Ricci Curvature and the Mechanics of Solids
Michael Eastwood
TL;DR
This paper explores the application of Ricci curvature and differential geometry concepts to continuum mechanics, particularly in developing advanced finite element methods for linear elasticity.
Contribution
It introduces a novel approach linking Ricci curvature with continuum mechanics to improve finite element schemes in linear elasticity.
Findings
New finite element schemes derived from differential geometric principles.
Enhanced understanding of the role of Ricci curvature in solid mechanics.
Potential for more accurate and stable elasticity simulations.
Abstract
We discuss some differential geometry pertaining to continuum mechanics and the route recently taken by D.N. Arnold, R.S. Falk, and R. Winther in deriving new improved finite element schemes in linear elasticity from constructions in projective geometry.
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Taxonomy
TopicsElasticity and Material Modeling · Advanced Differential Geometry Research · Geometric Analysis and Curvature Flows