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1.10.0
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NEML2 1.4.0
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Refer to System Documentation for detailed explanation about this system.
Define the nonlinear parameter as a function of temperature according to the Arrhenius law \( p = p_0 \exp \left( -\frac{Q}{RT} \right) \), where \( p_0 \) is the reference value, \( Q \) is the activation energy, \( R \) is the ideal gas constant, and \( T \) is the temperature.
activation_energy Activation energyideal_gas_constant The ideal gas constantreference_value Reference valuetemperature TemperatureDetailed documentation link
Map the flow rate (i.e., the consistency parameter in the KKT conditions) to the rate of internal variables. This object calculates the rate of equivalent plastic strain following associative flow rule, i.e. \( \dot{\varepsilon}_p = - \dot{\gamma} \frac{\partial f}{\partial k} \), where \( \dot{\varepsilon}_p \) is the equivalent plastic strain, \( \dot{\gamma} \) is the flow rate, \( f \) is the yield function, and \( k \) is the isotropic hardening.
equivalent_plastic_strain_rate Rate of equivalent plastic strainflow_rate Flow rateisotropic_hardening_direction Direction of associative isotropic hardening which can be calculated using Normality.Detailed documentation link
Map the flow rate (i.e., the consistency parameter in the KKT conditions) to the rate of internal variables. This object calculates the rate of kinematic plastic strain following associative flow rule, i.e. \( \dot{\boldsymbol{K}}_p = - \dot{\gamma} \frac{\partial f}{\partial \boldsymbol{X}} \), where \( \dot{\boldsymbol{K}}_p \) is the kinematic plastic strain, \( \dot{\gamma} \) is the flow rate, \( f \) is the yield function, and \( \boldsymbol{X} \) is the kinematic hardening.
flow_rate Flow ratekinematic_hardening_direction Direction of associative kinematic hardening which can be calculated using Normality.kinematic_plastic_strain_rate Rate of kinematic plastic strainDetailed documentation link
Map the flow rate (i.e., the consistency parameter in the KKT conditions) to the rate of internal variables. This object calculates the rate of plastic strain following associative flow rule, i.e. \( \dot{\boldsymbol{\varepsilon}}_p = - \dot{\gamma} \frac{\partial f}{\partial \boldsymbol{M}} \), where \( \dot{\boldsymbol{\varepsilon}}_p \) is the plastic strain, \( \dot{\gamma} \) is the flow rate, \( f \) is the yield function, and \( \boldsymbol{M} \) is the Mandel stress.
flow_direction Flow direction which can be calculated using Normalityflow_rate Flow rateplastic_strain_rate Rate of plastic strainDetailed documentation link
Map the flow rate (i.e., the consistency parameter in the KKT conditions) to the rate of internal variables. This object defines the non-associative Chaboche kinematic hardening. In the Chaboche model, back stress is directly treated as an internal variable. Rate of back stress is given as \( \dot{\boldsymbol{X}} = \left( \frac{2}{3} C \frac{\partial f}{\partial \boldsymbol{M}} - g \boldsymbol{X} \right) \dot{\gamma} - A \lVert \boldsymbol{X} \rVert^{a - 1} \boldsymbol{X} \), including kinematic hardening, dynamic recovery, and static recovery. \( \frac{\partial f}{\partial \boldsymbol{M}} \) is the flow direction, \( \dot{\gamma} \) is the flow rate, and \( C \), \( g \), \( A \), and \( a \) are material parameters.
A Static recovery prefactorC Kinematic hardening coefficienta Static recovery exponentback_stress Back stressflow_direction Flow directionflow_rate Flow rateg Dynamic recovery coefficientDetailed documentation link
Compose multiple models together to form a single model. The composed model can then be treated as a new model and composed with others. The system documentation provides in-depth explanation on how the models are composed together.
