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Recently, Arumugam et al. (2023) developed a constitutive relation for the response of isotropic inhomogeneous compressible elastic solids in order to describe the response of the trabecular bone. Since porous solids such as bones, cement concrete, rocks, metallic alloys, etc., are anisotropic, in this short note we develop a constitutive relation for such bodies that exhibit transverse isotropy and also having two preferred directions of symmetry. Another characteristic of bones is that they exhibit different response characteristics in tension and compression, and hence any constitutive relation that is developed has to be capable of describing this. Also, the material moduli depend on both the density and the mean value of the stress (mechanical pressure), as is to be expected in a porous solid. In the constitutive relation that is developed in this paper, though the stress and the linearized strain appear linearly in the constitutive relation, the relationship is nonlinear. We also derive the response of such solids when undergoing uniaxial extension and compression, simple shear and torsion.
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Residual stress and material symmetry
There seems to be a basic misconception in several recent papers concerning the material symmetry of bodies in configurations that are pre-stressed. In this short paper we point to the source of the error and show that the material symmetry that is possible depends on the nature of the pre-stress. We also extend the results for material symmetry which have been well known within the context of simple elastic solids to the general class of simple materials. This generalization has relevance to the material symmetry of biological solids that are viscoelastic.
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- PAR ID:
- 10529059
- Publisher / Repository:
- IJES_RajWineman_24
- Date Published:
- Journal Name:
- International Journal of Engineering Science
- Volume:
- 197
- Issue:
- C
- ISSN:
- 0020-7225
- Page Range / eLocation ID:
- 104013
- Subject(s) / Keyword(s):
- Material symmetry Pre-stress Residual stress Elastic materials Viscoelastic materials
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.ijengsci.2023.104013
