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This article is cited in 1 scientific paper (total in 1 paper)
Mechanics
Reference shape of bodies with enhanced kinematics. Part II. Second gradient and microstructure
K. G. Koifman Bauman Moscow State Technical University, Moscow, Russian Federation
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
The work develops differential-geometric methods for modeling finite incompatible deformations of hyperelastic solids with enhanced kinematics. The response of such bodies, along with the standard kinematic field represented by the deformation gradient, is characterized by additional tensor fields. As such, the paper considers: 1) the second deformation gradient and 2) the tensor field of the second rank, modeling the microstructure of the body. For each of these two cases, compatibility conditions are obtained and their geometric interpretation is proposed. Geometry is synthesized on the material manifold representing a body with enhanced kinematics. The corresponding affine connection has non-zero torsion and curvature, which can be useful for modeling a body with dislocations and disclinations.
Keywords:
hyperelasticity, body with enhanced kinematics, second gradient, microstructure, incompatible deformations, residual stresses, non-Euclidean geometry, material metric, material connection, curvature, torsion, non-metricity.
Received: 25.08.2023 Revised: 04.10.2023 Accepted: 05.12.2023
Citation:
K. G. Koifman, “Reference shape of bodies with enhanced kinematics. Part II. Second gradient and microstructure”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 29:4 (2023), 54–76
Linking options:
https://www.mathnet.ru/eng/vsgu718 https://www.mathnet.ru/eng/vsgu/v29/i4/p54
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Abstract page: | 25 | Full-text PDF : | 6 | References: | 11 |
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