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Then the differential equations reduce to a finite set of equations (usually linear) with finitely many unknowns. In other contexts one may be able to reduce the three-dimensional problem to a two-dimensional one, and/or replace the general stress and strain tensors by simpler models like uniaxial tension/compression, simple shear, etc.
The amount of stretch or compression along material line elements or fibers is the normal strain, and the amount of distortion associated with the sliding of plane layers over each other is the shear strain, within a deforming body. [2] This could be applied by elongation, shortening, or volume changes, or angular distortion. [3]
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.
A stretch in the xy-plane is a linear transformation which enlarges all distances in a particular direction by a constant factor but does not affect distances in the perpendicular direction. We only consider stretches along the x-axis and y-axis. A stretch along the x-axis has the form x' = kx; y' = y for some positive constant k.
With a stretching exponent β between 0 and 1, the graph of log f versus t is characteristically stretched, hence the name of the function. The compressed exponential function (with β > 1) has less practical importance, with the notable exception of β = 2, which gives the normal distribution.
In astrophysics, spaghettification (sometimes referred to as the noodle effect) [1] is the vertical stretching and horizontal compression of objects into long thin shapes (rather like spaghetti) in a very strong, non-homogeneous gravitational field. It is caused by extreme tidal forces.
Under such a condition, the above equation can obtain the direct-related stiffness for the degree of unconstrained freedom. The ratios between the reaction forces (or moments) and the produced deflection are the coupling stiffnesses. The elasticity tensor is a generalization that describes all possible stretch and shear parameters.
By convention, the strain is set to the horizontal axis and stress is set to vertical axis. Note that for engineering purposes we often assume the cross-section area of the material does not change during the whole deformation process. This is not true since the actual area will decrease while deforming due to elastic and plastic deformation.