Fractional derivative stress-strain relations are derived for compressible viscoelastic materials based on the continuum mechanics. Several types of stress tensor and strain tensors are specified to describe the dynamics of continuous media. Consequently there are many equivalent expressions of stress-strain relations. If memory effect is not taken into account, these relations are equivalently transformed from one to another by suitable tensor operations. However, if memory effect is included in the mechanics of the materials, different types of stress-strain relations can be derived depending on the choice of the type of stress tensor, or equivalently the choice of the strain energy function. In this paper, several types of fractional derivative stress-strain relations are proposed.
- Design Engineering Division and Computers and Information in Engineering Division
Three-Dimensional Fractional Derivative Models for Finite Deformation
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Fukunaga, M, & Shimizu, N. "Three-Dimensional Fractional Derivative Models for Finite Deformation." Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B. Washington, DC, USA. August 28–31, 2011. pp. 193-200. ASME. https://doi.org/10.1115/DETC2011-47552
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