfaces in contact, Wear, vol.336, pp.86-95, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01167763
, Fundamentals of fluid film lubrication, 2004.
Finite element modeling of elasto-plastic contact between rough surfaces, Journal of the Mechanics and Physics of Solids, vol.53, issue.11, pp.2385-2409, 2005. ,
Asperity contact theories: Do they predict linearity between contact area and load?, Journal of the Mechanics and Physics of Solids, vol.56, issue.8, pp.2555-2572, 2008. ,
The influence of the statistical properties of self-affine surfaces in elastic contacts: A numerical investigation, Journal of the Mechanics and Physics of Solids, vol.60, issue.5, pp.973-982, 2012. ,
The role of the roughness spectral breadth in elastic contact of rough surfaces, Journal of the Mechanics and Physics of Solids, vol.107, pp.22-5096, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01599693
From infinitesimal to full contact between rough surfaces: Evolution of the contact area, International Journal of Solids and Structures, vol.52, pp.83-102, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01113725
Elastic contact mechanics: percolation of the contact area and fluid squeeze-out, The European Physical Journal E, vol.35, issue.1, p.5, 2012. ,
Real contact area and friction property of rubber with two-dimensional regular wavy surface, Tribology International, vol.93, pp.523-529, 2016. ,
A note on the role of microscopically trapped lubricant at the tool-work interface, International Journal of Mechanical Sciences, vol.7, issue.5, pp.383-388, 1965. ,
Real area of contact and friction stress -The role of trapped lubricant, Wear, vol.43, issue.1, pp.45-53, 1977. ,
Direct Observation of Contact Behaviour to Interpret the Pressure Dependence of the Coefficient of Friction in Sheet Metal Forming, CIRP Annals -Manufacturing Technology, vol.44, issue.1, pp.209-212, 1995. ,
Theory of rubber friction and contact mechanics, The Journal of Chemical Physics, vol.115, issue.8, pp.3840-3861, 2001. ,
FEM Analysis of Hydrostatic Pressure Generated Within Lubricant Entrapped Into Pocket on Workpiece Surface in Upsetting Process, J. Tribol, vol.122, issue.4, p.822, 2000. ,
Permeation of Lubricant Trapped Within Pocket Into Real Contact Area on the End Surface of Cylinder, J. Tribol, vol.133, issue.1, p.11501, 2011. ,
Entrapment and escape of liquid lubricant in metal forming, Wear, vol.232, issue.2, pp.134-139, 1999. ,
Hydrostatic Pressurization and Depletion of Trapped Lubricant Pool During Creep Contact of a Rippled Indenter Against a Biphasic Articular Cartilage Layer, Journal of Biomechanical Engineering, vol.125, issue.5, p.585, 2003. ,
The role of lubricant entrapment at biological interfaces: Reduction of friction and adhesion in articular cartilage, Journal of Biomechanics, vol.44, issue.11, pp.2015-2020, 2011. ,
The Influence of Crack Face Friction and Trapped Fluid on Surface Initiated Rolling Contact Fatigue Cracks, J. Tribol, vol.110, issue.4, p.704, 1988. ,
Nucleation of slip-weakening rupture instability in landslides by localized increase of pore pressure, Journal of Geophysical Research: Solid Earth, vol.117 ,
Nucleation and arrest of dynamic slip on a pressurized fault, Journal of Geophysical Research: Solid Earth, vol.117 ,
The physics of glaciers, 2010. ,
A fractal permeability model for bi-dispersed porous media, International Journal of Heat and Mass Transfer, vol.45, issue.14, pp.2983-2993, 2002. ,
Micromechanical approach to the behavior of poroelastic materials, Journal of the Mechanics and Physics of Solids, vol.50, issue.10, pp.2203-2231, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-00140491
Elastic moduli of a cracked solid, International journal of Solids and structures, vol.12, issue.2, pp.81-97, 1976. ,
, Poromechanics, 2004.
Effect of fluid lubricant on the contact characteristics of rough elastic bodies in compression, Wear, vol.102, issue.3, pp.177-194, 1985. ,
Bearing Pressures and Cracks, Journal of Applied Mechanics, vol.18 ,
Modelling of a punch with a regular base relief sliding along a viscoelastic foundation with a liquid lubricant, Journal of Applied Mathematics and Mechanics, vol.76, issue.5, pp.582-589, 2012. ,
The contact of elastic regular wavy surfaces, International Journal of Mechanical Sciences, vol.27, issue.6, pp.383-396, 1985. ,
, Computational Contact Mechanics, 2006.
Contact problems in elasticity: a study of variational inequalities and finite element methods, vol.8, 1988. ,
Numerical methods in contact mechanics, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00785235
Large scale object-oriented finite element code design, Computer Methods in Applied Mechanics and Engineering, vol.142, issue.1, pp.165-187, 1997. ,
, Nonlinear material and structure analysis suite, 2017.
, Linear Theories of Elasticity and Thermoelasticity, Linear and Nonlinear Theories of Rods, Plates, and Shells, vol.II, 1984.
, Contact mechanics, 1987.
Formulation of Drucker-Prager cap model, Journal of Engineering Mechanics, vol.111, issue.7, pp.855-881, 1985. ,
Indentation by pore collapse in porous rocks, The 31th US Symposium on Rock Mechanics (USRMS), American Rock Mechanics Association, 1990. ,
Rudnicki and Rice's analysis of strain localization revisited, J. Appl. Mech, vol.60, issue.4, pp.842-846, 1993. ,
Conditions for compaction bands in porous rock, Journal of Geophysical Research: Solid Earth, vol.105, issue.B9, pp.21529-21536, 2000. ,
Spherical indentation of elastic-plastic solids, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.455, pp.2707-2728, 1999. ,
Elastic-plastic contact analysis of a sphere and a rigid flat, Journal of Applied Mechanics, vol.69, issue.5, pp.657-662, 2002. ,
Reassessing spherical indentation: Contact regimes and mechanical property extractions, International Journal of Solids and Structures, vol.47, issue.20, pp.2714-2732, 2010. ,
Self similar solutions to adhesive contact problems with incremental loading, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.305, pp.55-80, 1968. ,
The stress analysis of cracks, Handbook ,
Plane problems of cracks in dissimilar media, Journal of Applied Mechanics, vol.32, issue.2, pp.418-423, 1965. ,
Elastic fracture mechanics concepts for interfacial cracks, Journal of Applied Mechanics, vol.55, issue.1, pp.98-103, 1988. ,
Mechanics of fretting fatigue, Wear, vol.175, issue.1-2, pp.107-113, 1994. ,
A fretting crack initiation prediction taking into account the surface roughness and the crack nucleation process volume, International Journal of fatigue, vol.27, issue.5, pp.569-579, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00180854