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The spacing of independent displacement measurements varies with experimental setups, but is usually on the order of one micrometer. The traction patterns produced by cells frequently contain local maxima and minima that are smaller. Detection of these fine variations in local cellular traction with TFM remains challenging.
The following formula describes the viscous stress tensor for the special case of Stokes flow. It is needed in the calculation of the force acting on the particle. In Cartesian coordinates the vector-gradient is identical to the Jacobian matrix. The matrix I represents the identity-matrix.
The force measurement is used to calculate the engineering stress, σ, using the following equation: [5] σ = F n A {\displaystyle \sigma ={\frac {F_{n}}{A}}} where F is the tensile force and A is the nominal cross-section of the specimen.
Traction can also refer to the maximum tractive force between a body and a surface, as limited by available friction; when this is the case, traction is often expressed as the ratio of the maximum tractive force to the normal force and is termed the coefficient of traction (similar to coefficient of friction).
Cauchy observed that the force across an imaginary surface was a linear function of its normal vector; and, moreover, that it must be a symmetric function (with zero total momentum). The understanding of stress in liquids started with Newton, who provided a differential formula for friction forces (shear stress) in parallel laminar flow.
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
The term tractive effort is often qualified as starting tractive effort, continuous tractive effort and maximum tractive effort.These terms apply to different operating conditions, but are related by common mechanical factors: input torque to the driving wheels, the wheel diameter, coefficient of friction (μ) between the driving wheels and supporting surface, and the weight applied to the ...
Castigliano's method for calculating displacements is an application of his second theorem, which states: If the strain energy of a linearly elastic structure can be expressed as a function of generalised force Q i then the partial derivative of the strain energy with respect to generalised force gives the generalised displacement q i in the direction of Q i.