tmdsimpy.jax.nlforces.RoughContactFriction¶

class tmdsimpy.jax.nlforces.RoughContactFriction(Q, T, ElasticMod, PoissonRatio, Radius, TangentMod, YieldStress, mu, u0=0, meso_gap=0, gaps=None, gap_weights=None, tangent_model='TAN', N_radial_quad=100)¶

Bases: NonlinearForce

Rough contact friction element nonlinearity with microslip.

Parameters:

Q(3, N) numpy.ndarray: Transformation matrix from system DOFs (N) to nonlinear DOFs (3).
T(N, 3) numpy.ndarray: Transformation matrix from local nonlinear forces to global nonlinear forces.
ElasticModfloat: Elastic modulus (in Pa) for contacting asperities.
PoissonRatiofloat: Poisson’s ratio for contacting asperities.
Radiusfloat: Initial undeformed effective asperity radius in meters (half of real radius of one asperity in general [1]).
TangentModfloat: Plasticity hardening modulus (in Pa) of asperities in contact.
YieldStressfloat: Yield strength / yield stress (in Pa) for contacting asperities (before plastic hardening).
mufloat: Friction coefficient for tangential force limit proportional to normal force.
u0float, (2,) numpy.ndarray, or (3,) numpy.ndarray, optional: Sets the starting position for AFT friction evaluations. If float, then both tangential directions take that value. If a (2,) numpy.ndarray, then it sets the two tangential directions with these two values. If a (3,) numpy.ndarray, then it sets all three directions with the given values (but the normal direction should be irrelevant). The default is 0.
meso_gapfloat, optional: Initial gap between contact due to other (e.g. mesoscale) topology. This gap is added to the gaps of all asperities in the integral. The default is 0.
gaps(Nasp,) numpy.ndarray: Initial gaps between asperities that forces should be calculated between (excluding mesoscale topology).
gap_weights(Nasp,) numpy.ndarray: Integration weights for forces between asperities with initial gaps defined by the variable gaps.
tangent_model{‘TAN’, ‘MIF’}, optional: Tangential force displacement relationship to use for asperities in contact. ‘TAN’ corresponds to just the tangential stiffness then complete slip at the friction coefficient. ‘MIF’ corresponds to the Mindlin-Iwan Fit model, which approximates asperity microslip [1]. The default is ‘TAN’.
N_radial_quadint, optional: Number of radial quadrature points to use for each contact asperity when using the tangent_model == ‘MIF’. The default is 100.

Notes

This class implements two rough contact models from [1] for use in [2]. The Mindlin Iwan Fit (MIF) model is implemented in frequency domain for the first time here and was used in frequency domain with plasticity normal contact for the first time in [2].

Implementation currently requires exactly three nonlinear DOFs corresponding to a single location. The Nonlinear DOFs must first be both tangential displacement then normal displacement.

Implementation uses automatic differentiation with JAX.

References

[1] (1,2,3)

Porter, J. H., and M. R. W. Brake, 2023, “Towards a predictive, physics-based friction model for the dynamics of jointed structures””, Mechanical Systems and Signal Processing. 192:110210. https://doi.org/10.1016/j.ymssp.2023.110210

[2] (1,2)

Porter, J. H., and M. R. W. Brake. Under Review. “Efficient Model Reduction and Prediction of Superharmonic Resonances in Frictional and Hysteretic Systems.” Mechanical Systems and Signal Processing. arXiv:2405.15918.

__init__(Q, T, ElasticMod, PoissonRatio, Radius, TangentMod, YieldStress, mu, u0=0, meso_gap=0, gaps=None, gap_weights=None, tangent_model='TAN', N_radial_quad=100)¶

Methods

`__init__`(Q, T, ElasticMod, PoissonRatio, ...)
`aft`(U, w, h[, Nt, tol, max_repeats, ...])	Implementation of the alternating frequency-time (AFT) method to extract harmonic nonlinear force coefficients.
`force`(X[, update_hist, return_aux])	Static force evaluation based on global displacements.
`init_history`()	Method to initialize history variables to zero force and displacement.
`local_force_history`(unlt, unltdot, h, cst, ...)	Evaluate the local forces for steady-state harmonic motion used in AFT.
`nl_force_type`()	Method to identify the force type as hysteretic.
`reset_real_mu`()	Resets friction coefficient to initial value.
`set_aft_initialize`(X)	Set an initial slider position with zero force for AFT calculation.
`set_prestress_mu`()	Sets friction coefficient to zero while saving initial value in a different variable.
`update_history`(uxyn, Fm_curr, fxy_curr, ...)	Updates hysteretic states to be the input displacement and force.

aft(U, w, h, Nt=128, tol=1e-07, max_repeats=2, return_local=False, calc_grad=True)¶

Implementation of the alternating frequency-time (AFT) method to extract harmonic nonlinear force coefficients.

