contactlaw

ContactLawBase

Base class for contact laws. Define the relationship between the force and displacement increment

debugVariable instance-attribute

debugVariable: DebugVariable = DebugVariable()

Debug information

material instance-attribute

material: Material = Material(props)

The material.

name instance-attribute

name: str

The name of the contact law

options instance-attribute

options: Options = Options()

The options

CSL

CSL(idx: int, sv0: StateVariable, sv: StateVariable) -> float

Calculate critical void ratio. You must define the critical void ratio in the elastoplastic contact law, but it is not necessary for the nonlinear elastic contact law, though you can still define it to use in the nonlinear integration method.

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
ec	Critical void ratio TYPE: float

__init__

__init__(props: dict[str, float] = None)

Constructor for the base class of all contact laws.

abstractSetup

abstractSetup()

Post-initialization for the contact law.

check

check(idx: int, ddisp: ndarray, sv0: StateVariable, sv: StateVariable)

Check the increment is reasonable

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
ddisp	The displacement increment TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

dfdforce

dfdforce(idx: int, sv0: StateVariable, sv: StateVariable) -> ndarray

Calculate derivative of yield function with respect to the force:

\[ \frac{\partial F}{\partial \boldsymbol{f}} \]

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
dfdforce	Derivative of yield function with respect to the force TYPE: ndarray

dfdforce0

dfdforce0(idx: int, sv0: StateVariable, sv: StateVariable) -> ndarray

Calculate derivative of yield function with respect to the force:

\[ \frac{\partial F}{\partial \boldsymbol{f}} \]

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
dfdforce	Derivative of yield function with respect to the force TYPE: ndarray

dfdforce1

dfdforce1(idx: int, sv0: StateVariable, sv: StateVariable) -> ndarray

Calculate derivative of yield function with respect to the force:

\[ \frac{\partial F}{\partial \boldsymbol{f}} \]

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
dfdforce	Derivative of yield function with respect to the force TYPE: ndarray

dgdforce

dgdforce(idx: int, sv0: StateVariable, sv: StateVariable) -> ndarray

Calculate derivative of potential function with respect to the force:

\[ \frac{\partial G}{\partial \boldsymbol{f}} \]

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
dgdforce	Derivative of potential function with respect to the force TYPE: ndarray

dgdforce0

dgdforce0(idx: int, sv0: StateVariable, sv: StateVariable) -> ndarray

Calculate derivative of potential function with respect to the force:

\[ \frac{\partial G}{\partial \boldsymbol{f}} \]

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
dgdforce	Derivative of potential function with respect to the force TYPE: ndarray

dgdforce1

dgdforce1(
    idx: int, dfdforce: ndarray, sv0: StateVariable, sv: StateVariable
) -> ndarray

Calculate derivative of potential function with respect to the force:

\[ \frac{\partial G}{\partial \boldsymbol{f}} \]

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
dfdforce	Derivative of yield function with respect to the force TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
dgdforce	Derivative of potential function with respect to the force TYPE: ndarray

elasticStiffness

elasticStiffness(
    idx: int, fn: float, sv0: StateVariable, sv: StateVariable
) -> ndarray

Calculate the elastic stiffness matrix, a 3x3 matrix in the following form:

\[ \mathbf{K}_e = \begin{bmatrix} k_n & 0 & 0 \\ 0 & k_t & 0 \\ 0 & 0 & k_t \end{bmatrix} \]

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
fn	Normal force TYPE: float
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
Ke	Elastic stiffness matrix TYPE: ndarray

forceDisplacement

forceDisplacement(
    idx: int, ddisp: ndarray, Ke: ndarray, sv0: StateVariable, sv: StateVariable
) -> ndarray

Integrate the force-displacement contact law, update the following variables:

• sv.force: force

The following steps are performed:

• Go to the last step if the displacement increment is zero
• preIntegration: called before the integration
• integrate: integrate the force-displacement contact law to update the contact force
• postIntegration: called after the integration

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
ddisp	The displacement increment TYPE: ndarray
Ke	Elastic stiffness matrix TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
ndarray	The stiffness matrix

frictionCoefficient

frictionCoefficient(idx: int, sv0: StateVariable, sv: StateVariable) -> float

Calculate the friction coefficient combined with different criteria.

increment

increment(
    idx: int, ddisp: ndarray, Ke: ndarray, sv0: StateVariable, sv: StateVariable
) -> ndarray

Increment the displacement and calculate the force. The following steps are performed:

• preIncrement: called before the increment
• Return the stiffness matrix if the displacement increment is zero
• disp += ddisp: update the displacement
• K = stiffness: calculate the stiffness matrix
• force += K @ ddisp: update the force
• check: check the convergence
• postIncrement: called after the increment

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
ddisp	The displacement increment TYPE: ndarray
Ke	Elastic stiffness matrix TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
ndarray	The stiffness matrix

initialize

initialize(sv: StateVariable)

Initialize the state variables for the contact law

RETURNS	DESCRIPTION
sv	Initial state variables TYPE: StateVariable

integrate

integrate(
    idx: int, ddisp: ndarray, Ke: ndarray, sv0: StateVariable, sv: StateVariable
) -> ndarray

Integrate the force-displacement contact law, with a number of increments.

