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The stretch factor is important in the theory of geometric spanners, weighted graphs that approximate the Euclidean distances between a set of points in the Euclidean plane. In this case, the embedded metric S is a finite metric space, whose distances are shortest path lengths in a graph, and the metric T into which S is embedded is the ...
The isochoric deformation gradient is defined as ¯:= /, resulting in the isochoric deformation gradient having a determinant of 1, in other words it is volume stretch free. Using this one can subsequently define the isochoric left Cauchy–Green deformation tensor B ¯ := F ¯ ⋅ F ¯ T = J − 2 / 3 B {\displaystyle {\bar {\boldsymbol {B ...
A t-path is defined as a path through the graph with weight at most t times the spatial distance between its endpoints. The parameter t is called the stretch factor or dilation factor of the spanner. [1] In computational geometry, the concept was first discussed by L.P. Chew in 1986, [2] although the term "spanner" was not used in the original ...
Initially, this permanent deformation is non-uniformly distributed along the sample. During this process, dislocations escape from Cottrell atmospheres within the material. The resulting slip bands appear at the lower yield point and propagate along the gauge length, at constant stress, until the Lüders strain is reached, and deformation ...
In continuum mechanics, stress triaxiality is the relative degree of hydrostatic stress in a given stress state. [1] It is often used as a triaxiality factor, T.F, which is the ratio of the hydrostatic stress, , to the Von Mises equivalent stress, .
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.
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In simple contexts, a single number may suffice to describe the strain, and therefore the strain rate. For example, when a long and uniform rubber band is gradually stretched by pulling at the ends, the strain can be defined as the ratio between the amount of stretching and the original length of the band: