Read the results

sim.solver.solve writes no file. It returns a SolverResults holding the whole history in memory, one column per recorded increment, and Python picks the measures it wants from it. There is nothing to configure beforehand: every measure below is recorded at every increment, the tangent being the only optional one (solve(record_tangent=False) skips it).

res = sim.solver.solve(blocks, umat_name, props, nstatev, T_init=T_init)

e11, e22, e33, e12, e13, e23 = res["Strain"]   # strain integrated with the objective rate, (6, N)
lnV = res["LogStrain"]                          # ln V from F, whatever the rate
s11, s22, s33, s12, s13, s23 = res["Stress"]   # Cauchy stress, (6, N)
time, T = res["Time"], res["Temp"]             # (N,)
Wm, Wm_r, Wm_ir, Wm_d = res["Wm"]              # mechanical energies, (4, N)

print(res)          # SolverResults(mechanical, 100 increments, status=0, fields=[...])
res.keys()          # the names available in this run

Layout

Arrays follow the fedoo DataSet conventions: components first, one column per increment. A 6-component history is a (6, N) array in Voigt order [11, 22, 33, 12, 13, 23], a tensor history is (3, 3, N), a scalar history (N,). fedoo.util.voigt_tensors.StressTensorList(res["Stress"]) works directly on the returned arrays, and res.get_data(key) is the fedoo-style alias of res[key].

Increment bookkeeping

Key	Shape	Content
Block	(N,)	Block number of the increment (from 0)
Cycle	(N,)	Cycle of the block (from 0)
Step	(N,)	Step within the block (from 0)
Inc	(N,)	Increment within the step (from 0)
Time	(N,)	Simulation time at the end of the increment
Temp	(N,)	Temperature \(T\) at the end of the increment

Strain and stress measures

Every measure is recorded, whatever the control type of the block, so a single run gives every conjugate pair:

Key	Shape	Content
Strain	(6, N)	Eulerian strain integrated along the path with the objective rate of the run (corate): the strain the constitutive law sees. With the logarithmic rates ("logarithmic", "logarithmic_R", the default, "logarithmic_F") it is the logarithmic strain \(\ln \mathbf{V}\) up to the integration error; with "jaumann" or "green_naghdi" it is the integral of \(\mathbf{D}\) along the spin of the rate: path dependent, not a function of \(\mathbf{F}\), equal to \(\ln\mathbf{V}\) only on paths whose principal axes do not rotate (in simple shear it departs at third order in \(\gamma\)); with "truesdell" it is the Almansi strain \(\mathbf{e}_A = \frac{1}{2}(\mathbf{I} - \mathbf{b}^{-1})\), exactly, not a logarithmic strain
LogStrain	(6, N)	Logarithmic strain \(\ln \mathbf{V} = \frac{1}{2}\ln(\mathbf{F}\mathbf{F}^T)\), computed from \(\mathbf{F}\): exact whatever the rate. Use it, not Strain, when the logarithmic strain is wanted under "truesdell", "jaumann" or "green_naghdi"
GreenLagrange	(6, N)	Green-Lagrange strain \(\mathbf{E} = \frac{1}{2}(\mathbf{F}^T\mathbf{F} - \mathbf{I})\), from \(\mathbf{F}\): exact whatever the rate
F	(3, 3, N)	Deformation gradient \(\mathbf{F}\)
Stress	(6, N)	Cauchy stress \(\boldsymbol{\sigma}\)
Kirchhoff	(6, N)	Kirchhoff stress \(\boldsymbol{\tau} = J\boldsymbol{\sigma}\)
PKII	(6, N)	2nd Piola-Kirchhoff stress \(\mathbf{S}\)
R	(3, 3, N)	Rotation accumulated by the objective rate of the run; it is the \(\mathbf{R}\) of the polar decomposition \(\mathbf{F} = \mathbf{R}\mathbf{U}\) for "green_naghdi" and "logarithmic_R", differs from it for "jaumann" and "logarithmic", and for the convected rates "truesdell" and "logarithmic_F" it is not a rotation: it accumulates the frame increments \(\Delta\mathbf{F}\), i.e. it is \(\mathbf{F}\) itself (to round-off: runs start at \(\mathbf{F} = \mathbf{I}\))
DR	(3, 3, N)	Frame increment of the objective rate over the increment: the rotation \(\Delta\mathbf{R}\), or \(\Delta\mathbf{F} = \mathbf{F}_1\mathbf{F}_0^{-1}\) for "truesdell" and "logarithmic_F"

