基于Eshelby-Stroh公式各向异性弹性体接触问题研究
Study on contact problem of anisotropic elastic body based on Eshelby-Stroh formalism

摘要 针对线性各向异性弹性体小变形接触问题，将弹性体按是否与刚体压头发生接触进行划分，基于Eshelby-Stroh公式求解各个部分的位移函数和应力函数，进一步通过应力函数积分得到载荷值。考虑到求解结果存在交接处应力突变和非接触区域应力不近似于零的问题，采用整体位移约束法和线性叠加原理，通过迭代方式使位移函数和应力函数逼近理想解，解决了圆柱压头和倒圆角楔形压头与弹性体的接触问题。基于圆柱压头求得的载荷值接近弹性半空间法的求解结果，当级数总项数为400时，计算结果的相对误差仅为0.52%。基于圆柱压头和倒圆角楔形压头求得的载荷值与ABAQUS仿真结果较为吻合：圆柱压头载荷值的相对误差为0.67%；倒圆角楔形压头，对6个不同的圆角值进行计算，载荷的相对误差都小于2%。
Abstract：In order to solve infinitesimal deformation contact problem of a linear anisotropic elastic body, the elastic body is divided into several parts, according to the contact condition between the rigid body and the indenter. Based on Eshelby-Stroh formalism, the displacement function and stress function of each part are solved, and the load is obtained by integrating the stress function. Considering the stress mutation at junction and nonzero stress on the top of noncontact region, both whole displacement constraint method and linear superposition principle are used for getting ideal displacement function and stress function based on iteration. The contact problem between the cylindrical indenter and bounded elastic body and the contact problem between the rounded wedge indenter and elastic body are solved. The load results based on cylinder indenter are close to the results of elastic half space method. When the quantity of series is 400, the computing relative error is only 0.52%. The computed load results based on cylindrical indenter and rounded wedge indenter agree well with those of ABAQUS simulation. The relative error of cylindrical indenter load is 0.67%, and 6 rounded wedge indenters are computed with all the relative errors of load less than 2%.