additional_outputs Extra output variables to be extracted from the composed model in addition to the ones identified through dependency resolution.automatic_scaling Whether to perform automatic scaling. See neml2::NonlinearSystem::init_scaling for implementation details.automatic_scaling_miter Maximum number of automatic scaling iterations. No error is produced upon reaching the maximum number of scaling iterations, and the scaling matrices obtained at the last iteration are used to scale the nonlinear system.automatic_scaling_tol Tolerance used in iteratively updating the scaling matrices.models Models being composed togetherpriority Priorities of models in decreasing order. A model with higher priority will be evaluated first. This is useful for breaking cyclic dependency.Detailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Copy the value from one variable to another.
from Variable to copy value fromto Variable to copy value toDetailed documentation link
Calculate elastic strain given total and plastic strain (assuming additive decomposition), i.e. \( \boldsymbol{\varepsilon}_e = \boldsymbol{\varepsilon} - \boldsymbol{\varepsilon}_p \).
elastic_strain Elastic strainplastic_strain Plastic strainrate_form Whether the model defines the relationship in rate formtotal_strain Total strainDetailed documentation link
Calculates the elastic strain rate as \(\dot{\varepsilon} = d - d^p - \varepsilon w + w \varepsilon \) where \( d \) is the deformation rate, \( d^p \) is the plastic deformation rate, \( w \) is the vorticity, and \( \varepsilon \) is the elastic strain.
deformation_rate Name of the deformation rateelastic_strain Name of the elastic strainelastic_strain_rate Name of the elastic strain rateplastic_deformation_rate Name of the plastic deformation ratevorticity Name of the vorticityDetailed documentation link
Checks the value of the modified Rodrigues parameter by checking if \( \left\lVert r \right\rVert > t \), with \( t \) a threshold value set to 1.0 by default and replacing all the orientations that exceed this limit with their shadow parameters values.
input_orientation Name of input tensor of orientations to operate on.output_orientation Name of output tensorthreshold Threshold value for translating to the shadow parametersDetailed documentation link
Gurson-Tvergaard-Needleman yield function for poroplasticity. The yield function is defined as \( f = \left( \frac{\bar{\sigma}}{\sigma_y + k} \right)^2 + 2 q_1 \phi \cosh \left( \frac{1}{2} q_2 \frac{3\sigma_h-\sigma_s}{\sigma_y + k} \right) - \left( q_3 \phi^2 + 1 \right) \), where \( \bar{\sigma} \) is the von Mises stress, \( \sigma_y \) is the yield stress, \( k \) is isotropic hardening, \( \phi \) is the porosity, \( \sigma_h \) is the hydrostatic stress, and \( \sigma_s \) is the void growth back stress (sintering stress). \( q_1 \), \( q_2 \), and \( q_3 \) are parameters controlling the yield mechanisms.
flow_invariant Effective stress driving plastic flowisotropic_hardening Isotropic hardeningporo_invariant Effective stress driving porous flowq1 Parameter controlling the balance/competition between plastic flow and void evolution.q2 Void evolution rateq3 Pore pressurevoid_fraction Void fraction (porosity)yield_function Yield functionyield_stress Yield stressDetailed documentation link
Local mass balance used in conjunction with the GTNYieldFunction, \( \dot{\phi} = (1-\phi) \dot{\varepsilon}_p \).
plastic_strain_rate Plastic strain ratevoid_fraction Void fraction (porosity)void_fraction_rate Rate of void evolutionDetailed documentation link
Update an implicit model by solving the underlying implicit system of equations.
implicit_model The implicit model defining the implicit system of equations to be solvedsolver Solver used to solve the implicit systemDetailed documentation link
Map Cauchy stress to Mandel stress For isotropic material under small deformation, the Mandel stress and the Cauchy stress coincide.
cauchy_stress Cauchy stressmandel_stress Mandel stressDetailed documentation link
Calculates the Kocks-Mecking normalized activation as \(g = \frac{kT}{\mu b^3} \log \frac{\dot{\varepsilon}_0}{\dot{\varepsilon}} \) with \( \mu \) the shear modulus, \( k \) the Boltzmann constant, \( T \) the absolute temperature, \( b \) the Burgers vector length, \( \dot{\varepsilon}_0 \) a reference strain rate, and \( \dot{\varepsilon} \) the current strain rate.
