Non-metric connection and metric anomalies in materially uniform elastic solids

DOI10.1007/S10659-016-9578-1zbMath1362.74016arXiv1601.06905OpenAlexW2962722466WikidataQ125360937 ScholiaQ125360937MaRDI QIDQ2397116

Ayan Roychowdhury, Anurag Gupta

Publication date: 29 May 2017

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.06905

zbMATH Keywords

material inhomogeneitypoint defectsnon-metricitymetric anomaliescrystalline defects

Mathematics Subject Classification ID

Anisotropy in solid mechanics (74E10) Inhomogeneity in solid mechanics (74E05) Crystalline structure (74E15) Applications of differential geometry to physics (53Z05)

Related Items (9)

Finsler differential geometry in continuum mechanics: Fundamental concepts, history, and renewed application to ferromagnetic solids ⋮ Biological growth in bodies with incoherent interfaces ⋮ Growth and non-metricity in Föppl-von Kármán shells ⋮ A Variational Approach to Single Crystals with Dislocations ⋮ On structured surfaces with defects: geometry, strain incompatibility, stress field, and natural shapes ⋮ Generalized pseudo-Finsler geometry applied to the nonlinear mechanics of torsion of crystalline solids ⋮ Topological defects and metric anomalies as sources of incompatibility for piecewise smooth strain fields ⋮ On the relevance of generalized disclinations in defect mechanics ⋮ Finite incompatible deformations in elastic solids: relativistic approach

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A geometric theory of growth mechanics
• The fundamental theorem of surface theory for surfaces with little regularity
• An example of a smooth linear partial differential equation without solution
• The differential geometry of elementary point and line defects in Bravais crystals
• Theory of elasticity of coherent inclusions by means of non-metric geometry
• A view of the relation between the continuum theory of lattice defects and non-Euclidean geometry in the linear approximation
• Connection between non-metric differential geometry and mathematical theory of imperfections
• Homogeneity without uniformity: Towards a mathematical theory of functionally graded materials
• Geometrical foundations of continuum mechanics. An application to first- and second-order elasticity and elasto-plasticity
• Material inhomogeneities and their evolution. A geometric approch.
• Compatibility equations of nonlinear elasticity for non-simply-connected bodies
• Materially uniform simple bodies with inhomogeneities
• On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations
• Die Theorie der Disklinationen
• Die Theorie der nichtmetrischen Spannungen in Kristallen. (The theory of non-metric stresses in crystals)
• The geometry of discombinations and its applications to semi-inverse problems in anelasticity
• On Geometry of Point Defects and DislocationsThe Meaning of the Third Identity of Curvature Tensor
• Nonlinear tensor functions of several tensor arguments
• Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies
• Continuum elasticity with topological defects, including dislocations and extra-matter
• Line defects in solid continua and point particles in (2 + 1)-dimensional gravity
• Material homogeneity and strain compatibility in thin elastic shells
• Weyl geometry and the nonlinear mechanics of distributed point defects
• Continuous distributions of dislocations VI. Non-metric connexions
• Ricci-Calculus

This page was built for publication: Non-metric connection and metric anomalies in materially uniform elastic solids