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首页> 外文期刊>Archive of Applied Mechanics >Elastic spherical inhomogeneity in an infinite elastic solid: an exact analysis by an engineering treatment of the problem based on the corresponding cavity solution
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Elastic spherical inhomogeneity in an infinite elastic solid: an exact analysis by an engineering treatment of the problem based on the corresponding cavity solution

机译：无限弹性固体中的弹性球形不均匀性：基于相应的腔溶液的问题的工程处理精确分析

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摘要

In the present work, solutions are recapitulated according to the theory of elasticity for the deformations of an adhesive spherical inhomogeneity in an infinite matrix under remote uniform axial and axial-symmetrical radial tension. Stress fields in the inhomogeneity and at the interface in the matrix are provided, too. It is shown that the sphere is deformed to a spheroid under any of the loading cases considered. Due to the axial-symmetric setup of the problem, the deformation is fully described by the two displacement values at line segments on the principal axes of the spheroid. The displacements depend on the applied remote load and on two traction fields at the inhomogeneity-matrix interface. For any combination of inhomogeneity and matrix stiffness, the condition of compatibility of deformations yields a system of two linear equations with the two magnitudes of the tractions as unknowns. Thus, the problem is reduced to a formulation for solving a twofold statically indetermined structure. The system is solved and the exact solution of the general spherical inhomogeneity problem with differing stiffness in terms of Young's moduli and Poisson's ratios of inclusion and matrix is presented.
机译：在目前的工作中，根据远程均匀轴向和轴对称的径向张力下的无限基质中的粘合球形不均匀性的弹性理论重新携带解决方案。提供了不均匀性和矩阵中的界面中的应力场。结果表明，球体在考虑的任何装载案例下变形到球状体。由于问题的轴向对称设置，通过在球状体的主要轴线上的线段的两个位移值完全描述变形。位移取决于应用的远程负载和在不均匀矩阵接口处的两个牵引场。对于任何不均匀性和基质刚度的组合，变形的相容性的条件产生了两个线性方程的系统，其具有两个级数的两个级数作为未知。因此，该问题减少到用于求解双重不确定结构的制剂。提出了该系统，并提出了在杨氏模数和泊松的夹杂物和基质比例方面具有不同刚度的一般球形不均匀性问题的精确解。

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