activation_energy Output name of the activation energyb Magnitude of the Burgers vectoreps0 Reference strain ratek The Boltzmann constantshear_modulus The shear modulusstrain_rate Name of the effective strain ratetemperature Absolute temperatureDetailed documentation link
Switches between rate independent and rate dependent flow rules based on the value of the Kocks-Mecking normalized activation energy. For activation energies less than the threshold use the rate independent flow rule, for values greater than the threshold use the rate dependent flow rule. This version uses a soft switch between the models, based on a tanh sigmoid function.
activation_energy The input name of the activation energyflow_rate Output name for the mixed flow rateg0 Critical value of activation energyrate_dependent_flow_rate Input name of the rate dependent flow raterate_independent_flow_rate Input name of the rate independent flow ratesharpness A steepness parameter that controls the tanh mixing of the models. Higher values gives a sharper transition.Detailed documentation link
Calculates the temperature-dependent flow viscosity for a Perzyna-type model using the Kocks-Mecking model. The value is \( \eta = \exp{B} \mu \dot{\varepsilon}_0^\frac{-k T A}{\mu b^3} \) with \( \mu \) the shear modulus, \( \dot{\varepsilon}_0 \) a reference strain rate, \( b \) the Burgers vector, \( k\) the Boltzmann constant, \( T \) absolute temperature, \( A \) the Kocks-Mecking slope parameter, and \( B \) the Kocks-Mecking intercept parameter.
A The Kocks-Mecking slope parameterB The Kocks-Mecking intercept parameterb The Burgers vectoreps0 The reference strain ratek Boltzmann constantshear_modulus The shear modulustemperature Absolute temperatureDetailed documentation link
Calculates the temperature-dependent rate sensitivity for a Perzyna-type model using the Kocks-Mecking model. The value is \( n = \frac{\mu b^3}{k T A} \) with \( \mu \) the shear modulus, \( b \) the Burgers vector, \( k\) the Boltzmann constant, \( T \) absolute temperature, and \( A \) the Kocks-Mecking slope parameter.
A The Kocks-Mecking slope parameterb The Burgers vectork Boltzmann constantshear_modulus The shear modulustemperature Absolute temperatureDetailed documentation link
The yield stress given by the Kocks-Mecking model. \( \sigma_y = \exp{C} \mu \) with \( \mu \) the shear modulus and \( C \) the horizontal intercept from the Kocks-Mecking diagram.
C The Kocks-Mecking horizontal interceptshear_modulus The shear modulusDetailed documentation link
Relate elastic strain to stress for linear isotropic material. \( \boldsymbol{\sigma} = K \tr \boldsymbol{\varepsilon}_e + 2 G \text{dev} \boldsymbol{\varepsilon}_e \), where \( K \) and \( G \) are bulk and shear moduli, respectively. For convenience, this object only requests Young's modulus and Poisson's ratio, and handles the Lame parameter conversion behind the scenes.
compliance Whether the model defines the compliance relationship, i.e., mapping from stress to elastic strain. When set to false (default), the model maps elastic strain to stress.poisson_ratio Poisson's ratiorate_form Whether the model defines the stress-strain relationship in rate form. When set to true, the model maps elastic strain rate to stress rate.strain Elastic strainstress Stressyoungs_modulus Young's modulusDetailed documentation link
Map equivalent plastic strain to isotropic hardening following a linear relationship, i.e., \( k = H \varepsilon_p \) where \( H \) is the hardening modulus.
equivalent_plastic_strain Equivalent plastic strainhardening_modulus Hardening modulusisotropic_hardening Isotropic hardeningDetailed documentation link
Map kinematic plastic strain to back stress following a linear relationship, i.e., \( \boldsymbol{X} = H \boldsymbol{K}_p \) where \( H \) is the hardening modulus.
back_stress Back stresshardening_modulus Hardening moduluskinematic_plastic_strain Kinematic plastic strainDetailed documentation link
Simple linear slip system hardening defined by \( \dot{\tau} = \theta \sum_{i=1}^{n_{slip}} \left| \dot{\gamma}_i \right| \) where \( \theta \) is the hardening slope.
