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Solids_Shear modulus

Page history last edited by Karen Carleton 8 years, 7 months ago

Working content >MacroModels>Solids >Shear modulus

 

 

            You can also apply force parallel to a surface rather than perpendicular to it.  This causes the object to shear:

In this case, some of the solid molecules are moving past others.  Similar to stress, the shear stress, τ is just the applied force divided by the surface area, however it is now the surface area parallel to the force, rather than perpendicular to it.  If you think about it, in shear, this is the area of molecules that has to move past other ones as the object is distorted.  Just as strain is the result of stress, so shear strain, γ is the result of shear stress.  The shear strain is the displacement resulting from the applied shear force divided by the initial length of the solid.  And just as stress and strain were related by Young's modulus, so the shear stress and the shear strain are related by the shear modulus, which is called G.   The shear modulus is then related to the ratio of the shear stress and the shear strain.  In this case:

Formula

For most materials, the shear modulus is two to three times less than Young’s modulus.  Therefore, shear motion is larger for the same applied force.  This suggests that it is easier to shear most materials than it is to compress or stretch them.

            The forces applied to many biological structures are often applied along multiple directions such that there can be both longitudinal and tangential forces.  If one end of an object is pushed relative to the other, there may also be shear forces.  As a dog runs, much of the force is directed along the length of the leg, where the bone is strongest.  However, some of the force is perpendicular to the end of the bone closest to the ground and will result in a shear force along this direction.  Biological materials must be strong enough in this dimension to withstand these forces to enable organisms to move about in their environment.

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