Constitutive equation for friction with transition from static to kinetic friction and recovery of static friction

Anand, 1993, A constitutive model for interface friction, Comput. Mech., 12, 197, 10.1007/BF00369962 Bay, 1976, Real area of contact and friction stresses at high pressure sliding contact, Wear, 38, 201, 10.1016/0043-1648(76)90069-7 Bowden, 1958 Brockley, 1968, The time-dependence of static friction, J. Lubr. Tech. (ASME), 90, 35, 10.1115/1.3601558 Bureau, L., Baumberger, T, Caroli, C., Ronsin, O., 2001. Low-velocity friction between macroscopic solids. C.R. Acad. Sci. Paris, Series IV. Different Faces of Tribology, 2, 699–707. Cheng, 1985, An incremental constitutive relation of uniaxial contact friction for large deformation analysis, J. Appl. Mech. (ASME), 52, 639, 10.1115/1.3169114 Curnier, 1984, A theory of friction, Int. J. Solids Struct., 20, 637, 10.1016/0020-7683(84)90021-0 Courtney-Pratt, 1957, The effect of a tangential force on the contact metallic bodies, Proc. Roy. Soc. A, 238, 529, 10.1098/rspa.1957.0016 Derjaguin, B.V., Push, V.E., Tolstoi, D.M., 1957. A theory of stick-slipping of solids. In: Proc. Conf. Lubr. and Wear. Inst. Mech. Eng., London, pp. 257–268. Dokos, 1946, Sliding friction under extreme pressure – I, Trans. ASME, 68, A148, 10.1115/1.4009539 Drucker, 1988, Conventional and unconventional plastic response and representation, Appl. Mech. Rev. (ASME), 41, 151, 10.1115/1.3151888 Dunkin, 1996, Measurement of static friction coefficient between flat surfaces, Wear, 193, 186, 10.1016/0043-1648(95)06706-X Ferrero, 1997, Study of dry friction under small displacements and near-zero sliding velocity, Wear, 209, 322, 10.1016/S0043-1648(97)00027-6 Fredriksson, 1976, Finite element solution of surface nonlinearities in structural mechanics with special emphasis to contact and fracture mechanics problems, Comput. Struct., 6, 281, 10.1016/0045-7949(76)90003-1 Gearing, 2001, A plasticity model for interface friction: application to sheet metal forming, Int. J. Plasticity, 17, 237, 10.1016/S0749-6419(00)00034-6 Hashiguchi, K., 1972. On the yielding of frictional plastic body – hardening rule. In: Proc. 27th Annual Meeting, JSCE, pp. 105–108. Hashiguchi, 1980, Constitutive equations of elastoplastic materials with elastic–plastic transition, J. Appl. Mech. (ASME), 47, 266, 10.1115/1.3153653 Hashiguchi, K., 1985. Macrometric approaches – static-intrinsically time-independent. In: Constitutive Laws of Soils, Proc. Discussion Session 1A of 11th ICSMFE, San Francisco, pp. 25–56. Hashiguchi, 1989, Subloading surface model in unconventional plasticity, Int. J. Solids Struct., 25, 917, 10.1016/0020-7683(89)90038-3 Hashiguchi, 2002, Evaluation of typical conventional and unconventional plasticity models for prediction of softening behavior of soils, Geotechnique, 52, 561, 10.1680/geot.2002.52.8.561 Hashiguchi, 2005, Unconventional friction theory based on the subloading surface concept, Int. J. Solids Struct., 42, 1705, 10.1016/j.ijsolstr.2004.08.006 Hashiguchi, 2006, Gradient plasticity with the tangential subloading surface model and the prediction of shear band thickness of granular materials, Int. J. Plasticity, 22, 767 Hashiguchi, 2007, General corotational rate tensor and replacement of material-time derivative to corotational derivative of yield function, Comput. Model. Eng. Sci, 17, 55 Horowitz, 1989, Slip patterns in a spatially homogeneous fault model, J. Geophys. Res., 94, 10279, 10.1029/JB094iB08p10279 Howe, 1955, London-Van der Waals’ attractive forces between glass surface, Can. J. Chem., 33, 1375, 10.1139/v55-165 Kato, 1972, Some considerations on characteristics of static friction of machine tool sideway, J. Lubr. Tech. (ASME), 94, 234, 10.1115/1.3451699 Kikuchi, 1988 Kim, 2007, FE-analysis of sheet metal forming processes using continuous contact treatment, Int. J. Plasticity, 23, 544, 10.1016/j.ijplas.2006.07.004 Laulsen, 2001 Lee, 2008, Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheet: application to sheet springback, Int. J. Plasticity, 24, 545, 10.1016/j.ijplas.2007.05.004 Michalowski, 1978, Associated and non-associated sliding rules in contact friction problems, Archiv. Mech., 30, 259 Mroz, 1998, Constitutive model of adhesive and ploughing friction in metal-forming processes, Int. J. Mech. Sci., 40, 281, 10.1016/S0020-7403(97)00055-6 Peric, 1992, Computational model for 3-D contact problems with friction based on the penalty method, Int. J. Numer. Meth. Eng., 35, 1289, 10.1002/nme.1620350609 Oden, 1983, Algorithms and numerical results for finite element approximations of contact problems with non-classical friction laws, Comput. Struct., 19, 137, 10.1016/0045-7949(84)90212-8 Oden, 1983, Nonlocal and nonlinear friction laws and variational principles for contact problems in elasticity, J. Appl. Mech. (ASME), 50, 67, 10.1115/1.3167019 Oden, 1986, Models and computational methods for dynamic friction phenomena, Comput. Meth. Appl. Mech. Eng., 52, 527, 10.1016/0045-7825(85)90009-X Ozaki, 2007, Finite element analysis of particle assembly-water coupled frictional contact problem, Comput. Model. Eng. Sci., 18, 101 Rabinowicz, 1951, The nature of the static and kinetic coefficients of friction, J. Appl. Phys., 22, 1373, 10.1063/1.1699869 Rabinowicz, 1958, The intrinsic variables affecting the stick-slip process, Proc. Phys. Soc., 71, 668, 10.1088/0370-1328/71/4/316 Richardson, 1976, Surface friction under time-dependent loads, Wear, 37, 87, 10.1016/0043-1648(76)90183-6 Roscoe, 1968, On the generalized stress–strain behavior of “wet” clay, 535 Schofield, 1968 Seguchi, Y., Shindo, A., Tomita, Y., Sunohara, M., 1974. Sliding rule of friction in plastic forming of metal. Comput. Meth. Nonlinear Mech. University of Texas at Austin, pp. 683–692. Stupliewicz, 2003, Phenomenological model of real contact area evolution with account for bulk plastic deformation in metal forming, Int. J. Plasticity, 19, 323, 10.1016/S0749-6419(01)00037-7 Wriggers, 1990, Finite element formulation of large deformation impact–contact problems with friction, Comput. Struct., 37, 319, 10.1016/0045-7949(90)90324-U Wriggers, 2003 Yoon, 2006, Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function, Int. J. Plasticity, 22, 174, 10.1016/j.ijplas.2005.03.013