Symbolic and numerical solution of the axisymmetric indentation problem for a multilayered elastic coating
Symbolic and numerical solution of the axisymmetric indentation problem for a multilayered elastic coating
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DOI：
10.1016/j.ijsolstr.2013.04.017
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发表时间：
2013-08-15
影响因子：
3.6
通讯作者：
Oueslati, A.
中科院分区：
文献类型：
--
作者：
Constantinescu, A.;Korsunsky, A. M.;Oueslati, A.
本文用半解析方法求解多层弹性半空间的轴对称压痕问题。利用Papkovich-Neuber势和Hankel变换，得到了各层和衬底的应力场和位移场的封闭形式。利用适当的传递矩阵处理子层之间的粘结或滑动界面条件，然后将混合边值问题归结为Fredholm型积分方程。解的符号和数值计算在符号软件数学中以快速有效的数值算法的形式实现，可以快速确定任意刚性压头形状的载荷-位移曲线和复合弹性性质。给出并讨论了不同压头(平面、圆锥形、球形和钝锥形)和不同多层复合材料的一系列结果，并提供了完整的符号和数值计算作为补充资源。(C)2013爱思唯尔有限公司。保留所有权利。
This paper is concerned with a semi-analytical approach to the solution of the axisymmetric indentation problem for a multilayered elastic half-space. The stress and displacement fields for each layer and the substrate are derived in closed form by using the Papkovich-Neuber potentials and the Hankel transform. The bonded or sliding interface conditions between the sub-layers are handled by the use of the appropriate transfer matrix, and then the mixed boundary value problem is reduced to a Fredholm integral equation. Symbolic and numerical computations of the solution are implemented in the symbolic software Mathematica in the form of a fast and efficient numerical algorithm, allowing rapid determination of the load-displacement curves and composite elastic properties for an arbitrary rigid indenter shape. A series of results for different indenters (flat, conical, spherical and blunted conical punch shapes) and different multilayered composites is presented and discussed.The complete set of symbolic and numerical computations are provided as supplementary resources with the paper. (C) 2013 Elsevier Ltd. All rights reserved.