Dualistic theory of non-Riemannian material manifolds

DOI10.1016/0020-7225(81)90081-1zbMath0503.73094OpenAlexW2036407685WikidataQ115368191 ScholiaQ115368191MaRDI QIDQ1173448

Shun-ichi Amari

Publication date: 1981

Published in: International Journal of Engineering Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0020-7225(81)90081-1

zbMATH Keywords

stored energystress spacestrain spacedualistic theoryforces acting on dislocation and disclinationspotentials for dislocations and disclinationsstate of material bodytwo different types of material non-Riemannian spaces

Mathematics Subject Classification ID

Differential geometric aspects in vector and tensor analysis (53A45) Linear elasticity with initial stresses (74B10) Micromechanics of solids (74M25) Micromechanical theories (74A60) Plastic materials, materials of stress-rate and internal-variable type (74C99) Applications of global differential geometry to the sciences (53C80)

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Cites Work

• Modern differential geometric techniques in the theory of continuous distributions of dislocations
• On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations
• Die Theorie der Disklinationen
• Die Spannungsfunktionen des dreidimensionalen Kontinuums und des elastischen Körpers
• Ricci-Calculus
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