Elastoplastic contact model

Elastoplastic Contact Model and Relationships. Sridhar and Yovanovich [106] developed an elastoplastic contact conductance model that is summarized below in terms of the geometric parameters (1) ArlA , the real to apparent area ratio (2) n, the contact spot density (3) a, the mean contact spot radius and (4) X, which is the dimensionless mean plane separation ... 

M. R. Sridhar, Elastoplastic Contact Models for Sphere-Flat and Conforming Rough Surface Applications, PhD thesis, University of Waterloo, Waterloo, Ontario, Canada, 1994. 

M. R. Sridhar and M. M. Yovanovich, Elastoplastic Contact Model for Isotropic Conforming Rough Surfaces and Comparison with Experiments, ASMEJ. of Heat Transfer (118/1) 3-9,1996. 

The proposed elastoplastic contact conductance model moves smoothly between the elastic contact model of Mikic [66] and the plastic contact conductance model of Cooper, Mikic, and... 

For elastoplastic contacts, there are a number of contact models, notably models of Walton and Braun [15] and Thornton [16]. However, these models will not be discussed in this chapter. 

Progress in modelling and analysis of the crack problem in solids as well as contact problems for elastic and elastoplastic plates and shells gives rise to new attempts in using modern approaches to boundary value problems. The novel viewpoint of traditional treatment to many such problems, like the crack theory, enlarges the range of questions which can be clarified by mathematical tools. 

We have to stress that the analysed problems prove to be free boundary problems. Mathematically, the existence of free boundaries for the models concerned, as a rule, is due to the available inequality restrictions imposed on a solution. As to all contact problems, this is a nonpenetration condition of two bodies. The given condition is of a geometric nature and should be met for any constitutive law. The second class of restrictions is defined by the constitutive law and has a physical nature. Such restrictions are typical for elastoplastic models. Some problems of the elasticity theory discussed in the book have generally allowable variational formulation... 

Fig. 7. (a) Load-displacement curve of a typical elastoplastic material and (b) the schematic of the indentation model of Oliver and Pharr [40]. S—contact stiffness he— contact depth /imax—indenter displacement at peak load hf—plastic deformation after load removal hs—displacement of the surface at the perimeter of the contact. 

For elastoplastic and adhesive contacts, the models proposed by Thornton and Ning [14] and Pasha et al. [29] could be used, which will not be discussed here due to their complexity. 

Two of the most common classes of particle-dynamic simulations are termed hard-particle and soft-particle methods. Hard-particle methods calculate particle trajectories in response to instantaneous, binary collisions between particles, and allow particles to follow ballistic trajectories between collisions. This class of simulation permits only instantaneous contacts and is consequently often used in rapid flow situations such as are found in chutes, fluidized beds, and energetically agitated systems. Soft-particle methods, on the other hand, allow each particle to deform elastoplastically and compute responses using standard models from elasticity and tribology theory. This approach permits enduring particle contacts and is therefore the method of choice for mmbler apphcations. The simulations described in this chapter use soft-particle methods and have been validated and found to agree in detail with experiments. 

Abstract In this paper, a new phenomenological model is developed to account variable coefficient of friction (COF) in space and time. The COF is no longer considered as a global value valid for the whole contact area. A local value is introduced instead, which evolution is governed by the local history of the contact and the amount of slip. The framework is inspired from elastoplasticity. The evolution of the COF depends on two variables an isotropic evolution related to cumulated slip and a kinematic component computed from the actual relative position of the bodies. 

Mayeur, C, Sainsot, P and Flamand, L, 1995, "A numerical elastoplastic model for rough contact", Trans ASME, J. of Tribology, Vol 117, pp 422-429. 

Kalker [13] made a phenomenological mathematical description of a contact with three bodies based on the condition of an interfacial body that is weaker and more flexible than either of the first ones. The third body is modeled as an elastoplastic block of constant thickness, low stiffiiess, low yield limit, and strongly adhesive at the first body. The description of the third body is taken as a factor of empirical reduction of Kalker s coefficients Cij [7]. The actual creepage is then multiplied by a factor dependent on the flexibility of the two bodies (creepage and coefficients Cij) and the flexibility (thickness, elastic modulus, Poisson s ratio) of the third body. 

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