hardening_slope Hardening rateslip_hardening Name of current values of slip hardeningslip_hardening_rate Name of tensor to output the slip system hardening rates intosum_slip_rates Name of tensor containing the sum of the slip ratesDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a MillerIndex as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate MillerIndex defining the ordinate values of the interpolantDetailed documentation link
Object to setup a model for mixed stress/strain control. Copies the values of the fixed_values (the input strain or stress) and the mixed_state (the conjugate stress or strain values) into the stress and strain tensors used by the model.
cauchy_stress The name of the Cauchy stress tensorcontrol The name of the control signal. Values less than the threshold are strain control, greater are stress controlfixed_values The name of the fixed values, i.e. the actual strain or stress values being imposed on the modelmixed_state The name of the mixed state tensor. This holds the conjugate values to those being controlledstrain The name of the strain tensorthreshold The threshold to switch between strain and stress controlDetailed documentation link
Store the first derivatives of a scalar-valued function in given variables, i.e. \( u_i = \dfrac{f(\boldsymbol{v})}{v_i} \).
from Function arguments to take derivatives w.r.t.function Function to take derivativemodel The model which evaluates the scalar-valued functionto Variables to store the first derivativesDetailed documentation link
Define the Olevsky-Skorohod sintering stress to be used in conjunction with poroplasticity yield functions such as the GTNYieldFunction. The sintering stress is defined as \( \sigma_s = 3 \dfrac{\gamma}{r} \phi^2 \), where \( \gamma \) is the surface tension, \( r \) is the size of the particles/powders, and \( \phi \) is the void fraction.
particle_radius Particle radiussintering_stress Sintering stresssurface_tension Surface tensionvoid_fraction Void fractionDetailed documentation link
Defines the rate of the crystal orientations as a spin given by \( \Omega^e = w - w^p - \varepsilon d^p + d^p \varepsilon \) where \( \Omega^e = \dot{Q} Q^T \), \( Q \) is the orientation, \( w \) is the vorticity, \( w^p \) is the plastic vorticity, \( d^p \) is the plastic deformation rate, and \( \varepsilon \) is the elastic stretch.
elastic_strain The name of the elastic strain tensororientation_rate The name of the orientation rate (spin)plastic_deformation_rate The name of the plastic deformation rateplastic_vorticity The name of the plastic vorticityvorticity The name of the voriticty tensorDetailed documentation link
Calculate the over stress \( \boldsymbol{O} = \boldsymbol{M} - \boldsymbol{X} \), where \( \boldsymbol{M} \) is the Mandel stress and \( \boldsymbol{X} \) is the back stress.
back_stress Back stressmandel_stress Mandel stressover_stress Over stressDetailed documentation link
Perzyna's viscous approximation of the consistent yield envelope (with a power law), i.e. \( \dot{\gamma} = \left( \frac{\left< f \right>}{\eta} \right)^n \), where \( f \) is the yield function, \( \eta \) is the reference stress, and \( n \) is the power-law exponent.
exponent Power-law exponentflow_rate Flow ratereference_stress Reference stressyield_function Yield functionDetailed documentation link
Caclulates the plastic deformation rate as \( d^p = \sum_{i=1}^{n_{slip}} \dot{\gamma}_i Q \operatorname{sym}{\left(d_i \otimes n_i \right)} Q^T \) with \( d^p \) the plastic deformation rate, \( \dot{\gamma}_i \) the slip rate on the ith slip system, \(Q \) the orientation, \( d_i \) the slip system direction, and \( n_i \) the slip system normal.
crystal_geometry_name The name of the Data object containing the crystallographic information for the materialorientation The name of the orientation matrix tensorplastic_deformation_rate The name of the plastic deformation rate tensorslip_rates The name of the tensor containg the current slip ratesDetailed documentation link
Caclulates the plastic vorcitity as \( w^p = \sum_{i=1}^{n_{slip}} \dot{\gamma}_i Q \operatorname{skew}{\left(d_i \otimes n_i \right)} Q^T \) with \( d^p \) the plastic deformation rate, \( \dot{\gamma}_i \) the slip rate on the ith slip system, \(Q \) the orientation, \( d_i \) the slip system direction, and \( n_i \) the slip system normal.
