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 , 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}).
x ˙
The time derivative of the independent variable. For example, if x is specified as above, then 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

Impact = { max ( k ( x 1 x ) e S T E P ( x , x 1 d , c max , x 1 , 0 ) x ˙ , 0 ) , i f   x < x 1 0 , i f   x x 1 }

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)"
/>