Similarity analysis of inelastic contact

Analysis of mechanical contact of solids is of interest not only regarding a variety of mechanical assemblies but also on a smaller scale such as roughness properties of surfaces and compaction Of powder particles. Indentation testing is another prominent problem in the context. To analyse the phenomena involved is inherently difficult at application essentially due to the presence of large strains, nonlinear material behaviour, time dependence and moving contact boundaries. Recently, progress has been made, however, to explicitly solve basic boundary value problems especially due to advances in computational techniques. A substantial ingredient which facilitates solution procedures is self-similarity and it is the present purpose to explore in detail the advantages in a general setting when this feature prevails. A viscoplastic framework is laid down for a wide class of constitutive properties where strain-hardening plasticity, creep and aiso nonlinear elasticity arise as special cases. It is then shown that when surface shapes and material properties are modelled by homogeneous functions, associated boundary value problems posed may be reduced to stationary ones. As a consequence, within Hertziun kinematics, relations between contact impression and regions become independent of loading and time and the connection to loading characteristics does not usually require a full solution of the problem. In particular it is shown that for general head-shapes it proves efftcient to use an approach where an intermediate fiat die solution serves as a basic tool also for hereditary materials. An invariant computational procedure based on the intermediate problem is arrived at and decisive results shown to be found by simple cumulative superposition. Illustrations are given analytically for ellipsoidal contact of Newtonian fluids and by detailed computations for spherical indentation of viscoplastic solids for which also universal hardness formulae are proposed. For several bodies in contact it is shown how general results may be extracted from fundamental solutions for a half-space. © 1997 Elsevier Science Ltd.