Abstract
The aim of this chapter is to provide a brief drive-through a vast area of mathematical modelling of material properties in continuum mechanics. The readers are encouraged to seek further knowledge from other sources listed in the reference.
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Notes
- 1.
For small infinitesimal deformation it is insignificant to differentiate between strain tensor \(\hat{\textbf{E}}\) or left stretch tensor \(\textbf{V}\).
- 2.
This linear relation is called the physical linearity.
- 3.
The reflection tensor is an orthogonal tensor with determinant equals –1.
- 4.
Refer Appendix for the Voigt Notation and complete derivation of orthotropic structure of material tensor.
- 5.
Refer to the Gâteaux variation in the appendix for the derivative of the invariant of a tensor with respect to a tensor.
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Mohamed, N.A.N. (2023). Constitutive Relations. In: Introduction to Continuum Mechanics for Engineers. Springer, Singapore. https://doi.org/10.1007/978-981-99-0811-0_4
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DOI: https://doi.org/10.1007/978-981-99-0811-0_4
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