pymecht.SampleExperiment module

class pymecht.SampleExperiment.SampleExperiment(mat_model, disp_measure, force_measure)[source]

Bases: object

An abstract class, which defines the sample geometry and experimental conditions. It also defines the coordinate system to be used.

disp_controlled(inp, params=None)[source]

Simulates the experiment with the deformation measure as the input

Parameters:

  • inp (scalar, list, or numpy array) – The input to the experiment. It can be a scalar, a list, or a numpy array

  • params (ParamDict or dict) – A dictionary of parameters. If None, the default parameters are used. The default is None.

Returns:

The resulting force measure. It is a scalar if the input is a scalar, a list if the input is a list, and a numpy array if the input is a numpy array.

Return type:

scalar, list, or numpy array

force_controlled(forces, params=None, x0=None)[source]

Simulates the experiment with the force measure as the input (solves via Newton iteration)

Parameters:

  • forces (scalar, list, or numpy array) – The input to the experiment. It can be a scalar, a list, or a numpy array

  • params (ParamDict or dict) – A dictionary of parameters. If None, the default parameters are used. The default is None.

  • x0 (scalar or numpy array) – The initial guess for the displacement. If None, the default is used. The default is None.

Returns:

The resulting deformation measure. It is a scalar if the input is a scalar, a list if the input is a list, and a numpy array if the input is a numpy array.

Return type:

scalar, list, or numpy array

property parameters

Parameters of the sample and the material model(s) constituting it, as a ParamDict

class pymecht.SampleExperiment.LinearSpring(mat_model=<class 'pymecht.MatModel.MatModel'>, disp_measure='stretch', force_measure='force')[source]

Bases: SampleExperiment

For simulating a linear spring (can be used to apply Robin boundary condition)

Parameter

Description (default)

L0

Length of spring (1)

k0

Stiffness (1)

f0

Force (0)

A0

Cross-section area (1)
Parameters:

  • mat_model (MatModel) – A material model object of type MatModel (not used), default MatModel()

  • disp_measure (str) –

    The measure of displacement with the following options:

    • ’stretch’ : Ratio of deformed to reference length (default)

    • ’deltal’ : Change in length or radius

    • ’length’ or ‘radius’ : Deformed length/radius

  • force_measure (str) –

    The measure of force with the following options:

    • ’force’ : Force acting on the spring (default)

    • ’stress’ : The Cauchy stress

    • ’pressure’ : The pressure

class pymecht.SampleExperiment.UniaxialExtension(mat_model, disp_measure='stretch', force_measure='cauchy')[source]

Bases: SampleExperiment

For simulating uniaxial extension of a sample

Parameter

Description (default)

L0

Length of sample (1)

A0

Cross-section area (1)
Parameters:

  • mat_model (MatModel) – A material model object of type MatModel

  • disp_measure (str) –

    The measure of displacement with the following options:

    • ’stretch’ : The stretch ratio (default)

    • ’strain’ : The Green-Lagrange strain

    • ’deltal’ : The change in length

    • ’length’ : The length

  • force_measure (str) –

    The measure of force with the following options:

    • ’force’ : The force per unit area

    • ’cauchy’ : The Cauchy stress (default)

    • ’1pk’ or ‘1stpk’ or ‘firstpk’ : The first Piola-Kirchhoff stress

    • ’2pk’ or ‘2ndpk’ or ‘secondpk’ : The second Piola-Kirchhoff stress

class pymecht.SampleExperiment.PlanarBiaxialExtension(mat_model, disp_measure='stretch', force_measure='cauchy')[source]

Bases: SampleExperiment

For simulating planar biaxial extension of a planar sample

Parameter

Description (default)

L10

Ref length: 1st axis (1)

L20

Ref length: 2nd axis (1)

thick

Sample thicknesse (1)
Parameters:

  • mat_model (MatModel) – A material model object of type MatModel

  • disp_measure (str) –

    The measure of displacement with the following options:

    • ’stretch’ : The stretch ratio (default)

    • ’strain’ : The Green-Lagrange strain

    • ’deltal’ : The change in length

    • ’length’ : The length

  • force_measure (str) –

    The measure of force with the following options:

    • ’force’ : The force per unit area

    • ’tension’ : The force per unit thickness

    • ’cauchy’ : The Cauchy stress (default)

