Transformation Properties of the Lagrangian and Eulerian Strain Tensors

2002/11/01 by Thomas B. Bahder, Bahder, Thomas B.
Engineering · Physics and Astronomy · #Classical Physics (physics.class-ph) #Composite Material Mechanics #Elasticity and Material Modeling #Elasticity and Wave Propagation #FOS: Physical sciences #General Physics (physics.gen-ph) #physics.class-ph #physics.gen-ph

paper · pdf · doi:10.48550/arxiv.physics/0211003

35 pages double-space, 3 figures

arxiv created 2002/11/01 · openalex publication_date 2002/11/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A coordinate independent derivation of the Eulerian and Lagrangian strain tensors of finite deformation theory is given based on the parallel propagator, the world function, and the displacement vector field as a three-point tensor. The derivation explicitly shows that the Eulerian and Lagrangian strain tensors are two-point tensors, each a function of both the spatial and material coordinates. The Eulerian strain is a two-point tensor that transforms as a second rank tensor under transformation of spatial coordinates and transforms as a scalar under transformation of the material coordinates. The Lagrangian strain is a two-point tensor that transforms as scalar under transformation of spatial coordinates and transforms as a second rank tensor under transformation of the material coordinates. These transformation properties are needed when transforming the strain tensors from one frame of reference to another moving frame.

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