Amstutz, Hans ; Vormwald, Michael (2024)
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, 2021, 91 (4)
doi: 10.26083/tuprints-00023442
Artikel, Zweitveröffentlichung, Verlagsversion
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Kurzbeschreibung (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 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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2024 |
| Autor(en): | Amstutz, Hans ; Vormwald, Michael |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Elastic spherical inhomogeneity in an infinite elastic solid: an exact analysis by an engineering treatment of the problem based on the corresponding cavity solution |
| Sprache: | Englisch |
| Publikationsjahr: | 18 März 2024 |
| Ort: | Darmstadt |
| Publikationsdatum der Erstveröffentlichung: | April 2021 |
| Ort der Erstveröffentlichung: | Berlin ; Heidelberg |
| Verlag: | Springer |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Archive of Applied Mechanics |
| Jahrgang/Volume einer Zeitschrift: | 91 |
| (Heft-)Nummer: | 4 |
| DOI: | 10.26083/tuprints-00023442 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/23442 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung DeepGreen |
| Kurzbeschreibung (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 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. |
| Freie Schlagworte: | Spherical inhomogeneity, Elastic inhomogeneity, Stress analysis, Strain analysis |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-234426 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 600 Technik, Medizin, angewandte Wissenschaften > 624 Ingenieurbau und Umwelttechnik 600 Technik, Medizin, angewandte Wissenschaften > 690 Hausbau, Bauhandwerk |
| Fachbereich(e)/-gebiet(e): | 13 Fachbereich Bau- und Umweltingenieurwissenschaften 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Institut für Stahlbau und Werkstoffmechanik 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Institut für Stahlbau und Werkstoffmechanik > Fachgebiet Werkstoffmechanik |
| Hinterlegungsdatum: | 18 Mär 2024 13:44 |
| Letzte Änderung: | 19 Mär 2024 07:44 |
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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 Mär 2024 13:44) [Gegenwärtig angezeigt]
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