Search results
Results from the WOW.Com Content Network
As it is a second order tensor, the stress deviator tensor also has a set of invariants, which can be obtained using the same procedure used to calculate the invariants of the stress tensor. It can be shown that the principal directions of the stress deviator tensor s i j {\displaystyle s_{ij}} are the same as the principal directions of the ...
After the stress distribution within the object has been determined with respect to a coordinate system (,), it may be necessary to calculate the components of the stress tensor at a particular material point with respect to a rotated coordinate system (′, ′), i.e., the stresses acting on a plane with a different orientation passing through ...
Thus the stress state of the material must be described by a tensor, called the (Cauchy) stress tensor; which is a linear function that relates the normal vector n of a surface S to the traction vector T across S. With respect to any chosen coordinate system, the Cauchy stress tensor can be represented as a symmetric matrix of 3×3
In continuum mechanics, the most commonly used measure of stress is the Cauchy stress tensor, often called simply the stress tensor or "true stress". However, several alternative measures of stress can be defined: [1] [2] [3] The Kirchhoff stress (). The nominal stress ().
The viscous stress tensor is formally similar to the elastic stress tensor (Cauchy tensor) that describes internal forces in an elastic material due to its deformation. Both tensors map the normal vector of a surface element to the density and direction of the stress acting on that surface element.
Along with axial stress and radial stress, circumferential stress is a component of the stress tensor in cylindrical coordinates. It is usually useful to decompose any force applied to an object with rotational symmetry into components parallel to the cylindrical coordinates r, z, and θ. These components of force induce corresponding stresses ...
All but the last term of can be written as the tensor divergence of the Maxwell stress tensor, giving: = +, As in the Poynting's theorem, the second term on the right side of the above equation can be interpreted as the time derivative of the EM field's momentum density, while the first term is the time derivative of the momentum density for ...
Stress calculation: For each configuration with applied shear strain, perform a DFT calculation to determine the resulting stress tensor. Shear stress vs. shear strain curve: Plot the calculated shear stress against the applied shear strain for each increment.The slope of the stress-strain curve in its linear region provides the shear modulus ...