Elastic modulii relation for a sphere

[monty37]

say i derive the relationship between the 3 elastic modulii for a sphere.
i consider the 3 co-ordinate axes.if stress is applied only along x-axis,there would be a resulting strain along Y and Z.

My book derived it for a cube,that was quite simple,but i cannot imagine the resulting strain caused in a sphere unlike a cube.

vol of sphere=4/3(3.14)r^3

 

[Mapes]

Why would there be a difference? The stress-strain relationship (for small strains) applies to any infinitesimal element, regardless of the size or shape of the object. If the stress is the same, then the strain will be the same, sphere or cube.

 

[monty37]

but the expression for strain would vary in case of a sphere,right

say p/E is the stress on one of the sides of the cube

then resulting strains would be say 1*p/(m*E) on the other faces

but in case of a sphere we cannot consider faces .

 

[nasu]

say i derive the relationship between the 3 elastic modulii for a sphere.
i consider the 3 co-ordinate axes.if stress is applied only along x-axis,there would be a resulting strain along Y and Z.

My book derived it for a cube,that was quite simple,but i cannot imagine the resulting strain caused in a sphere unlike a cube.

vol of sphere=4/3(3.14)r^3

The elastic moduls are a characteristic of the material not of the specific piece of material.
I suppose you are talking about the elastic stiffness (or compliance) coefficients.