    • ’1pk’ or ‘1stpk’ or ‘firstpk’ : The first Piola-Kirchhoff stress

    • ’2pk’ or ‘2ndpk’ or ‘secondpk’ : The second Piola-Kirchhoff stress

class pymecht.SampleExperiment.TubeInflation(mat_model, disp_measure='radius', force_measure='pressure')[source]

Bases: SampleExperiment

For simulating uniform axisymmetric inflation of a tube

Parameter

Description (default)

Ri

Internal radius (1)

thick

Thickness (0.1)

omega

Opening angle (radians) (0)

L0

Length of sample (1)

lambdaZ

Longitudinal stretch (1)
Parameters:

  • mat_model (MatModel) – A material model object of type MatModel

  • disp_measure (str) –

    The measure of displacement with the following options:

    • ’stretch’ : Ratio of deformed to reference internal radius

    • ’deltar’ : Change in internal radius

    • ’radius’ : Deformed internal radius (default)

    • ’area’ : Deformed internal area

  • force_measure (str) –

    The measure of force with the following options:

    • ’force’ : Total force acting on the tube length

    • ’pressure’ : Internal pressure acting on the tube (default)

disp_controlled(inp, params=None)[source]

Simulates the experiment with the deformation measure as the input

Parameters:

  • inp (scalar, list, or numpy array) – The input to the experiment. It can be a scalar, a list, or a numpy array

  • params (ParamDict or dict) – A dictionary of parameters. If None, the default parameters are used. The default is None.

Returns:

The resulting force measure. It is a scalar if the input is a scalar, a list if the input is a list, and a numpy array if the input is a numpy array.

Return type:

scalar, list, or numpy array

outer_radius(inp, params)[source]

Computes the outer radius of the tube at the given deformed state

Parameters:

  • inp (scalar, list, or numpy array) – Deformation measure at which the outer radius is to be computed

  • params (ParamDict or dict) – The parameters of the material model

Returns:

The outer radius of the tube

Return type:

scalar

cauchy_stress(inp, params=None, n=10, pressure=None)[source]

Computes the Cauchy stress at the given inp points

Parameters:

  • inp (scalar) – Deformation measure at which the stress is to be computed, scalar

  • params (ParamDict or dict) – A dictionary of parameters. If None, the default parameters are used. The default is None.

  • n (int) – The number of points along the thickness to report stresses at, default is 10

  • pressure (scalar) – The pressure corresponding to the deformed radius (optional: if not provided, it will be computed)

Returns:

xi : Normalized thickness values at which the stresses are reported (n points)

Stresses : The Cauchy stress tensors at the thickness locations (nX3X3 array)

Return type:

tuple (xi,Stresses)

class pymecht.SampleExperiment.LayeredSamples(*samplesList)[source]

Bases: object

An abstract class that allows building samples with layers

property parameters

Parameters of the layered sample and the material model(s) constituting each layer, as a ParamDict

disp_controlled(inp, params=None)[source]

Simulates the experiment with the deformation measure as the input

Parameters:

  • inp (scalar, list, or numpy array) – The input to the experiment. It can be a scalar, a list, or a numpy array

  • params (ParamDict or dict) – A dictionary of parameters. If None, the default parameters are used. The default is None.

Returns:

The resulting force measure. It is a scalar if the input is a scalar, a list if the input is a list, and a numpy array if the input is a numpy array.

Return type:

scalar, list, or numpy array

force_controlled(forces, params=None, x0=None)[source]

Simulates the experiment with the force measure as the input (solves via Newton iteration)

Parameters:

  • forces (scalar, list, or numpy array) – The input to the experiment. It can be a scalar, a list, or a numpy array

  • params (ParamDict or dict) – A dictionary of parameters. If None, the default parameters are used. The default is None.

  • x0 (scalar or numpy array) – The initial guess for the displacement. If None, the default is used. The default is None.

Returns:

The resulting deformation measure. It is a scalar if the input is a scalar, a list if the input is a list, and a numpy array if the input is a numpy array.

