Incompressible Elasticity#

You can use the IncompressibleElasticity component to solve the quasistatic incompressible elasticity equation. Estimating realistic distributions of initial stress fields consistent with gravitational body forces can be quite difficult due to our lack of knowledge of the deformation history. A simple way to approximate the lithostatic load is to solve for the stress field imposed by gravitational body forces assuming an incompressible elastic material. This limits the volumetric deformation. In this context we do not include inertia, so the IncompressibleElasticity component does not include an inertial term. Gravitational body forces are included if the gravity_field is set in the Problem. Table 18 lists the elastic bulk rheology implemented for the incompressible elaticity equation.

Table 18 Incompressible elasticity bulk rheology.#
Bulk Rheology	Description
`IsotropicLinearincompElasticity`	Isotropic, linear incompressible elasticity

Table 19 Properties defining incompressible elasticity bulk rheologies.#
Subfield	L	LM	GM	PL	Components
`density`	X	X	X	X
`vp` (P-wave speed)	X	X	X	X
`vs` (S-wave speed)	X	X	X	X
`body_force`	O	O	O	O	x, y, z
`gravitational_acceleration`	O	O	O	O	x, y, z
`shear_modulus`	I	I	I	I
`bulk_modulus`	I	I	I	I
`reference_stress`	O	O	O	O	xx, yy, zz, xy, yz, xz
`reference_strain`	O	O	O	O	xx, yy, zz, xy, yz, xz

X: required value in auxiliary field spatial database
O: optional value in auxiliary field spatial database
I: internal auxiliary subfield; computed from spatial database values L: isotropic, linear elasticity
ML: isotropic linear Maxwell viscoelasticity
GM: isotropic generalized linear Maxwell viscoelasticity
PL: isotropic power-law viscoelasticity

Table 20 Derived subfields that are available for output for incompressible elasticity bulk rheologies.#
Subfield	L	LM	GM	PL	Components
`cauchy_stress`	✓	✓	✓	✓	xx, yy, zz, xy, yz, xz
`cauchy_strain`	✓	✓	✓	✓	xx, yy, zz, xy, yz, xz