Elasticity#

You can use the Elasticity component to solve the elasticity equation with or without inertia. Whether inertia or body forces are included is determined by the Elasticity property settings. Gravitational body forces are included if the gravity_field is set in the Problem. Table 15 lists the various elastic, viscoelastic, and elastoplastic bulk constitutive models implemented for the elaticity equation.

Table 15 Elasticity bulk rheologies#
Bulk Rheology	Description
`IsotropicLinearElasticity`	Isotropic, linear elasticity
`IsotropicLinearMaxwell`	Isotropic, linear Maxwell viscoelasticity
`IsotropicLinearGenMaxwell`	Isotropic, generalized Maxwell viscoelasticity
`IsotropicPowerLaw`	Isotropic, power-law viscoelasticity
`IsotropicDruckerPrager`	Isotropic, Drucker-Prager elastoplasticity

Warning

The IsotropicDruckerPrager rheology has not yet been implemented in PyLith v3.

Table 16 Properties defining elasticity bulk rheologies#
Subfield	L	LM	GM	PL	DP	Components
`density`	X	X	X	X	X
`vp` (P-wave speed)	X	X	X	X	X
`vs` (S-wave speed)	X	X	X	X	X
`body_force`	O	O	O	O	O	x, y, z
`gravitational_acceleration`	O	O	O	O	O	x, y, z
`shear_modulus`	I	I	I	I	I
`bulk_modulus`	I	I	I	I	I
`reference_stress`	O	O	O	O	O	xx, yy, zz, xy, yz, xz
`reference_strain`	O	O	O	O	O	xx, yy, zz, xy, yz, xz
`maxwell_time`		I
`viscosity`		X
`viscosity_1`			X
`viscosity_2`			X
`viscosity_3`			X
`shear_ratio_1`			X
`shear_ratio_2`			X
`shear_ratio_3`			X
`total_strain`		X	X	X		xx, yy, zz, xy, yz, xz
`viscous_strain`		X		X		xx, yy, zz, xy, yz, xz
`viscous_strain_1`			X			xx, yy, zz, xy, yz, xz
`viscous_strain_2`			X			xx, yy, zz, xy, yz, xz
`viscous_strain_3`			X			xx, yy, zz, xy, yz, xz
`power_law_exponent`				X
`power_law_reference_strain_rate`				X
`power_law_reference_stress`				X
`deviatoric_stress`				X
`cohesion`					X
`friction_angle`					X
`dilatation_angle`					X
`alpha_yield`					I
`alpha_flow`					I
`beta`					I
`plastic_strain`					X	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
DP: isotropic Drucker-Prager elastoplasticity

Table 17 Derived subfields that are available for output for elasticity bulk rheologies.#
Subfield	L	LM	GM	PL	DP	Components
`cauchy_stress`	✓	✓	✓	✓	✓	xx, yy, zz, xy, yz, xz
`cauchy_strain`	✓	✓	✓	✓	✓	xx, yy, zz, xy, yz, xz