Some Notes on Friction and Instabilities

These lectures address some topics related to instability, bifurcation and non-smoothness in finite dimensional frictional contact problems, as well as instability, ill-posedness and regularization procedures in some infinite dimensional problems.

[1]  Xavier Chateau,et al.  Buckling of elastic structures in unilateral contact with or without friction , 1991 .

[2]  A. Needleman.  Material rate dependence and mesh sensitivity in localization problems , 1988 .

[3]  M. Renardy.  Ill-posedness at the boundary for elastic solids sliding under Coulomb friction , 1992 .

[4]  J. Mandel.  Conditions de Stabilité et Postulat de Drucker , 1966 .

[5]  S. Dirkse,et al.  The path solver: a nommonotone stabilization scheme for mixed complementarity problems , 1995 .

[6]  George G. Adams,et al.  Steady Sliding of Two Elastic Half-Spaces With Friction Reduction due to Interface Stick-Slip , 1998 .

[7]  Walter D. Morris.  The Linear Complementarily Problem (R. W. Cottle, J.-S. Pang, and R. E. Stone) , 1993, SIAM Rev..

[8]  A. Klarbring.  On discrete and discretized non-linear elastic structures in unilateral contact (stability, uniqueness and variational principles) , 1988 .

[9]  R. Brach.  Rigid Body Collisions , 1989 .

[10]  On the well-posedness of the initial value problem in elasto-plastodynamics for a linear comparison solid , 1995 .

[11]  M. Marques.  Differential Inclusions in Nonsmooth Mechanical Problems , 1993 .

[12]  D. Stewart.  Convergence of a Time‐Stepping Scheme for Rigid‐Body Dynamics and Resolution of Painlevé's Problem , 1998 .

[13]  Maria Comninou,et al.  Elastic Interface Waves Involving Separation , 1977 .

[14]  G. Björkman.  Path following and critical points for contact problems , 1992 .

[15]  H. Blok.  Fundamental Mechanical Aspects of Boundary Lubrication , 1940 .

[16]  C. Scholz.  The Mechanics of Earthquakes and Faulting , 1990 .

[17]  J. Dieterich.  Time-dependent friction and the mechanics of stick-slip , 1978 .

[18]  A. F. D'Souza,et al.  Self-excited vibrations induced by dry friction, part 1: Experimental study , 1990 .

[19]  G. Saxcé,et al.  New Inequality and Functional for Contact with Friction: The Implicit Standard Material Approach∗ , 1991 .

[20]  Nicolas Triantafyllidis,et al.  A gradient approach to localization of deformation. I. Hyperelastic materials , 1986 .

[21]  Anders Klarbring,et al.  Derivation and analysis of rate boundary - value problems of frictional contact , 1990 .

[22]  S W E Earles,et al.  Oscillatory Instabilities Generated in a Double-Pin and Disc Undamped System: A Mechanism of Disc-cbrake Squeal , 1984 .

[23]  J. T. Oden,et al.  Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws , 1987 .

[24]  Instability and ill‐posedness in the deformation of granular materials , 1990 .

[25]  R. Ibrahim.  Friction-Induced Vibration, Chatter, Squeal, and Chaos—Part I: Mechanics of Contact and Friction , 1994 .

[26]  A. Klarbring.  Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction , 1990, Ingenieur-Archiv.

[27]  Stephen M. Robinson,et al.  Normal Maps Induced by Linear Transformations , 1992, Math. Oper. Res..

[28]  Raouf A. Ibrahim,et al.  Friction-Induced Vibration, Chatter, Squeal, and Chaos—Part II: Dynamics and Modeling , 1994 .

[29]  J. A. C. Martins,et al.  Dynamic Surface Solutions in Linear Elasticity and Viscoelasticity With Frictional Boundary Conditions , 1995 .

[30]  J. A. C. Martins,et al.  Stability of finite-dimensional nonlinear elastic systems with unilateral contact and friction , 2000 .

[31]  H. Petryk,et al.  Material instabilities in elastic and plastic solids , 2000 .

[32]  T. Thomas,et al.  Contact of rough surfaces: A review of experimental work , 1980 .

[33]  Maria Comninou,et al.  Elastic Interface Waves and Sliding Between Two Solids , 1978 .

[34]  J. Rice.  Localization of plastic deformation , 1976 .

[35]  M. Raous,et al.  Dynamic stability of finite dimensional linearly elastic systems with unilateral contact and Coulomb friction , 1999 .

