The present paper provides a generalized Maugis-Dugdale analytical model of adhesive contact between an axisymmetric rigid punch of arbitrary shape and a graded elastic half-space with Young's modulus varying with depth according to a power-law. Based on the principle of superposition and an equivalent indentation method to solve an axisymmetric external crack problem, a series of closed-form solutions are derived for power-law punch profiles which reduce to the existing solutions for homogeneous isotropic materials and for paraboloidal geometries as special cases. A complete transition between the JKR and DMT type models is captured through a generalized Tabor parameter. Finite element analysis is performed to validate the obtained analytical solutions and examine the effect of interaction potential form on the pull-off force. Further important findings from this study include: (1) The pull-off force for non-paraboloidal punch profiles is found to be largely dependent on the form of the interaction potential, which is distinct from the familiar paraboloid case; (2) For the so-called Gibson solid, the independence of the pull-off force on the Tabor parameter is valid only for the paraboloidal punch profiles; (3) A three-dimensional adhesion map has been constructed to aid the appropriate choice of different contact models involving power-law graded elastic materials.

本论文提供了任意形状的轴对称刚性冲头与杨氏模量根据幂律随深度变化的梯度弹性半空间之间粘附接触的广义 Maugis-Dugdale 分析模型。基于叠加原理和等效压痕法求解轴对称外裂纹问题，推导出幂律冲头轮廓的一系列封闭形式解，简化为均匀各向同性材料和抛物面几何形状的现有解。案件。JKR 和 DMT 类型模型之间的完整转换是通过广义 Tabor 参数捕获的。进行有限元分析以验证获得的解析解并检查相互作用势形式对拉脱力的影响。这项研究的进一步重要发现包括： (1) 发现非抛物面冲头轮廓的拉断力在很大程度上取决于相互作用势的形式，这与熟悉的抛物面情况不同；(2) 对于所谓的 Gibson 实体，拉断力对 Tabor 参数的独立性仅对抛物面冲头轮廓有效；(3) A three-dimensional adhesion map has been constructed to aid the appropriate choice of different contact models involving power-law graded elastic materials. 拉断力对 Tabor 参数的独立性仅对抛物面冲头轮廓有效；(3) A three-dimensional adhesion map has been constructed to aid the appropriate choice of different contact models involving power-law graded elastic materials. 拉断力对 Tabor 参数的独立性仅对抛物面冲头轮廓有效；(3) A three-dimensional adhesion map has been constructed to aid the appropriate choice of different contact models involving power-law graded elastic materials.