ThermoNTFA Documentation

The python package thermontfa with our reference implementation of the thermo-plastic NTFA contains following classes:

class thermontfa.TabularInterpolation(temps: ndarray = None, data: ndarray = None, const_extrapolate: bool = False)

Bases: object

Tabular interpolation for the thermo-mechanical NTFA

Performs a linear interpolation of the NTFA system matrices for a given temperature given tabular data at sufficiently many temperature points. It can be initialized with given tabular data or based on a HDF5 file (*.h5).

__init__(temps: ndarray = None, data: ndarray = None, const_extrapolate: bool = False) → None

Initialize the tabular interpolator for given data at prescribed temperatures temps.

Parameters:

  • temps (np.ndarray) – temperature points on which tabular data is available. The shape of the numpy array is expected to be (N_t,).

  • data (np.ndarray) – tabular data, e.g., a batch of NTFA system matrices with shape (N_t, ...).

  • const_extrapolate – If true, a constant extrapolation instead of a linear extrapolation is performed. The default value is false.

temps: ndarray = array([], dtype=float64)
temp_min: float = 0.0
temp_max: float = 0.0
dim: Tuple[int, ...] = ()
const_extrapolate: bool = False
data: ndarray = array([], dtype=float64)
classmethod from_h5(file_name: str, dset_temps: str, dset_data: str, transpose_dims: Tuple[int, ...] | None = None, const_extrapolate: bool = False) → Self

Initialize the tabular interpolator based on tabular data stored in a HDF5 file (*.h5).

This is a factory method and returns a new instance of the TabularInterpolation class. It is expected that the HDF5 file contains a data set with path dset_temps that contains a list of the temperature points on which tabular data is available. The shape of this dataset is expected to be (N_t,). Additionaly, the HDF5 file must contain a data set with path dset_data that contains the tabular data, e.g., a batch of NTFA system matrices with shape (N_t, ...). The order of axes/dimensions of the data set with path dset_data can be changed by transposing to the axis order given in transpose_dims.

Parameters:

  • file_name (str) – path of the HDF5 file

  • dset_temps (str) – path to the desired dataset in the HDF5 file

  • dset_data

  • const_extrapolate (bool) – “linear” or “constant”

  • transpose_dims (Tuple[int, ...], optional) – axis order for transposition

Returns:

new instance of the TabularInterpolation class

Return type:

TabularInterpolation

interpolate(temp: float) → ndarray

Perform a linear interpolation based on the available tabular data at a given temperature temp

Parameters:

temp (float) – temperature point for interpolation

Returns:

interpolated quantity

Return type:

np.ndarray

class thermontfa.ThermoMechNTFA(file_name: str, group_name: str, sig_y: Callable[[float, float, bool], float], N_max: int | None = None, tol: float = 0.0001, verbose: bool = False)

Bases: object

Thermo-mechanical NTFA

Represents a material routine that describes the effective behavior of a thermo-elasto-plastic composite material with temperature-dependent material parameters in both phases.

__init__(file_name: str, group_name: str, sig_y: Callable[[float, float, bool], float], N_max: int | None = None, tol: float = 0.0001, verbose: bool = False) → None

Initialize the thermo-mechanical NTFA from an HDF5 file (*.h5)

Seek the data in HDF5 file named file_name within the group group_name. The following data sets containing tabular data for the NTFA are expected in the group: - temperatures: list of temperature points of the tabular data, shape: (N_temp,) - A_bar: shape: (N_temp, N_modes, 6) - C_bar: shape: (N_temp, 6, 6) - D_xi: shape: (N_temp, N_modes, N_modes) - tau_theta: shape: (N_temp, 6) - tau_xi: shape: (N_temp, N_modes)

In addition, the group in the HDF5 file must contain the following data sets: - v_frac: volume fraction of the different phases - SIG_phases: stress data different phases

Parameters:

  • file_name (str) – path to the HDF5 file

  • group_name (str) – group in the HDF5 file that contains the NTFA tabular data

  • sig_y (Callable[[float, float, bool], float]) – function/callable that returns the yield stress sig_y(theta, q_n, derivative) given the temperature theta and the current isotropic hardening variable q_n. If derivative = True, the derivative should also be returned.

