On numerical evaluation of Eshelby tensor for superspherical and superellipsoidal inclusions in isotropic elastic material

2020 ◽  
Vol 192 ◽  
pp. 107964
Author(s):  
Keiji Yanase ◽  
Hirak Chatterjee ◽  
Sujit Kumar Ghosh
Keyword(s):  
Elastic Material ◽  
Numerical Evaluation ◽  
Eshelby Tensor ◽  
Isotropic Elastic Material

General theory of small elastic deformations superposed on finite elastic deformations

1952 ◽  
Vol 211 (1104) ◽  
pp. 128-154 ◽  
Keyword(s):  
General Theory ◽  
Elastic Material ◽  
Finite Deformation ◽  
Plane Surface ◽  
Thin Sheet ◽  
Potential Functions ◽  
Homogeneous Deformation ◽  
Infinitesimal Deformation ◽  
Elastic Deformations ◽  
Isotropic Elastic Material

Using tensor notations a general theory is developed for small elastic deformations, of either a compressible or incompressible isotropic elastic body, superposed on a known finite deformation, without assuming special forms for the strain-energy function. The theory is specialized to the case when the finite deformation is pure homogeneous. When two of the principal extension ratios are equal the changes in displacement and stress due to the small superposed deformation are expressed in terms of two potential functions in a manner which is analogous to that used in the infinitesimal deformation of hexagonally aeolotropic materials. The potential functions are used to solve the problem of the infinitesimally small indentation, by a spherical punch, of the plane surface of a semi-infinite body of incompressible isotropic elastic material which is first subjected to a finite pure homogeneous deformation symmetrical about the normal to the force-free plane surface. The general theory is also applied to the infinitesimal deformation of a thin sheet of incompressible isotropic elastic material which is first subjected to a finite pure homogeneous deformation by forces in its plane. A differential equation is obtained for the small deflexion of the sheet due to small forces acting normally to its face. This equation is solved completely in the case of a clamped circular sheet subjected to a pure homogeneous deformation having equal extension ratios in the plane of the sheet, the small bending force being uniformly distributed over a face of the sheet. Finally, equations are obtained for the homogeneously deformed sheet subjected to infinitesimal generalized plane stress, and a method of solution by complex variable technique is indicated.

Optimum Elastic Restraint for Pressurised Circular Plates

1963 ◽  
Vol 67 (632) ◽  
pp. 525-526
Author(s):  
Charles W. Bert
Keyword(s):  
Effective Stress ◽  
Elastic Material ◽  
Unit Volume ◽  
List Type ◽  
Maximum Deflection ◽  
Type Number ◽  
Circular Plates ◽  
Uniform Thickness ◽  
Isotropic Elastic Material ◽  
Elastically Restrained

SummaryFor uniform-thickness, solid circular plates made of isotropic elastic material and elastically restrained at the edge, expressions are derived for the optimum support stiffness to minimise the following quantities: 1.The largest effective stress based on several different strength theories.2.The largest effective stress per unit of maximum deflection or per unit volume displaced.

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