Determination on elastic fields induced by non-elastic shear deformation with an elliptic inhomogeneity in transversely isotropic media

Abstract

本文求解了横观各向同性介质中椭圆夹 杂内受非弹性剪切变形引起的弹性场。采用各向异性弹性力学平面问题的复变函数解法,结合保角变换,获得夹杂内应变能和基体内边界的应力分布和相应的应变能 的表达式。进一步,根据最小应变能原理,获得表征夹杂平衡边界的两个特征剪切应变,从而得到了弹性场的解析解。通过应力转换关系,验证了应力解满足夹杂边 界上法向正应力和剪应力的连续条件,表明了该解的正确性。本文解可用于复合材料断裂强度的分析中。 The elastic fields induced by non-elastic shear deformations with an elliptic inhomongeneity embedded in the transversely isotropic matrix were presented. Conformal transformation and complex function method for anisotropic elastic media were used to determine the strain energy in the inhomongeneity, the stress distributions in the matrix at the interior boundary of the inhomongeneity and corresponding strain energy in the matrix. Further, two characteristic shear strains associated with the equilibrium boundary of the inhomongeneity were obtained by the use of principle of minimum strain energy, and the analytical solutions for the elastic fields were thus derived. The present solutions are proven to satisfy the continuity conditions for normal and shearing stresses on the surface of the ellipse, and can be applied to analysis the fracture behavior of such composite materials.