One Hundred Years of Hertz Contact

Johnson, Kenneth L.

doi:10.1243/pime_proc_1982_196_039_02

Cited by 322 publications

(148 citation statements)

References 39 publications

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“…This particular issue is not realistic because when the contact begins, both elastic and damping force components must be null. Moreover, at the end of the contact, the deformation is null, the relative contact velocity is negative and, consequently, the resulting contact force is also negative, which does not make sense from the physical point of view because the bodies can not attract each other [3,47,48].…”

Section: General Issues Of Continuous Contact Force Modelsmentioning

confidence: 99%

“…Undeniably, the classical problem of the contact mechanics is a quite old topic in engineering applications [1,2]. The pioneering work on the frictionless collision between rigid bodies was due to Hertz who developed the theory with his name during the Christmas vacation of 1880 at the age of twenty-three [3]. The contact problem has been an intensive topic of research over the last decades and deserved the attention of many authors, which led to the development of relevant work and even to the publication of a good number of textbooks totally devoted to this issue, such as those by Goldsmith [4], Brach [5], Pfeiffer and Glocker [6], Johnson [7], Stronge [8], Wriggers [9], among others.…”

Section: Introductionmentioning

confidence: 99%

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On the continuous contact force models for soft materials in multibody dynamics

et al. 2010

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Section: General Issues Of Continuous Contact Force Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the continuous contact force models for soft materials in multibody dynamics

et al. 2010

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“…The magnitude of penetration, G, could be calculated from the components of relative displacements. Employing Johnson's formula based on Hertz theory [16], the normal contact force, P, could be calculated as function of material properties * , as:…”

Section: Ic4m 2016mentioning

confidence: 99%

Multibody Dynamics Formulation for Modeling and Simulation of Roller Chain Using Spatial Operator

Omar

2016

MATEC Web of Conferences

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Abstract. This paper proposes a new approach for modeling and simulating roller-chain drives using multibody formulations. The presented approach models the chain links as spatial decoupled dynamic bodies. The chain links are modeled using two different dynamic representations for the pin-link and the bushing-link. The bushing-link is modeled with two descendent dynamic bodies to represent the rollers. The adjacent pin and bushing links are connected by compliant bushing force elements. An efficient search algorithm is used to detect the contact between the roller and the sprocket teeth while a nonlinear force module is used to predict the contact force. A generalized sprocket representation is used to model the sprocket. The spatial motion of the chain links allows the out-of-plane vibrational motion of the links as well as simulating sprockets misalignment. Using the compliant connection between links avoids using the iterative calculation needed to satisfy the joint constraint equations leading to more efficient calculation scheme. The nonlinear dynamic equations of motion are solved using recursive approach. Complex roller chains drives, bicycle chain and conveyance systems can be easily modeled and analyzed using the proposed approach.

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“…In this approach the particles are assumed to be of spherical shape, having a small contact area and the deformation of the particles follows the classical Hertz contact theory (Hertz 1896;Johnson 1982;Johnson 1985). Under such conditions the porosity of the medium is close to the percolation limit, which allows an application of simplified analytical techniques.…”

Section: Mechanical Behaviour Of a Pack Of Compressible Particlesmentioning

confidence: 99%

On the residual opening of hydraulic fractures

Neto

Kotousov

2013

Int J Fract

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Hydraulic stimulation technologies are currently widely applied across resource and power generation industries to increase productivity of oil/gas or hot water reservoirs. These technologies utilise a pressurised fluid, which is applied inside the well to initiate and drive fractures as well as to open a network of natural fractures. To prevent the opened fractures from complete closure during production stage, small particles (proppants) are normally injected with the pressurised fluid. These particles are subjected to confining stresses when the fluid pressure is removed, which lead to a partial closure of the opened fractures.The residual fracture openings are the main outcome of such hydraulic stimulations as these openings significantly affect the permeability of the reservoirs and, subsequently, well productivity. Past research was largely focused on the assessment of conditions and characteristics of fluid driven fractures as well as proppant placement techniques. Surprisingly, not much work was devoted to the assessment of the residual fracture profiles. In this work we develop a simplified non-linear model of residual closure of a crack filled with deformable particles under remote compressive stresses. It is demonstrated that the closure profile is significantly influenced by the distribution and compressibility of the particles, which are often ignored in the existing analytical or semi-analytical models.

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One Hundred Years of Hertz Contact

Cited by 322 publications

References 39 publications

On the continuous contact force models for soft materials in multibody dynamics

On the continuous contact force models for soft materials in multibody dynamics

Multibody Dynamics Formulation for Modeling and Simulation of Roller Chain Using Spatial Operator

On the residual opening of hydraulic fractures

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