Nonlinear traveling wave propagation in a Neo-Hookean cylindrical rod with torsional eigenstrain

Motaghian, Seyedemad; Rahimian, M.

doi:10.1016/j.ijnonlinmec.2020.103411

Cited by 3 publications

(1 citation statement)

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“…the four-dimensional relativistic spacetime theories and the infinite-dimensional configuration space theories [9,11,12,14]. On another front, investigations have been focused on the applications of Riemannian and non-Riemannian geometries for static and dynamic analyses of three-dimensional continua that possess crystallographic defects such as dislocations and disclinations [15][16][17][18], or have been affected by eigenstrains caused by factors such as inclusions [19][20][21]. Another important field of research in geometric continuum mechanics is devoted to anholonomic deformations, where the components of the deformation gradient fail to be integrable functions of the referential coordinates [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Strain, disfigurement and flexure tensors in continuum kinematics

Emami,

Eskandari-Ghadi

2023

Proc. R. Soc. A.

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In the differential geometric formulation of nonlinear elasticity, the strain tensor can intrinsically be regarded as a measure of change of the metric of the Riemannian manifold that embodies the continuum undergoing a deformation. Here, this classical concept is revisited and complemented with two newly defined higher order deformation measures, namely the disfigurement and flexure tensors, which respectively measure the change of the Levi-Civita connexion and the Riemann curvature of the continuum. The strain, disfigurement and flexure tensors can, thereby, roughly indicate the alteration of the geometry of a deforming body in the zeroth, first and second orders, respectively. In this light, one may predict that the disfigurement and flexure tensors should be related to the first and second covariant derivatives of the strain tensor. While this is true, the exact strain-disfigurement-flexure relations, as derived in this paper, are found to be involved and non-trivial, offering a deeper understanding of the deformation. In our discussions, distance-preserving, geodesic-preserving and curvature-preserving deformations are studied as three special cases to help better interpret the above-mentioned deformation measures. Some related results have also been found as by-products that might be of current interest or prove useful in future investigations.

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