Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Simple shear
Summary
Simple shear is a deformation in which parallel planes in a material remain parallel and maintain a constant distance, while translating relative to each other.
In fluid mechanics, simple shear is a special case of deformation where only one component of velocity vectors has a non-zero value:
And the gradient of velocity is constant and perpendicular to the velocity itself:
where is the shear rate and:
The displacement gradient tensor Γ for this deformation has only one nonzero term:
Simple shear with the rate is the combination of pure shear strain with the rate of 1/2 and rotation with the rate of 1/2:
The mathematical model representing simple shear is a shear mapping restricted to the physical limits. It is an elementary linear transformation represented by a matrix. The model may represent laminar flow velocity at varying depths of a long channel with constant cross-section. Limited shear deformation is also used in vibration control, for instance base isolation of buildings for limiting earthquake damage.
Deformation (mechanics)
In solid mechanics, a simple shear deformation is defined as an isochoric plane deformation in which there are a set of line elements with a given reference orientation that do not change length and orientation during the deformation. This deformation is differentiated from a pure shear by virtue of the presence of a rigid rotation of the material. When rubber deforms under simple shear, its stress-strain behavior is approximately linear. A rod under torsion is a practical example for a body under simple shear.
If e1 is the fixed reference orientation in which line elements do not deform during the deformation and e1 − e2 is the plane of deformation, then the deformation gradient in simple shear can be expressed as
We can also write the deformation gradient as
In linear elasticity, shear stress, denoted , is related to shear strain, denoted , by the following equation:
where is the shear modulus of the material, given by
Here is Young's modulus and is Poisson's ratio. Combining giv
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.