Amstutz, Hans ; Vormwald, Michael (2021)
Elastic spherical inhomogeneity in an infinite elastic solid: an exact analysis by an engineering treatment of the problem based on the corresponding cavity solution.
In: Archive of Applied Mechanics, 91 (4)
doi: 10.1007/s00419020018429
Article, Bibliographie
This is the latest version of this item.
Abstract
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 axialsymmetrical 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 axialsymmetric 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 inhomogeneitymatrix 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.
Item Type:  Article 

Erschienen:  2021 
Creators:  Amstutz, Hans ; Vormwald, Michael 
Type of entry:  Bibliographie 
Title:  Elastic spherical inhomogeneity in an infinite elastic solid: an exact analysis by an engineering treatment of the problem based on the corresponding cavity solution 
Language:  English 
Date:  August 2021 
Journal or Publication Title:  Archive of Applied Mechanics 
Volume of the journal:  91 
Issue Number:  4 
DOI:  10.1007/s00419020018429 
Corresponding Links:  
Abstract:  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 axialsymmetrical 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 axialsymmetric 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 inhomogeneitymatrix 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. 
Divisions:  13 Department of Civil and Environmental Engineering Sciences 13 Department of Civil and Environmental Engineering Sciences > Institute of Steel Constructions and Material Mechanics 13 Department of Civil and Environmental Engineering Sciences > Institute of Steel Constructions and Material Mechanics > Fachgebiet Werkstoffmechanik 
Date Deposited:  06 Aug 2021 09:10 
Last Modified:  19 Mar 2024 07:43 
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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. (deposited 18 Mar 2024 13:44)
 Elastic spherical inhomogeneity in an infinite elastic solid: an exact analysis by an engineering treatment of the problem based on the corresponding cavity solution. (deposited 06 Aug 2021 09:10) [Currently Displayed]
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