Return type:

scalar, list, or numpy array

class pymecht.SampleExperiment.LayeredUniaxial(*samplesList)[source]

Bases: LayeredSamples

A class for building layered uniaxial samples

Parameters:

*samplesList (list of UniaxialExtension) – Any number of UniaxialExtension objects constituting the layers

Examples

>>> import pymecht as pmt
>>> mat_model = pmt.MatModel('nh')
>>> s1 = pmt.UniaxialExtension(mat_model)
>>> s2 = pmt.UniaxialExtension(mat_model)
>>> s3 = pmt.UniaxialExtension(mat_model)
>>> layered_sample = pmt.LayeredUniaxial(s1,s2,s3)
class pymecht.SampleExperiment.LayeredPlanarBiaxial(*samplesList)[source]

Bases: LayeredSamples

A class for building layered biaxial samples

Parameters:

*samplesList (list of PlanarBiaxialExtension) – Any number of PlanarBiaxialExtension objects constituting the layers

Examples

>>> import pymecht as pmt
>>> mat_model = pmt.MatModel('nh')
>>> s1 = pmt.PlanarBiaxialExtension(mat_model)
>>> s2 = pmt.PlanarBiaxialExtension(mat_model)
>>> s3 = pmt.PlanarBiaxialExtension(mat_model)
>>> layered_sample = pmt.LayeredPlanarBiaxial(s1,s2,s3)
class pymecht.SampleExperiment.LayeredTube(*samplesList)[source]

Bases: LayeredSamples

A class for building layered tube samples

Parameters:

*samplesList (list of TubeInflation) – Any number of TubeInflation objects constituting the layers

Examples

>>> import pymecht as pmt
>>> mat_model = pmt.MatModel('nh')
>>> s1 = pmt.TubeInflation(mat_model)
>>> s2 = pmt.TubeInflation(mat_model)
>>> s3 = pmt.TubeInflation(mat_model)
>>> layered_sample = pmt.LayeredPlanarBiaxial(s1,s2,s3)
disp_controlled(inp, params=None)[source]

Simulates the experiment with the deformation measure as the input

Parameters:

  • inp (scalar, list, or numpy array) – The input to the experiment. It can be a scalar, a list, or a numpy array

  • params (ParamDict or dict) – A dictionary of parameters. If None, the default parameters are used. The default is None.

Returns:

The resulting force measure. It is a scalar if the input is a scalar, a list if the input is a list, and a numpy array if the input is a numpy array.

Return type:

scalar, list, or numpy array

cauchy_stress(inp, params=None, n=10)[source]

Computes the Cauchy stress at the given inp points

Parameters:

  • inp (scalar, list, or numpy array) – Deformation measure at which the stress is to be computed, scalar

  • params (ParamDict or dict) – The parameters of the material model

  • n (int) – The number of points along the thickness (of each layer) to report stresses at, default is 10

Returns:

xi : Normalized thickness values at which the stresses are reported (n points)

Stresses : The Cauchy stress tensors at the thickness locations ((nXnlayers)X3X3 array)

Return type:

tuple (xi,Stresses)

pymecht.SampleExperiment.specify_single_fiber(sample, angle=0, degrees=True, verbose=True)[source]

Assign single fiber direction to all materials in a sample

Parameters:

  • sample (SampleExperiment) – The sample to which fiber directions need to be assigned

  • angle (float or Param) –

    The angle of the fiber direction, default 0

    for UniaxialExtension or PlanarBiaxialExtension

    with respect to the x-axis and in the xy plane

    for TubeInflation

    with respect to the theta-axis and in the theta-z plane

  • degrees (bool) – If True, the angle is asssumed to be in degrees. If False, it is assumed to be in radians; default True

  • verbose (bool) – If True, the function prints the angle after assigning, default True

pymecht.SampleExperiment.specify_two_fibers(sample, angle, degrees=True, verbose=True)[source]

Assign two symmetric fiber directions to all materials in a sample

Parameters:

  • sample (SampleExperiment) – The sample to which fiber directions need to be assigned

  • angle (float or Param) –

    The angle of the fiber directions (assigned as \(\pm\) angle)

    for UniaxialExtension or PlanarBiaxialExtension

    with respect to the x-axis and in the xy plane

    for TubeInflation

    with respect to the theta-axis and in the theta-z plane

  • degrees (bool) – If True, the angle is asssumed to be in degrees. If False, it is assumed to be in radians; default True

  • verbose (bool) – If True, the function prints the angle after assigning, default True