Analytical solution of the contact problem of a rigid indenter and an anisotropic linear elastic layer

被引:33
作者
Batra, R. C. [1 ]
Jiang, W. [1 ]
机构
[1] Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, M-C 0219, Blacksburg, VA 24061 USA
关键词
Analytical solution; Cylindrical indenter; Orthotropic layer; General anisotropic layer; Flat punch;
D O I
10.1016/j.ijsolstr.2008.06.016
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
We use the Stroh formalism to study analytically generalized plane strain deformations of a linear elastic anisotropic layer bonded to a rigid substrate, and indented by a rigid cylindrical indenter. The mixed boundary-value problem is challenging since the a priori unknown deformed indented surface of the layer contacting the rigid cylinder is to be determined as a part of the solution of the problem. For a rigid parabolic prismatic indenter contacting either an isotropic layer or an orthotropic layer and a flat rigid punch indenting a half space, the computed solutions are found to agree well with those available in the literature. Parametric studies have been conducted to delimit the length and the thickness of the layer for which the derived relation between the axial load and the indentation depth caused by the rigid cylinder is valid. The indentation of a face centered cubic crystal with the plane of indentation oriented differently from the principal planes of symmetry has also been studied to illustrate the applicability of the technique to general layers made of anisotropic materials. Results presented herein can serve as benchmarks with which to compare solutions obtained by other methods. (C) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码:5814 / 5830
页数:17
相关论文
共 34 条
[21]   Indentation of elastically anisotropic half-spaces by cones and parabolae of revolution [J].
Swadener, JG ;
Pharr, GM .
PHILOSOPHICAL MAGAZINE A-PHYSICS OF CONDENSED MATTER STRUCTURE DEFECTS AND MECHANICAL PROPERTIES, 2001, 81 (02) :447-466
[22]   Contact deformation and stress in orthotropic plates [J].
Swanson, SR .
COMPOSITES PART A-APPLIED SCIENCE AND MANUFACTURING, 2005, 36 (10) :1421-1429
[23]   Hertzian contact of orthotropic materials [J].
Swanson, SR .
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2004, 41 (07) :1945-1959
[24]   USE OF STATICAL INDENTATION LAWS IN THE IMPACT ANALYSIS OF LAMINATED COMPOSITE PLATES [J].
TAN, TM ;
SUN, CT .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1985, 52 (01) :6-12
[25]  
Ting T. C., 1996, Anisotropic Elasticity: Theory and Applications
[27]   Estimation of the Young's modulus of articular cartilage using an arthroscopic indentation instrument and ultrasonic measurement of tissue thickness [J].
Töyräs, J ;
Lyyra-Laitinen, T ;
Niinimäki, M ;
Lindgren, R ;
Nieminen, MT ;
Kiviranta, I ;
Jurvelin, JS .
JOURNAL OF BIOMECHANICS, 2001, 34 (02) :251-256
[28]   CONTACT ON A TRANSVERSELY ISOTROPIC HALF-SPACE, OR BETWEEN 2 TRANSVERSELY ISOTROPIC BODIES [J].
TURNER, JR .
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 1980, 16 (05) :409-419
[29]   Analytical solution for rectangular thick laminated plates subjected to arbitrary boundary conditions [J].
Vel, SS ;
Batra, RC .
AIAA JOURNAL, 1999, 37 (11) :1464-1473
[30]   The generalized plane strain deformations of thick anisotropic composite laminated plates [J].
Vel, SS ;
Batra, RC .
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2000, 37 (05) :715-733