Real contact mechanisms and finite element formulation—a coupled thermomechanical approach

Zavarise, Giorgio; Wriggers, Peter; Stein, Erwin; Schrefler, B. A.

doi:10.1002/nme.1620350409

Cited by 121 publications

(76 citation statements)

References 20 publications

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“…An even earlier work on this topic from the same research group can be found in [3]. The paper by Zavarise et al [4] is another example of early works by other researchers on this topic.…”

Section: Introductionmentioning

confidence: 94%

An Eulerian approach for simulating frictional heating in disc-pad systems

Strömberg

2011

European Journal of Mechanics - A/Solids

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Thermal stresses as a result from frictional heating must be considered when designing disc brakes, clutches or other rotating machine components with sliding contact conditions. The rotational symmetry of the disc in these kind of applications makes it possible to model these systems using an Eulerian approach instead of a Lagrangian framework. In this paper such an approach is developed and implemented. The disc is formulated in an Eulerian frame where the convective terms are defined by the angular velocity. By utilizing the Eulerian framework, a node-tonode formulation of the contact interface is obtained, producing most accurate frictional heat power solutions. The energy balance of the interface is postulated by introducing an interfacial temperature. Both frictional power and contact conductances are included in this energy balance. The contact problem is solved by a non-smooth Newton method. By adopting the augmented Lagrangian approach, this is done by rewriting Signorini's contact conditions to an equivalent semi-smooth equation. The heat transfer in the disc is discretized by a Petrov-Galerking approach, i.e. the numerical difficulties due to the non-symmetric convective matrix appearing in a pure Galerkin discretization is treated by following the streamline-upwind approach. In such 1 *Manuscript with Highlighted Changes Click here to view linked References M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPTmanner a stabilization is obtained by adding artificial conduction along the streamlines. For each time step the thermoelastic contact problem is first solved for the temperature field from the previous time step. Then, the heat transfer problem is solved for the corresponding frictional power. In such manner a temperature history is obtained sequentially via the trapezoidal rule. In particular the parameter is set such that both the Crank-Nicolson and the Galerkin methods are utilized. The method seems very promising. This is demonstrated by solving a two-dimensional benchmark as well as a real disc brake system in three dimension.

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“…An even earlier work on this topic from the same research group can be found in [3]. The paper by Zavarise et al [4] is another example of early works by other researchers on this topic.…”

Section: Introductionmentioning

confidence: 94%

An Eulerian approach for simulating frictional heating in disc-pad systems

Strömberg

2011

European Journal of Mechanics - A/Solids

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“…The implementation of more complex contact laws should therefore be straightforward. Examples of more advanced mechanical/thermal contact interface laws (for frictionless contact), based on microgeometrical and statistical considerations, can be found in [24][25][26][27][28]. Furthermore, [29] is noted, in which homogenization of thermal contact resistances is suggested.…”

Section: Contact Formulationmentioning

confidence: 99%

Finite element analysis of transient thermomechanical rolling contact using an efficient arbitrary Lagrangian–Eulerian description

2014

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A theoretical and computational framework for the analysis of thermomechanically coupled transient rolling contact, based on an arbitrary Lagrangian-Eulerian (ALE) kinematical description, is developed. A finite element formulation featuring 2D cylinder-plate rolling contact is implemented. The implementation features penalty-type contact formulations for mechanical and thermal contact. It is noted that the ALE formulation allows for a simplified time description, a compact computational domain and localized mesh refinement. Numerical simulations considering stationary and transient rolling conditions are presented. Highlighted aspects include the influence of variations in thermal contact conductivity, rolling speed and external mechanical load on the contact interface heat flow. The model is shown to give predictions in qualitative agreement with results in the literature. For the velocity range studied, numerical issues such as spurious numerical dissipation/oscillations in the temperature field are noted to have a prominent influence. These phenomena are addressed using a Streamline-Upwind Petrov-Galerkin stabilization scheme together with a bubble function approach.

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“…If 1/α = 0 the penetration is prevented and the relation (15) leads to a barrier function as in [30]. The barrier contact law (1/α = 0) has been used in many papers about ANM, for instance [31] [13].…”

Section: Contact Modeling : the Mechanical Partmentioning

confidence: 99%

Automatic solver for non‐linear partial differential equations with implicit local laws: Application to unilateral contact

Lejeune

Boudaoud

Potier‐Ferry

et al. 2013

Numerical Meth Engineering

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In general, nonlinear continuum mechanics combine global balance equations and local constitutive laws. In this work, frictionless contact between a rigid tool and a thin elastic shell is considered. This class of boundary value problems involves two nonlinear algebraic laws: the first one gives explicitly the stress field as a function of the strain throughout the continuum part, while the second one is a nonlinear equation relating the contact forces and the displacement at the boundary.Given the fact that classical computational approaches sometimes require significant effort in implementation of complex nonlinear problems, a computation technique based on Automatic Differentiation of constitutive laws is presented in this paper. The procedure enables to compute automatically the higher-order derivatives of these constitutive laws and thereafter to define Taylor series that are the basis of the continuation technique called Asymptotic Numerical Method. The algorithm is about the same with an explicit or an implicit constitutive relation. In the modeling of forming processes, many tool shapes can be encountered. The presented computational technique permits an easy implementation of these complex surfaces, for instance in a finite element code: the user is only required to define the tool geometry and the computer is able to get the higher-order derivatives.

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Real contact mechanisms and finite element formulation—a coupled thermomechanical approach

Cited by 121 publications

References 20 publications

An Eulerian approach for simulating frictional heating in disc-pad systems

An Eulerian approach for simulating frictional heating in disc-pad systems

Finite element analysis of transient thermomechanical rolling contact using an efficient arbitrary Lagrangian–Eulerian description

Automatic solver for non‐linear partial differential equations with implicit local laws: Application to unilateral contact

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