What are the units of gamma in the linear elasticity tutorial?

General
1

https://jsdokken.com/dolfinx-tutorial/chapter2/linearelasticity_code.html

# Scaled variable
import pyvista
from dolfinx import mesh, fem, plot, io, default_scalar_type
from dolfinx.fem.petsc import LinearProblem
from mpi4py import MPI
import ufl
import numpy as np
L = 1
W = 0.2
mu = 1
rho = 1
delta = W / L
gamma = 0.4 * delta**2
beta = 1.25
lambda_ = beta
g = gamma

In terms of the acceleration of gravity being described… So far I have been made aware of the gravitational constant being described as 9.81 m/s**2. Here an acceleration is described:

*gamma = 0.4 * delta**2*

So far I don’t really understand yet what units are being talked of in terms of gamma (ex. metric, imperial). So also the 0.4, is there a basis for it? Why is 0.4 being chosen here? Is there someplace that describes this formulation for gamma and delta ratio?

2

There might be a relation in terms of gamma to:

F = G * (m1 * m2) / r^2

G being described as the gravitational constant. So a kilogram might be used to put in two masses in this variation so some units of force come out that would have to be related to kilograms if kilograms are used to measure with. So there are ksg or kilograms of force there is also a Newton which is related to the movement of 1kg.

There is a gravitational constant in units Nm**2 to choose from and the corresponding units to it are kilograms so in that format there is a newton meters per second unit of force I guess to measure an acceleration with at this point…

There is an inversely proportional to the square of the distance between their centers to account for which seems to be maybe why delta is there to account for it…

3

This is discussed here:
https://jsdokken.com/dolfinx-tutorial/chapter2/elasticity_scaling.html