Parameters:

U(N*Nhc,) numpy.ndarray: Displacement harmonic DOFs (global)
wfloat: Frequency in rad/s. Needed in case there is velocity dependency.
hnumpy.ndarray, sorted: List of harmonics. The list corresponds to Nhc harmonic components.
Ntint power of 2, optional: Number of time steps used in evaluation. The default is 128.
tolfloat, optional: This argument is ignored, and is included for compatability of interface. The default is 1e-7.
max_repeatsint, optional: Number of hysteresis loops to calculate to reach steady state. Maximum value allowed. The default is 2.
return_localbool, optional: If False, it uses self.Q and self.T to convert forces and gradients back to global domain. If True, it does not apply these transforms to the results. This should mainly be used for post-processing analysis of harmonic solutions. The default is False.
calc_gradbool, optional: Flag where True indicates that the gradients should be calculated and returned. If False, then returns only (Fnl,) as a tuple. The default is True.

Returns:

Fnl(N*Nhc,) numpy.ndarray: Nonlinear hamonic force coefficients in frequency domain.
dFnldU(N*Nhc,N*Nhc) numpy.ndarray: Jacobian of Fnl with respect to U
dFnldw(N*Nhc,) numpy.ndarray: Jacobian of Fnl with respect to w

Notes

The tolerance tol is ignored because slider model is expected to converge to steady-state with two cycles of the hysteresis loop. max_repeats is followed if more cycles are desired.

A numpy kron operation is utilized to convert forces back to physical domain. This operation may result in many unnecessary calculations that could be eliminated to speed up AFT.

force(X, update_hist=False, return_aux=False)¶

Static force evaluation based on global displacements.

Parameters:

X(N,) numpy.ndarray: Physical displacements for all DOFs of the system.
update_histbool, optional: Flag to update displacement and force history. The default is False.
return_auxbool, optional: Flag to return extra results about the simulation (aux) The default is False.

Returns:

F(N,) numpy.ndarray

Forces corresponding to physical DOFs.

dFdX(N,N) numpy.ndarray

Derivatives of forces F with respect to displacements X.

auxTuple of extra results includes (Fm_prev, deltabar, Rebar, a)

Fm_prev(Nasp,) numpy.ndarray: Maximum normal force for each asperity at the current instant or any previous instant.
fxy_curr(Nasp,2) numpy.ndarray or (Nasp,Nrad,2) numpy.ndarray: Sizes are for the ‘TAN’ and ‘MIF’ models respectively. Forces for ‘TAN’ or tractions for ‘MIF’ model at each integrated location.
deltabar(Nasp,) numpy.ndarray: Permanent deformation displacement of each asperity.
Rebar(Nasp,) numpy.ndarray: Flattened (new) radius of each asperity.
a(Nasp,) numpy.ndarray: Radius of contact area of each asperity.
quad_radii_curr(Nasp,Nrad) numpy.ndarray: Quadrature radial positions for each asperity (rows) and discrete radial locations (columns). Output is only relevant for the ‘MIF’ model and is irrelevant for the ‘TAN’ model.

Notes

When contact models are used in the presence of plasticity, static forces may behave poorly. Specifically, the contact radius is discontinuous upon normal load reversal and thus tangential stiffness is discontinuous. This can potentially cause a large jump in tangential force based on slight normal displacement variations and break solvers. This is not a problem for frequency domain approaches (e.g., aft) because the maximum displacement is known and all times can operate on the elastic unloading curve.

init_history()¶

Method to initialize history variables to zero force and displacement.

Returns:

None.

tmdsimpy.jax.nlforces.RoughContactFriction¶

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