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
ddisp	The displacement increment calculated from the elastic trial from the force increment TYPE: ndarray
Ke	Elastic stiffness matrix TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
ndarray	The stiffness matrix at the end of the increment

maintainYieldSurface

maintainYieldSurface(
    idx: int,
    ddisp: ndarray,
    dforce: ndarray,
    sv0: StateVariable,
    sv: StateVariable,
)

Revert state variables from elastic state to maintain the force state on the yield surface

Notes

This method should be overridden when the force state is already plastic, but the mixed load iteration converges to the elastic state. This is similar to the yield surface correction method, but the force state is in the elastic region initially caused by the mixed load iteration. However, previous mixed load iteration indicates that the force state is already in the plastic region. This method is used to update the state variables to keep the force state on the yield surface.

If you override this method, make sure to initialize the sv.cscalars["plastic"] state variable to an array of zeros with the same size as the number of integration points in the initialize method of the contact law.

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
ddisp	Displacement increment TYPE: ndarray
dforce	Force increment TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	Current state variables TYPE: StateVariable

plasticModulus

plasticModulus(
    idx: int, dgdforce: ndarray, sv0: StateVariable, sv: StateVariable
) -> float

Plastic modulus in the equation of plastic multiplier including dgdforce, coefficient of plastic multiplier:

\[ \sum\frac{\partial F}{\partial\kappa}\frac{\partial\kappa}{\partial\boldsymbol{\delta}^p} \frac{\partial G}{\partial\boldsymbol{f}} \]

make sure to define the derivative of plastic multiplier with respect to plastic displacement dkappa_ddispp (\(\frac{\partial\kappa}{\partial\boldsymbol{\delta}^p}\)) attribute in this class since it will be used in the updateHardeningVariables method to update hardening variables.

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
dgdforce	Derivative of potential function with respect to the force TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
Kp	Plastic modulus in the equation of plastic multiplier TYPE: float

plasticModulus0

plasticModulus0(
    idx: int, dgdforce: ndarray, sv0: StateVariable, sv: StateVariable
) -> ndarray

Plastic modulus in the equation of plastic multiplier, coefficient of plastic multiplier:

\[ \sum\frac{\partial F}{\partial\kappa}\frac{\partial\kappa}{\partial\boldsymbol{\delta}^p} \]

make sure to define the derivative of plastic multiplier with respect to plastic displacement dkappa_ddispp (\(\frac{\partial\kappa}{\partial\boldsymbol{\delta}^p}\)) attribute in this class since it will be used in the updateHardeningVariables method to update hardening variables.

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
dgdforce	Derivative of potential function with respect to the force TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
Kp	Plastic modulus in the equation of plastic multiplier TYPE: ndarray

plasticModulus1

plasticModulus1(
    idx: int, dgdforce: ndarray, sv0: StateVariable, sv: StateVariable
) -> float

Plastic modulus in the equation of plastic multiplier including dgdforce, coefficient of plastic multiplier:

\[ \sum\frac{\partial F}{\partial\kappa}\frac{\partial\kappa}{\partial\boldsymbol{\delta}^p} \frac{\partial G}{\partial\boldsymbol{f}} \]

make sure to define the derivative of plastic multiplier with respect to plastic displacement dkappa_ddispp (\(\frac{\partial\kappa}{\partial\boldsymbol{\delta}^p}\)) attribute in this class since it will be used in the updateHardeningVariables method to update hardening variables.

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
dgdforce	Derivative of potential function with respect to the force TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
Kp	Plastic modulus in the equation of plastic multiplier TYPE: float

postIncrement

postIncrement(
    idx: int, ddisp: ndarray, sv0: StateVariable, sv: StateVariable
) -> None

Post-processing after each increment for the contact law

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
ddisp	The displacement increment TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

postIntegration

postIntegration(
    idx: int, ddisp: ndarray, sv0: StateVariable, sv: StateVariable
) -> None

Post-processing after the contact integration

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
ddisp	The displacement increment TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

potentialFunction

potentialFunction(
    idx: int, fn: float, fr: float, sv0: StateVariable, sv: StateVariable
) -> float

Calculate potential function. You are required to define the potential function of the contact force and the state variables:

\[ G = G(\boldsymbol{f}, \kappa) \]

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
fn	Normal force TYPE: float
fr	Shear force TYPE: float
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
float	Value of the potential function

preIncrement

preIncrement(
    idx: int, ddisp: ndarray, sv0: StateVariable, sv: StateVariable
) -> None

Pre-processing before each increment for the contact law

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
ddisp	The displacement increment TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

preIntegration

preIntegration(
    idx: int, ddisp: ndarray, sv0: StateVariable, sv: StateVariable
) -> None

Pre-processing before the contact integration

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
ddisp	The displacement increment TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

setup

setup()

Set up specific contact law.