  • N_max (int) – maximum number of NTFA modes that should be used. If None, all available modes are used.

  • verbose (bool) – If debug information should be printed.

file_name: str
group_name: str
sig_y: Callable[[float, float, bool], float]
tol: float
verbose: bool = False
A_bar: TabularInterpolation
C_bar: TabularInterpolation
D_xi: TabularInterpolation
tau_theta: TabularInterpolation
tau_xi: TabularInterpolation
sig_phases: List
interpolate(theta: float) → None

Interpolate NTFA matrices to current temperature theta if the given tolerance is exceeded

Parameters:

theta – Temperature

stress(eps: ndarray, theta: float, xi: ndarray, i_phase: int | None = None)

Compute the stress given strain eps, plastic mode activations xi. If i_phase is given, the stress is computed only for the phase with index i_phase.

Parameters:

  • eps (int, optional) – Strain

  • theta – Temperature

  • xi – Plastic mode activations

  • i_phase – Phase index for the stress computation. If None, overall stress is computed.

Returns:

Computed stress

UMAT_mixed(eps_idx: ndarray, eps_n: ndarray, deps: ndarray, sig_bc: ndarray, theta: float, q_n: float, xi_n: ndarray) → Tuple[ndarray, ndarray, ndarray, float, ndarray]

Run the UMAT using partial eps-BC, e.g., uniaxial tension test.

Parameters:

  • eps_idx (nd-array, dtype=int) – Indices of eps that are prescribed. If None, then all components of sig_bc are prescribed.

  • eps_n (nd-array, dtype=float, shape=[6]) – Strain at the beginning of the increment.

  • deps (nd-array, dtype=float, shape=[6]) – Strain increment. Only deps[eps_idx] is used.

  • sig_bc (nd-array, dtype=float, shape=[6]) – Stress at the end of the increment. Only non eps_idx components are used.

  • theta (float) – Temperature at the end of the time increment.

  • q_n (float) – Hardening variable at the beginning of the time increment.

  • xi_n (nd-array, dtype=float) – Reduced coefficients at the beginning of the time increment.

Returns:

E - Full strain tensor at the end of the increment, i.e. the entries not within eps_idx are set

Return type:

np.ndarray, dtype=float, shape=[6]

Returns:

S - Stress at the end of the increment. Only S[eps_idx] is non-zero.

Return type:

np.ndarray, dtype=float

Returns:

C - Stiffness tensor at the end of the increment

Return type:

np.ndarray, dtype=float, shape=[6, 6]

Returns:

q - Hardening variable at the end of the time increment

Return type:

float

Returns:

xi - Reduced coefficients at the end of the time increment

Return type:

nd.ndarray, dtype=float

solve(eps: ndarray, deps: ndarray, theta: float, q_n: float, xi_n: ndarray) → Tuple[ndarray, float, ndarray, ndarray]

Solve for stress S, hardening variable q, reduced coefficients xi, and stiffness C given the strain eps, strain increment deps, temperature theta, hardening variable q_n, and reduced coefficients xi_n.

Parameters:

  • eps (np.ndarray) – Strain

  • deps (np.ndarray) – Strain increment

  • theta (float) – Temperature

  • q_n (float) – Hardening variable at the beginning of the time increment

  • xi_n (np.ndarray) – Reduced coefficients at the beginning of the time increment

Returns:

S - Stress

Return type:

np.ndarray

Returns:

q - Hardening variable at the end of the time increment

Return type:

float

Returns:

xi - Reduced coefficients at the end of the time increment

Return type:

np.ndarray

Returns:

C - Stiffness

Return type:

np.ndarray