Note

Internally the finite-strain solver carries the Kirchhoff stress \(\boldsymbol{\tau}\): the constitutive kernels and the energies \(W_m\) work on it, and the prescribed PKII and Biot stresses are derived from it. Kirchhoff is that stress as integrated; Stress is the Cauchy stress \(\boldsymbol{\sigma} = \boldsymbol{\tau}/J\) formed at output and stays the default measure. See Stress measure and tangent rate for the kernel contract and the sim.umat boundary used by fedoo.

Note

In small deformations (control_type="small_strain") the rate plays no role: all strain measures reduce to the infinitesimal strain and all stress measures to the Cauchy stress. Shear strain components are engineering shears \(\gamma_{ij} = 2\varepsilon_{ij}\).

Energies, state variables, tangent

Key	Shape	Content
Wm	(4, N)	Mechanical energies \([W_m, W_m^r, W_m^{ir}, W_m^d]\): total, stored (recoverable), irrecoverable stored, dissipated, per reference volume. \(W_m\) is the work \(\int \mathbf{P} : \mathrm{d}\mathbf{F}\) whatever the rate (see Stress measure and tangent rate)
Statev	(nstatev, N)	The internal state variables of the constitutive model, in the order the model defines them (see Constitutive model (UMAT) catalog). Under finite strain, the tensorial ones of the kernels fed the logarithmic strain are components in the frame that follows the material (the material axes rotated with the body), not in the lab frame
TangentMatrix	(6, 6, N)	Tangent operator \(\mathbf{L}_t\) of the mechanical problem (record_tangent=True, the default)

Thermomechanical runs

A block of StepThermomeca steps adds the thermal histories and, with record_tangent, the coupled tangents in place of TangentMatrix:

Key	Shape	Content
Q	(N,)	Heat flux prescribed on the RVE
r	(N,)	Heat source
Wt	(3, N)	Thermal energies \([W_t, W_t^r, W_t^{ir}]\)
dSdE	(6, 6, N)	\(\partial\boldsymbol{\sigma}/\partial\boldsymbol{\varepsilon}\)
dSdT	(6, N)	\(\partial\boldsymbol{\sigma}/\partial T\)
drdE	(6, N)	\(\partial r/\partial\boldsymbol{\varepsilon}\)
drdT	(N,)	\(\partial r/\partial T\)

Q and r are of opposite signs: the solver enforces the 0D heat balance of the RVE, \(Q = -r\), at every increment. r is the heat rate the constitutive model produces (thermomechanical couplings and dissipation, net of the heat stored as \(\rho c_p \dot T\)) and Q the flux exchanged with the surroundings that balances it. An adiabatic step (thermal_control="heat_flux", Q = 0) therefore reads r = 0, the temperature rise absorbing the sources.

Completion status

res.status is 0 when the whole path ran, 1 when the solver aborted early (Newton loop not converging at the minimal increment). By default solve raises a RuntimeError on abort; solve(raise_on_abort=False) returns the partial history instead, so it can be inspected up to the failing increment.

Saving and tabulating

res.save("run.npz")                              # compressed numpy archive
res = sim.solver.SolverResults.load("run.npz")   # same object back

df = res.to_dataframe()                          # pandas DataFrame
df[["Time", "Strain_11", "Stress_11"]].to_csv("run.csv", index=False)

to_dataframe flattens the scalar histories and every 2-D history: the 6-component ones become <key>_11 … <key>_23 columns, Wm and Statev become Wm_0 … and Statev_0 …; the (3, 3, N) and (6, 6, N) histories are left out of the table and read from res directly.

Note

Pre-2.0, an output.dat file in data/ selected the measures written to a result text file. Nothing reads it any more: everything it could select is in SolverResults, and the C++ solver writes no file.