[36]  H. Kreiss,et al.  Initial-Boundary Value Problems and the Navier-Stokes Equations , 2004 .

[37]  A. F. D'Souza,et al.  Self-excited vibrations induced by dry friction, part 2: Stability and limit-cycle analysis , 1990 .

[38]  M. Raous,et al.  Bifurcations and Instabilities in Some Finite Dimensional Frictional Contact Problems , 1999 .

[39]  F. Simões,et al.  Instability and ill-posedness in some friction problems , 1998 .

[40]  Vikas Prakash,et al.  Frictional Response of Sliding Interfaces Subjected to Time Varying Normal Pressures , 1998 .

[41]  J. Oden,et al.  Nonlocal and Nonlinear Friction Laws and Variational Principles for Contact Problems in Elasticity , 1983 .

[42]  M. Frémond.  Rigid bodies collisions , 1995 .

[43]  On the stability and post-critical behavior of elastic structures with dry friction , 1992 .

[44]  Q. S. Nguyen,et al.  Bifurcation and stability of dissipative systems , 1993 .

[45]  M. Marques,et al.  Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction , 1993 .

[46]  C. Andrew,et al.  Paper 22: Metal Surfaces in Contact under Normal Forces: Some Dynamic Stiffness and Damping Characteristics: , 1967 .

[47]  R. Luciano,et al.  Stress-penalty method for unilateral contact problems: mathematical formulation and computational aspects , 1994 .

[48]  Joos Vandewalle,et al.  The generalized linear complementarity problem and an algorithm to find all its solutions , 1992, Math. Program..

[49]  George G. Adams,et al.  Self-excited oscillations of two elastic half-spaces sliding with a constant coefficient of friction , 1995 .

[50]  Z. Bažant,et al.  Nonlocal damage theory , 1987 .

[51]  Jeffrey C. Trinkle,et al.  Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with coulomb friction , 1996, Math. Program..

[52]  R. T. Spurr.  A Theory of Brake Squeal , 1961 .

[53]  D. Stewart,et al.  AN IMPLICIT TIME-STEPPING SCHEME FOR RIGID BODY DYNAMICS WITH INELASTIC COLLISIONS AND COULOMB FRICTION , 1996 .

[54]  John R. Rice,et al.  Slip dynamics at an interface between dissimilar materials , 2001 .

[55]  J. Moreau,et al.  Unilateral Contact and Dry Friction in Finite Freedom Dynamics , 1988 .

[56]  J. Trinkle,et al.  On Dynamic Multi‐Rigid‐Body Contact Problems with Coulomb Friction , 1995 .

[57]  J. Oden,et al.  A study of static and kinetic friction , 1990 .

[58]  A. Ruina.  Slip instability and state variable friction laws , 1983 .

[59]  Y. Fung.  Foundations of solid mechanics , 1965 .

[60]  Quoc Son Nguyen.  Stabilité et mécanique non linéaire , 2000 .

[61]  I. Vardoulakis,et al.  The thickness of shear bands in granular materials , 1987 .

[62]  G. Adams.  Dynamic Instabilities in the Sliding of Two Layered Elastic Half-Spaces , 1998 .

[63]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[64]  M. Cocu,et al.  Existence of solutions of Signorini problems with friction , 1984 .

[65]  Anders Klarbring,et al.  Contact, Friction, Discrete Mechanical Structures and Mathematical Programming , 1999 .

[66]  John R. Rice,et al.  Fault rupture between dissimilar materials: Ill-posedness, regularization, and slip-pulse response , 2000 .

[67]  J. T. Oden,et al.  Models and computational methods for dynamic friction phenomena , 1984 .

[68]  F. Simões,et al.  ON SOME SOURCES OF INSTABILITY/ILL-POSEDNESS IN ELASTICITY PROBLEMS WITH COULOMB'S FRICTION , 1995 .

[69]  N. Back,et al.  Review of the Research on Fixed and Sliding Joints , 1973 .

[70]  E. Rabinowicz.  The Intrinsic Variables affecting the Stick-Slip Process , 1958 .

[71]  Joaquim J. Júdice,et al.  A Complementarity Eigenproblem in the Stability Analysis of Finite Dimensional Elastic Systems with Frictional Contact , 2001 .

[72]  James Barber,et al.  Stability of the three‐dimensional Coulomb friction law , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[73]  B. Mills,et al.  Vibrations Induced by Dry Friction , 1963 .