crystal_geometry_name The name of the Data object containing the crystallographic information for the materialorientation The name of the orientation matrix tensorplastic_vorticity The name of the plastic vorticity tensorslip_rates The name of the tensor containg the current slip ratesDetailed documentation link
Power law slip rule defined as \( \dot{\gamma}_i = \dot{\gamma}_0 \left| \frac{\tau_i}{\hat{\tau}_i} \right|^{n-1} \frac{\tau_i}{\hat{\tau}_i} \) with \( \dot{\gamma}_i \) the slip rate on system \( i \), \( \tau_i \) the resolved shear, \( \hat{\tau}_i \) the slip system strength, \( n \) the rate senstivity, and \( \dot{\gamma}_0 \) a reference slip rate.
crystal_geometry_name Name of the Data object containing the crystallographic informationgamma0 Reference slip raten Rate sensitivity exponentresolved_shears Name of the resolved shear tensorslip_rates Name of the slip rate tensorslip_strengths Name of the tensor containing the slip system strengthsDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a Quaternion as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate Quaternion defining the ordinate values of the interpolantDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a R2 as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate R2 defining the ordinate values of the interpolantDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a R3 as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate R3 defining the ordinate values of the interpolantDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a R4 as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate R4 defining the ordinate values of the interpolantDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a R5 as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate R5 defining the ordinate values of the interpolantDetailed documentation link
Solve the consistent plasticity yield envelope by solving the equivalent complementarity condition
\[ r = \dot{\gamma} - f^p - \sqrt{{\dot{\gamma}}^2 + {f^p}^2} \]
flow_rate Flow rateyield_function Yield functionDetailed documentation link
Calculates the resolved shears as \( \tau_i = \sigma : Q \operatorname{sym}\left(d_i \otimes n_i \right) Q^T \) where \( \tau_i \) is the resolved shear on slip system i, \( \sigma \) is the Cauchy stress \( Q \) is the orientation matrix, \( d_i \) is the slip direction, and \( n_i \) is the slip system normal.
crystal_geometry_name The name of the data object with the crystallographic informationorientation The name of the orientation matrixresolved_shears The name of the resolved shearsstress The name of the Cauchy stress tensorDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a Rot as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate Rot defining the ordinate values of the interpolantDetailed documentation link
Convert a Rot (rotation represented in Rodrigues format) to R2 (a full rotation matrix).
from Rot to convertto R2 to store the resulting rotation matrixDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a SFFR4 as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate SFFR4 defining the ordinate values of the interpolantDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a SFR3 as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate SFR3 defining the ordinate values of the interpolantDetailed documentation link
Define the backward Euler time integration residual \( r = s - s_n - (t - t_n) \dot{s} \), where \(s\) is the variable being integrated, \(\dot{s}\) is the variable rate, and \(t\) is time. Subscripts \(n\) denote quantities from the previous time step.
automatic_scaling Whether to perform automatic scaling. See neml2::NonlinearSystem::init_scaling for implementation details.automatic_scaling_miter Maximum number of automatic scaling iterations. No error is produced upon reaching the maximum number of scaling iterations, and the scaling matrices obtained at the last iteration are used to scale the nonlinear system.automatic_scaling_tol Tolerance used in iteratively updating the scaling matrices.time Timevariable Variable being integratedvariable_rate Variable rateDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Calculate the first order discrete time derivative of a force variable as \( \dot{f} = \frac{f-f_n}{t-t_n} \), where \( f \) is the force variable, and \( t \) is time.
force The force variable to take time derivative withtime TimeDetailed documentation link
Perform forward Euler time integration defined as \( s = s_n + (t - t_n) \dot{s} \), where \(s\) is the variable being integrated, \(\dot{s}\) is the variable rate, and \(t\) is time. Subscripts \(n\) denote quantities from the previous time step.
time Timevariable Variable being integratedDetailed documentation link
Calculate the invariant of a symmetric second order tensor (of type SR2).
