Hypo-ISA¶
Hypoplasticity combined with Intergranular Strain Anisotropy (ISA). ISA replaces the original intergranular-strain extension with an elastoplastic formulation of the intergranular strain, giving a clean small-strain stiffness, hysteresis and accumulation behaviour. This is the model used in the calibration shown on the home page and is a strong default for cyclic loading. A time integrator parameter selects forward Euler (1) or modified Euler (2).
At a glance
- Class:
ACT.models.hypoplasticity_isa - numgeo name:
Hypo-ISA - Parameters with search bounds: 16
- Imported as:
from ACT.models import hypoplasticity_isa
Units and angles
Use degrees for phic, matching the ACT defaults and bounds. The current
numgeo material also accepts radians for values at or below one, but mixing the two
conventions in one search interval is unsafe. Enter hs in GPa; ACT
converts it to kPa for numgeo. The other material parameters are
dimensionless. Optional phantom_E and pmin values use kPa.
Default search bounds¶
These are the built-in lower/upper bounds used when a parameter is optimized. Override any of them with set_bounds.
| Parameter | Lower | Upper | Description |
|---|---|---|---|
phic |
25 | 45 | critical-state friction angle (degrees in ACT) |
ec |
0.5 | 1.5 | critical void-ratio factor e_c0 |
ed |
0.36 | 1.0 | minimum void-ratio factor e_d0 |
hs |
1e-3 | 45 | granulate hardness (GPa in ACT) |
n |
0.1 | 0.5 | compression exponent |
alpha |
0.0 | 0.5 | pyknotropy / fabric exponent |
beta |
0.1 | 6. | barotropy exponent |
R |
1e-4 | 2.5e-4 | size of the elastic / intergranular-strain locus |
mR |
2. | 12. | intergranular-strain stiffness factor (reversal) |
beta_h0 |
0.05 | 1.0 | ISA hardening parameter (initial) |
beta_hmax |
1.0 | 5.0 | ISA hardening parameter (maximum) |
chi0 |
1. | 10. | ISA hardening exponent (initial) |
chi_max |
5 | 50 | ISA hardening exponent (maximum) |
eps_acc |
1e-2 | 0.05 | ISA accumulation parameter |
cz |
100 | 5000 | fabric-evolution parameter |
fei |
1.05 | 1.25 | maximum-to-critical void-ratio factor \(e_{i0}/e_{c0}\) |
Setting parameters¶
Assign initial / fixed parameter values with set(...):
from ACT.models import hypoplasticity_isa
model = hypoplasticity_isa()
model.set(phic=..., fei=..., ec=..., ed=..., hs=..., n=...)
Full set signature
set(phic=None,fei=None,ec=None,ed=None,hs=None,n=None,alpha=None,beta=None, R=None,mR=None,beta_h0=None,beta_hmax=None,chi0=None,chi_max=None,eps_acc=None,cz=None, phantom_E=None, phantom_nu=None, pmin=None, integrator=None)
Available set parameters: phic, fei, ec, ed, hs, n, alpha, beta, R, mR, beta_h0, beta_hmax, chi0, chi_max, eps_acc, cz, phantom_E, phantom_nu, pmin, integrator.
Choosing free parameters¶
Narrow the search interval of selected parameters, then list the ones to optimize in globals.setup:
model.set_bounds(phic=[25.0, 45.0], ec=[0.5, 1.5], ed=[0.36, 1.0], hs=[1e-3, 45])
globals.setup(Model=model, Free_parameter=["phic", "ec", "ed", "hs", "n", "alpha"], ...)
Parameters that accept a set_bounds override: phic, fei, ec, ed, hs, n, alpha, beta, R, mR, beta_h0, beta_hmax, chi0, chi_max, eps_acc, cz.
Reading & updating single parameters¶
model.update("phic", value) # set one parameter
x = model.get_parameter("phic") # read one parameter
See the models overview for the common interface shared by all models, and Optimization for how the free parameters are searched.