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Historical Origin and Recent Development on Normal Directional Impact Models for Rigid Body Contact Simulation: A Critical Review

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Abstract

The impact is one of the most abundant phenomena in the field of multi-body dynamics when two or more bodies come in close vicinity and depending on the interaction properties and geometry, all the interacting bodies experience certain impulsive force for an infinitesimal duration. Nowadays, impact modelling becomes an intrinsic part in the modelling of structural pounding, granular materials, crash and machinery analysis, robotics and bio-mechatronics applications. Since the time of Newton, numerous literatures have been published on the modelling of both normal and oblique contact phenomena. The scope of this critical review is limited to consolidate the existing knowledge on the computational model of normal directional impact on rigid bodies. The literature related to modelling of oblique impact, soft body impact, impact damage in composites and associated stress wave propagation are excluded from the scope of this critical review. Smooth and non-smooth mechanics are two schools of thought in simulating the normal directional impact. In this review, the shortcomings of all the classes of compliance and non-smooth models are analysed in the unified dimensionless frame-work to compare their response output with the conventional stereo-mechanical model. This review opens a new avenue for future researchers in selecting a proper contact formulation for specific application.

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Abbreviations

K :

Stiffness of the linear spring

M :

Mass of the impact

δ, δ P , δ max, x :

Relative indentation, plastic deformation, and maximum penetration, dimensionless penetration

R i , ΔR, L :

Radius of impacting solids, radial clearance, length of cylinder joint

ν :

Poisson’s ratio

E :

Young’s modulus

F, F max, \( \tilde{F} \) :

Restoring force and the maximum possible force, dimensionless force

A :

Impacting area

ξ, C :

Damping ratio, coefficient of damping

t h :

Thickness of the spur gears

\( \dot{\delta }_{N}^{ - } ,\dot{\delta }_{N}^{ + } ,\dot{\delta },\dot{x} \) :

Pre-impact relative velocity, post-impact relative velocity, velocity during virtual penetration, dimensionless velocity during virtual penetration

ɛ N :

Coefficient of restitution

\( \Lambda _{N} ,{\tilde{\Lambda }}_{N} {,\Lambda }_{NC} ,\Lambda _{NE} \) :

Impulse, dimensionless impulse, impulse in compression phase and impulse in restitution phase

\( \Phi ^{ + } ,\Phi ^{ - } ,\Xi ,{\tilde{\Xi }} \) :

Kinetic energy of pre-impact, post-impact, energy loss, and no dimensional energy loss

\( t,\Delta T, \tau \) :

Time, total time for contact duration, non-dimensional time

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  1. Department of Mechanical Engineering, The University of Auckland, 20 Symonds Street, Auckland, 1010, New Zealand

    Arnab Banerjee, Avishek Chanda & Raj Das

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  1. Arnab Banerjee
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Correspondence to Arnab Banerjee.

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Banerjee, A., Chanda, A. & Das, R. Historical Origin and Recent Development on Normal Directional Impact Models for Rigid Body Contact Simulation: A Critical Review. Arch Computat Methods Eng 24, 397–422 (2017). https://doi.org/10.1007/s11831-016-9164-5

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