invariant Invariantinvariant_type Type of invariant. Options are I1, I2, and VONMISES.tensor SR2 which is used to calculate the invariant ofDetailed documentation link
Interpolate a SR2 as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate SR2 defining the ordinate values of the interpolantDetailed documentation link
Calculate the first order discrete time derivative of a state variable as \( \dot{s} = \frac{s-s_n}{t-t_n} \), where \( s \) is the state variable, and \( t \) is time.
state The state variable to take time derivative withtime TimeDetailed documentation link
Calculate linear combination of multiple SR2 tensors as \( u = c_i v_i \) (Einstein summation assumed), where \( c_i \) are the coefficients, and \( v_i \) are the variables to be summed.
coefficients Weights associated with each variablefrom_var SR2 tensors to be summedto_var The sumDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a SSFR5 as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate SSFR5 defining the ordinate values of the interpolantDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a SSR4 as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate SSR4 defining the ordinate values of the interpolantDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a SWR4 as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate SWR4 defining the ordinate values of the interpolantDetailed documentation link
Define the backward Euler time integration residual \( r = s - s_n - (t - t_n) \dot{s} \), where \(s\) is the variable being integrated, \(\dot{s}\) is the variable rate, and \(t\) is time. Subscripts \(n\) denote quantities from the previous time step.
automatic_scaling Whether to perform automatic scaling. See neml2::NonlinearSystem::init_scaling for implementation details.automatic_scaling_miter Maximum number of automatic scaling iterations. No error is produced upon reaching the maximum number of scaling iterations, and the scaling matrices obtained at the last iteration are used to scale the nonlinear system.automatic_scaling_tol Tolerance used in iteratively updating the scaling matrices.time Timevariable Variable being integratedvariable_rate Variable rateDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Calculate the first order discrete time derivative of a force variable as \( \dot{f} = \frac{f-f_n}{t-t_n} \), where \( f \) is the force variable, and \( t \) is time.
force The force variable to take time derivative withtime TimeDetailed documentation link
Perform forward Euler time integration defined as \( s = s_n + (t - t_n) \dot{s} \), where \(s\) is the variable being integrated, \(\dot{s}\) is the variable rate, and \(t\) is time. Subscripts \(n\) denote quantities from the previous time step.
time Timevariable Variable being integratedDetailed documentation link
Interpolate a Scalar as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate Scalar defining the ordinate values of the interpolantDetailed documentation link
Calculate the first order discrete time derivative of a state variable as \( \dot{s} = \frac{s-s_n}{t-t_n} \), where \( s \) is the state variable, and \( t \) is time.
state The state variable to take time derivative withtime TimeDetailed documentation link
Calculate linear combination of multiple Scalar tensors as \( u = c_i v_i \) (Einstein summation assumed), where \( c_i \) are the coefficients, and \( v_i \) are the variables to be summed.
coefficients Weights associated with each variablefrom_var Scalar tensors to be summedto_var The sumDetailed documentation link
Calculates the slip system strength for all slip systems as \( \hat{\tau}_i = \bar{\tau} + \tau_0 \) where \( \hat{\tau}_i \) is the strength for slip system i, \( \bar{\tau} \) is an evolving slip system strength (one value of all systems), defined by another object, and \( \tau_0 \) is a constant strength.
constant_strength The constant slip system strengthcrystal_geometry_name Name of the Data object containing the crystallographic informationslip_hardening The name of the evovling, scalar strengthslip_strengths Name of the slip system strengthsDetailed documentation link
Calculates the sum of the absolute value of all the slip rates as \( \sum_{i=1}^{n_{slip}} \left| \dot{\gamma}_i \right| \).
crystal_geometry_name The name of the Data object containing the crystallographic informationslip_rates The name of individual slip ratessum_slip_rates The outut name for the scalar sum of the slip ratesDetailed documentation link
Define the (cummulative, as opposed to instantaneous) linear isotropic thermal eigenstrain, i.e. \( \boldsymbol{\varepsilon}_T = \alpha (T - T_0) \boldsymbol{I} \), where \( \alpha \) is the coefficient of thermal expansion (CTE), \( T \) is the temperature, and \( T_0 \) is the reference (stress-free) temperature.