stiffness

stiffness(
    idx: int, ddisp: ndarray, sv0: StateVariable, sv: StateVariable
) -> ndarray

Stiffness matrix for the contact law. You are required to define the nonlinear relationship between the force and displacement increment:

\[ \begin{bmatrix} \mathrm{d}f_n \\ \mathrm{d}f_s \\ \mathrm{d}f_t \end{bmatrix} = \begin{bmatrix} K_{nn} & K_{ns} & K_{nt} \\ K_{sn} & K_{ss} & K_{st} \\ K_{tn} & K_{ts} & K_{tt} \end{bmatrix} \begin{bmatrix} \mathrm{d}\delta_n \\ \mathrm{d}\delta_s \\ \mathrm{d}\delta_t \end{bmatrix} \]

symmetricContactScalars

symmetricContactScalars() -> List[str]

Symmetric contact scalar variables.

symmetricContactVectors

symmetricContactVectors() -> List[str]

Symmetric contact vector variables.

updateHardeningVariables

updateHardeningVariables(
    idx: int,
    dlambda: float,
    ddispp: ndarray,
    sv0: StateVariable,
    sv: StateVariable,
)

Update hardening variables, the derivative of plastic multiplier with respect to plastic strain is available in the dkappa_ddispp (:math:\frac{\partial\kappa}{\partial\boldsymbol{\delta}^p}) attribute:

\[ \mathrm{d}\kappa = \frac{\partial\kappa}{\partial\boldsymbol{\delta}^p}\mathrm{d}\boldsymbol{\delta}^p \]

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
dlambda	Plastic multiplier TYPE: float
ddispp	Plastic displacement increment TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

yieldFunction

yieldFunction(
    idx: int, fn: float, fr: float, sv0: StateVariable, sv: StateVariable
) -> float

Calculate yield function. You are required to define the yield function of the contact force and the state variables:

\[ F = F(\boldsymbol{f}, \kappa) \]

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
fn	Normal force TYPE: float
fr	Shear force TYPE: float
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
float	Value of the yield function

yieldFunctionCorrection

yieldFunctionCorrection(
    idx: int, Ke: ndarray, sv0: StateVariable, sv: StateVariable
)

Update state variables after every plastic increment to keep the force state on the yield surface

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
Ke	The stiffness matrix TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

yieldFunctions

yieldFunctions(
    idx: int, fn: ndarray, fr: ndarray, sv0: StateVariable, sv: StateVariable
) -> ndarray

Calculate yield function for multiple times

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
fn	Normal force TYPE: ndarray
fr	Shear force TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	State variables TYPE: StateVariable

RETURNS	DESCRIPTION
ndarray	Values of the yield function

ElastoplasticContactLaw

Bases: ContactLawBase

Base class for elastoplastic contact laws.

plasticMethod instance-attribute

plasticMethod: str

The plastic method

CPPM

CPPM(
    idx: int, Ke: ndarray, ddisp: ndarray, sv0: StateVariable, sv: StateVariable
) -> ndarray

Solve plastic problem (plastic strain) with the closest point projection method (CPPM)

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
Ke	The stiffness matrix TYPE: ndarray
ddisp	Displacement increment TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	Current state variables TYPE: StateVariable

RETURNS	DESCRIPTION
Kep	Elasto-plastic stiffness matrix TYPE: ndarray

ExplicitCPA

ExplicitCPA(
    idx: int, Ke: ndarray, ddisp: ndarray, sv0: StateVariable, sv: StateVariable
) -> ndarray

Solve plastic problem (plastic strain) with the explicit or cutting plane algorithm (CPA)

PARAMETER	DESCRIPTION
idx	Index of the integration point TYPE: int
Ke	The stiffness matrix TYPE: ndarray
ddisp	Displacement increment TYPE: ndarray
sv0	Initial state variables TYPE: StateVariable
sv	Current state variables TYPE: StateVariable

RETURNS	DESCRIPTION
Kep	Elasto-plastic stiffness matrix TYPE: ndarray

abstractSetup

abstractSetup()

isCPA

isCPA() -> bool

Whether tha plastic method is CPA.

isCPPM

isCPPM() -> bool

Whether tha plastic method is CPPM.

isExplicit

isExplicit() -> bool

Whether tha plastic method is explicit.

setPlasticMethod

setPlasticMethod(method: str)

Set the plastic method

PARAMETER	DESCRIPTION
method	The plastic method TYPE: str

stiffness

stiffness(
    idx: int, ddisp: ndarray, sv0: StateVariable, sv: StateVariable
) -> ndarray

NonlinearElasticContactLaw

Bases: ContactLawBase

Nonlinear elastic contact law

dfdforce

dfdforce(idx: int, sv0: StateVariable, sv: StateVariable) -> ndarray

postIncrement

postIncrement(
    idx: int, ddisp: ndarray, sv0: StateVariable, sv: StateVariable
) -> None

yieldFunction

yieldFunction(
    idx: int, fn: float, fr: float, sv0: StateVariable, sv: StateVariable
) -> float