Strain quantities — strain • structr

Converts different quantifications of strain.

Usage

longitudinal_strain(l, l0)

angular_strain(psi, degree = TRUE)

quadratic_elongation(e = NULL, l = NULL, l0 = NULL)

stretch(e = NULL, l = NULL, l0 = NULL, lambda = NULL)

Arguments

l, l0: numeric. Final and original length, respectively
psi: numeric. Angle
degree: logical. Whether psi is given in degree (the default) or radians
e: numeric. Elongation
lambda: numeric. Quadratic elongation

Details

Longitudianal strain (also elongation) is the change in length divided by the original length: $$e = (l-l_o)/l_o$$

Angular strain is the change in angle between two lines that were initially perpendicular" $$\gamma = \tan \psi$$

Stretch is the ratio of the final length and the original length: $$s = \sqrt{\lambda} = l/l_o = 1 + e$$

Quadratic elongation is the quadratic stretch: $$\lambda = s^2 = (l/l_o)^2 = (1+e)^2$$

Examples

longitudinal_strain(l=10,l0=5) 
#> [1] 1
angular_strain(25)
#> [1] 0.4663077
quadratic_elongation(l=10,l0=5)
#> [1] 4
stretch(l=10,l0=5)
#> [1] 2