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elastic materials'
- Thread starter Bakk
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Just happen to see your email. Hope the following information is useful to you.
By definition, an orthotropic material has at least 2 orthogonal planes of symmetry, where material properties are independent of direction within each plane. Such materials require 9 independent variables (i.e. elastic constants) in their constitutive matrices.
In contrast, a material without any planes of symmetry is fully anisotropic and requires 21 elastic constants, whereas a material with an infinite number of symmetry planes (i.e. every plane is a plane of symmetry) is isotropic, and requires only 2 elastic constants.
Rgds
MASS
Just happen to see your email. Hope the following information is useful to you.
By definition, an orthotropic material has at least 2 orthogonal planes of symmetry, where material properties are independent of direction within each plane. Such materials require 9 independent variables (i.e. elastic constants) in their constitutive matrices.
In contrast, a material without any planes of symmetry is fully anisotropic and requires 21 elastic constants, whereas a material with an infinite number of symmetry planes (i.e. every plane is a plane of symmetry) is isotropic, and requires only 2 elastic constants.
Rgds
MASS
The response from Starmass is exactly correct. However, you may want simpler terms for understanding. An example of an isotropic material is steel or aluminum. Their stress-strain relationship can be simplified down to just two elasticity values, E and G. This is because when you compress, pull, or shear this material in one direction, the values of E and G will give you the material strains in all directions.
Common orthotropic materials are fiberglass and wood. Their elasticity properties in perpendicular directions are not related because the fiber direction properties are dominated by the fiber's strength while the perpendicular-to-fiber direction is dominated by the matrix strength. Consequently, one neads more elasticity constants to evaluate the deformations of such materials. For example, two different E values for parallel to fiber and for perpendicular to fiber directions.
Common orthotropic materials are fiberglass and wood. Their elasticity properties in perpendicular directions are not related because the fiber direction properties are dominated by the fiber's strength while the perpendicular-to-fiber direction is dominated by the matrix strength. Consequently, one neads more elasticity constants to evaluate the deformations of such materials. For example, two different E values for parallel to fiber and for perpendicular to fiber directions.
To be strictly correct, scofie's statement "An example of an isotropic material is steel or aluminum" is only correct for annealed material.
Any material that has been deformed, e.g., rolled, extruded, forged, wire drawn, etc. contains an anisotropic grain structure (deformation texture). Any material that has been heat treated (other than annealing or stress relieving) also contains residual stresses.
Physical Metallurgy Handbook, chapter 4, Plastic Deformation (2003) and Metals Handbook, 9th edn., vol. 14, pp. 877-899 (1988) covers deformation anisotropy thoroughly. For example, one table with anisotropy values for rolled sheet of different metals.
Residual stresses & distortion from heat treatments and transformations are well-known, see Physical Metallurgy Handbook, chapter 17. I would expect any metallurgist to be familiar with the symmetric residual stress pattern for a quenched cylindrical bar (tensile in center, compressive toward surface).
Any material that has been deformed, e.g., rolled, extruded, forged, wire drawn, etc. contains an anisotropic grain structure (deformation texture). Any material that has been heat treated (other than annealing or stress relieving) also contains residual stresses.
Physical Metallurgy Handbook, chapter 4, Plastic Deformation (2003) and Metals Handbook, 9th edn., vol. 14, pp. 877-899 (1988) covers deformation anisotropy thoroughly. For example, one table with anisotropy values for rolled sheet of different metals.
Residual stresses & distortion from heat treatments and transformations are well-known, see Physical Metallurgy Handbook, chapter 17. I would expect any metallurgist to be familiar with the symmetric residual stress pattern for a quenched cylindrical bar (tensile in center, compressive toward surface).
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