IMPACT

The IMPACT function models impact forces acting on bodies during collision. The elastic properties of the boundary surface between the two bodies can be tuned as desired.

Format

$Impact (x, \dot{x}, x_{1}, k, e, c_{\max}, d)$

Arguments

$x$: The independent variable. For example, to use the z-displacement of I marker with respect to J marker as resolved in the reference frame of RM marker as the independent variable, specify $x$ as DZ({marker_i.idstring}, {marker_j.idstring}, {marker_rm.idstring}).
$\dot{x}$: The time derivative of the independent variable. For example, if $x$ is specified as above, then $\dot{x}$ will be VZ({marker_i.idstring}, {marker_j. idstring}, {marker_rm.idstring}).
$x_{1}$: The lower bound of $x$ . If $x$ is less than $x_{1}$ , the impact function returns a positive value, otherwise it returns zero.
$k$: The stiffness of the boundary surface interaction. It must be non-negative.
$e$: The exponent of the force deformation characteristic. For a stiffening spring characteristic, $e$ must be greater than 1.0 and for a softening spring characteristic, $e$ must be less than 1.0. It must always be positive.
$c_{\max}$: The maximum damping coefficient. It must be non-negative.
$d$: The penetration at which the full damping coefficient is applied. It must be positive.

Definition

(1)

Impact = {\begin{matrix} \max (k {(x_{1} - x)}^{e} - S T E P (x, x_{1} - d, c_{\max}, x_{1}, 0) * \dot{x}, 0), & i f x < x_{1} \\ 0, & i f x \geq x_{1} \end{matrix}}

Example

<Reference_Variable
     id                    = "30300700"
     type                  = "EXPRESSION"
     expr                  = "IMPACT(DZ(10301030,30302030),
                              VZ(10301030,30302030),2.5,2500,1,1000,2.5)"
/>
OR
<Force_Vector_TwoBody
     id                    = "10501"
     type                  = "ForceOnly"
     i_marker_id           = "10515721"
     j_floating_marker_id  = "10516722"
     ref_marker_id         = "10516720"
     fx_expression         = "0"
     fy_expression         = "0"
     fz_expression         = "IMPACT(DZ(10515720,10516720,10515720),
                              VZ(10515720,10516720,10515720),1,10000.0,1.0,0.5,0.1)"
/>