Simcenter Madymo How can I define rate dependency in a surface compliance contact characteristic?

Surface compliance definition for characteristic-based contact definitions

In so-called "characteristic-based" contact definitions in Simcenter Madymo, the compression of (one or both of) the surface(s) in contact is represented by the penetration depth of the (non-deforming) surfaces in contact. To determine the contact forces following the surface penetration, a surface compliance characteristic needs to be assigned to the surface. Such a compliance characteristic is defined using the element CHARACTERISTIC.CONTACT. 

In CHARACTERISTIC.CONTACT, the surface compliance can be defined as a force-penetration characteristic (CONTACT_MODEL=FORCE) or a stress-strain characteristic (CONTACT_MODEL=STRESS). The characteristic can include both reversible and dissipative components, where the reversible component is set via LOAD_FUNC (defined as a force-penetration or stress-strain function (defined in FUNCTION.XY).

Dissipative components of the surface compliance characteristic can be modeled through hysteresis and/or damping. Hysteresis modelling is often found to be misused to represent dissipation that is actually rate-dependent behavior of the material in contact. Where hysteresis modelling can well be used to model for instance plastic deformation (HYS_MODEL=1), rate-dependent behavior should be modelled using damping components.

For a force-based contact characteristic (without hysteresis included), the contact force is calculated as:

   

where F = total contact force, F_e = elastic contact force (LOAD_FUNC), λ = contact penetration, C_d = damping coefficient (DAMP_COEF), F_d  = damping force (DAMP_VEL_FUNC)  and f_d  = damping amplification factor (DAMP_AMP_FUNC).
 

Example model

The simple example model that is attached to this article, illustrates how DAMP_VEL_FUNC and DAMP_AMP_FUNC under CHARACTERISTIC.CONTACT can be used to model rate dependency in surface compliance characterization. In this example a force-penetration (CONTACT_MODEL=FORCE) characteristic is defined, which is assigned to a SURFACE.PLANE_CENTRE. The surface with compliance characteristic represents the top surface on a foam pad, on which a rigid ball (SURFACE.ELLIPSOID) is dropped. The contact between the ball and foam surface is defined using CONTACT.MB_MB, referring to the master surface (the plane surface with foam characteristic assigned to it) as the compliant surface (CONTACT_TYPE=MASTER).



The function 'FoamCntLO_fun' is used as LOAD_FUNC to define the elastic component of the plate surface compliance. While DAMP_COEF is not used (left equal to 0), rate dependent dissipation is defined using only the damping force function DAMP_VEL_FUNC ('FoamCntDV_fun') and the damping amplification factor function DAMP_AMP_FUNC ('FoamCntDA_fun'). A good reason for not using DAMP_COEF in contact characteristics is that contact damping forces could become extremely high when for example airbag fabric FE nodes would make contact (sometimes having nodal velocities in the hundreds of meters per second). 

By defining a linear x=y function for the DAMP_AMP_FUNC, the damping amplification factor is kept equal to the elastic force for all levels of compression (contact penetration). This then allows us to use DAMP_VEL_FUNC to define the ratio between damping and elastic force as a function of the penetration rate. Note that DAMP_AMP_FUNC is defined in the first quadrant only (as no negative elastic forces occur in contact), where DAMP_VEL_FUNC is defined in the first and third quadrant (penetration rates are positive for loading phase and negative in unloading phase).

In the example model, the ratio between damping and elastic force is set constant for higher penetration rates, using a DEFINE variable (set to 0.25 in picture below). For lower penetration rates (< 1m/s), the function drops off smoothly to avoid step-wise contact force changes during transitions from loading to unloading phase and vice-versa.







To illustrate the effect of the rate dependency defined in the compliance characteristic, results from two simulations are compared in the picture below. In red the response with ratio between damping and elastic components set to 0.05; in green the response with ratio between damping and elastic components set to 0.25. Next to the overlayed kinematics at end time (500ms), the plots on the right show the contact-force-versus-penetration cycles during times of contact (upper) and the ball height above the foam surface versus time (lower). As expected, a higher ratio results in more dissipation during contact and thus a lower rebound of the ball out of the foam.

Further remarks

Some limitations to the definition and use of damping in contact characteristics:

• for FORCE-based contact characteristics (CONTACT_MODEL = FORCE) referred to in CONTACT.FE_FE, the damping parameters and functions in the characteristic are not considered and NO damping forces are applied.
• for STRESS-based contact characteristics (CONTACT_MODEL = STRESS), damping forces work ONLY in the contact loading phase (positive penetration rates), in the unloading phase (negative penetration rates), NO damping forces are applied.