The bead is considered to represent the center of mass of an element, and they are connected with SLS model; each SLS element contains of two Hookean springs and a dashpot
, also referred to as the Newton model or the perfect liquid, is the viscous element in which the force is proportional to the rate of extension.
For the network represented by the spring and the dashpot
at the bottom, the stretches ([[lambda].sub.1], [[lambda].sub.2]) are due to both the spring and the dashpot
; we adopt the well-established multiplication rule that [35-37]
Therefore, the following assumptions, linking external and internal damping coefficients, are made: (i) linear distribution of local damping forces, due to a uniform disposition of external dashpots
on the cross-section; (ii) negligible material bulk viscous deformation.
A road vehicle is modeled as a combination of several rigid bodies, each of which is connected by a set of springs and dashpots
which model the elastic and damping effects of the tires and suspension systems, respectively.
It is idealized as a series of lumped masses supported by the suspension systems, as represented by the springs and dashpots
, which in turn are acting on the bridge.
Linear viscoelastic rheological models, which are obtained through the serial or parallel connection of Hookean elastic elements (springs) and Newtonian viscous parts (dashpots
), are usually used to describe the phenomena occurring in such materials.
The viscous components can be modeled as dashpots
such that the stress-strain rate relationship can be given as,
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When the unbonded particles or particles with bond breakage are in contact with each other, springs and dashpots
are introduced into the contact points in both normal and tangential directions, and compressive normal force [f.sub.n] and tangential (frictional) force [f.sub.s] act at the contact points.
where J(t) is the creep compliance; t is the time; [E.sub.i] is elastic constant for springs; and [[mu].sub.i] is viscous constant for dashpots
(i = 1 and 2).
, and spring-dashpot combinations are used to represent superelasticity (SE), the shape memory effect (SME), and the SE-SME combination, respectively.