应用数学和力学2025，Vol.46Issue(12)：1550-1559,10.DOI:10.21656/1000-0887.450260
考虑微尺度效应的球-平面接触问题分析
Investigation of the Sphere-Plane Contact Problem Under Micro-Scale Effects
摘要
Abstract
Based on the surface elasticity and couple stress theories,a 3D contact problem between a rigid spherical indenter and an elastic half-space at the micro and nano scale was studied.The size effects of materi-als were described with the characteristic material lengths of the surface and the material.Through combination of the surface elasticity theory and the couple stress theory,the frequency response function in the elastic half-space under normal loading was derived.Then,with the conjugate gradient method and the fast Fourier trans-form,a 3D semi-analytical contact model was established.The proposed model was then used to analyze the effects of surface residual stress,surface material constants,and the characteristic material lengths on the con-tact pressure,stress,and displacement on the contact surface.The results show that,compared with the clas-sical contact solution,the contact pressure at the contact edge of the surface decrease sharply under the size effects.Additionally,the normal stress on the surface remains continuous and without abrupt changes at the contact edge,while the tangential stress is non-zero,and the normal displacement of the surface decreases.Furthermore,as the characteristic material length of the material increases,the direction of the tangential stress on the surface will reverse.关键词
接触问题/表面弹性理论/偶应力理论/尺度效应/共轭梯度法Key words
contact problem/surface-elasticity theory/couple stress theory/size effect/conjugate gradient method分类
数理科学引用本文复制引用
马维维,王宇星,沈火明,刘娟..考虑微尺度效应的球-平面接触问题分析[J].应用数学和力学,2025,46(12):1550-1559,10.基金项目
国家自然科学基金(青年科学基金项目)(12402113) （青年科学基金项目）
四川省自然科学基金(青年基金项目)(2023NSFC1300) （青年基金项目）
四川省自然科学基金(重点项目)(2024NSFC0037) （重点项目）