CTE Coefficient of thermal expansioneigenstrain Eigenstrainreference_temperature Reference (stress-free) temperaturetemperature TemperatureDetailed documentation link
Calculate the total strain by summing the elastic and plastic strain.
elastic_strain Elastic strainplastic_strain Plastic strainrate_form Whether to define the relationship in rate formtotal_strain Total strainDetailed documentation link
Define the backward Euler time integration residual \( r = s - s_n - (t - t_n) \dot{s} \), where \(s\) is the variable being integrated, \(\dot{s}\) is the variable rate, and \(t\) is time. Subscripts \(n\) denote quantities from the previous time step.
automatic_scaling Whether to perform automatic scaling. See neml2::NonlinearSystem::init_scaling for implementation details.automatic_scaling_miter Maximum number of automatic scaling iterations. No error is produced upon reaching the maximum number of scaling iterations, and the scaling matrices obtained at the last iteration are used to scale the nonlinear system.automatic_scaling_tol Tolerance used in iteratively updating the scaling matrices.time Timevariable Variable being integratedvariable_rate Variable rateDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a Vec as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate Vec defining the ordinate values of the interpolantDetailed documentation link
Voce isotropic hardening model, \( h = R \left[ 1 - \exp(-d \varepsilon_p) \right] \), where \( R \) is the isotropic hardening upon saturation, and \( d \) is the hardening rate.
equivalent_plastic_strain Equivalent plastic strainisotropic_hardening Isotropic hardeningsaturated_hardening Saturated isotropic hardeningsaturation_rate Hardening saturation rateDetailed documentation link
Voce hardening for a SingleSlipStrength type model defined by \( \dot{\tau} = \theta_0 \left( 1 - \frac{\tau}{\tau_f} \right) \sum_{i=1}^{n_{slip}} \left| \dot{\gamma}_i \right| \) where \( \theta_0 \) is the initial rate of work hardening, \( \tau_f \) is the saturated, maximum value of the slip system strength, and \( \dot{\gamma}_i \) is the slip rate on each system.
initial_slope The initial rate of hardeningsaturated_hardening The final, saturated value of the slip system strengthslip_hardening Name of current values of slip hardeningslip_hardening_rate Name of tensor to output the slip system hardening rates intosum_slip_rates Name of tensor containing the sum of the slip ratesDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Perform explicit discrete exponential time integration of a rotation. The update can be written as \( s = \exp\left[ (t-t_n)\dot{s}\right] \circ s_n \), where \( \circ \) denotes the rotation operator.
time Timevariable Variable being integratedDetailed documentation link
Define the implicit discrete exponential time integration residual of a rotation variable. The residual can be written as \( r = s - \exp\left[ (t-t_n)\dot{s}\right] \circ s_n \), where \( \circ \) denotes the rotation operator.
automatic_scaling Whether to perform automatic scaling. See neml2::NonlinearSystem::init_scaling for implementation details.automatic_scaling_miter Maximum number of automatic scaling iterations. No error is produced upon reaching the maximum number of scaling iterations, and the scaling matrices obtained at the last iteration are used to scale the nonlinear system.automatic_scaling_tol Tolerance used in iteratively updating the scaling matrices.time Timevariable Variable being integratedDetailed documentation link
Interpolate a WR2 as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate WR2 defining the ordinate values of the interpolantDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a WSR4 as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate WSR4 defining the ordinate values of the interpolantDetailed documentation link
A parameter that is just a constant value, generally used to refer to a parameter in more than one downstream object.
value The constant value of the parameterDetailed documentation link
Interpolate a WWR4 as a function of the given argument. See neml2::Interpolation for rules on shapes of the interpolant and the argument. This object performs a linear interpolation.
abscissa Scalar defining the abscissa values of the interpolantargument Argument used to query the interpolantordinate WWR4 defining the ordinate values of the interpolantDetailed documentation link
Classical macroscale plasticity yield function, \( f = \bar{\sigma} - \sigma_y - h \), where \( \bar{\sigma} \) is the effective stress, \( \sigma_y \) is the yield stress, and \( h \) is the isotropic hardening.
effective_stress Effective stressisotropic_hardening Isotropic hardeningyield_function Yield functionyield_stress Yield stressDetailed documentation link
1.10.0