Materials Scientists notes that Aluminum is orthotropic, while we as Engineers use it as isotropic. Why both groups are correct in their own ways? Include definitions of orthotropic and isotropic in your answer.
Solution
An orthotropic material has three mutually orthogonal twofold axes of rotational symmetry so that its material properties are; in general, different along each axis. Aluminium has orthotropic properties that vary from point to point inside the volume of the object. This suggests that orthotropic is the property of a point within an object rather than for the object as a whole (unless the object is homogeneous). The associated planes of symmetry are also defined for a small region around a point and do not necessarily have to be identical to the planes of symmetry of the whole object. An isotropic material is one which looks the same in every direction. We cannot define any special direction using the material properties. In other words, none of the properties depend the orientation; it is perfectly rotationally symmetric. Note that in order to be isotropic the material must be homogenous on the length scale of interest, i.e. the same at every point in the material. Hence engineers use it as an isotropic.
Orthotropic: An orthotropic material has at least 2 orthogonal planes of symmetry, where material properties are independent of direction within each plane. Such materials require nine independent variables (i.e. elastic constants) in their constitutive matrices.
Isotropic: Isotropic has a stress-strain relationship that is independent of the orientation a the coordinate system at a point. An isotropic material is the one having the same elastic properties in Al directions at any one point of the body.
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Materials Scientists notes that Aluminum is orthotropic- while we as E.docx
1. Materials Scientists notes that Aluminum is orthotropic, while we as Engineers use it as
isotropic. Why both groups are correct in their own ways? Include definitions of orthotropic and
isotropic in your answer.
Solution
An orthotropic material has three mutually orthogonal twofold axes of rotational symmetry so
that its material properties are; in general, different along each axis. Aluminium has orthotropic
properties that vary from point to point inside the volume of the object. This suggests that
orthotropic is the property of a point within an object rather than for the object as a whole (unless
the object is homogeneous). The associated planes of symmetry are also defined for a small
region around a point and do not necessarily have to be identical to the planes of symmetry of the
whole object. An isotropic material is one which looks the same in every direction. We cannot
define any special direction using the material properties. In other words, none of the properties
depend the orientation; it is perfectly rotationally symmetric. Note that in order to be isotropic
the material must be homogenous on the length scale of interest, i.e. the same at every point in
the material. Hence engineers use it as an isotropic.
Orthotropic: An orthotropic material has at least 2 orthogonal planes of symmetry, where
material properties are independent of direction within each plane. Such materials require nine
independent variables (i.e. elastic constants) in their constitutive matrices.
Isotropic: Isotropic has a stress-strain relationship that is independent of the orientation a the
coordinate system at a point. An isotropic material is the one having the same elastic properties
in Al directions at any one point of the body.
