Structural optimization of contact problems using Cahn–Hilliard model

Myliski, A.; Wrblewski, M.

doi:10.1016/j.compstruc.2016.03.013

Cited by 24 publications

(5 citation statements)

References 30 publications

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“…Future research will also include the treatment and investigation of the wear evolution process in terms of the shape optimization problem. The location and shape of the contact area may be considered as a design variable [36]. The volume of the worn material or the dissipated power may be chosen as an optimization criterion.…”

Section: Discussionmentioning

confidence: 99%

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Power Dissipation and Wear Modeling in Wheel–Rail Contact

Myśliński,

Chudzikiewicz

2023

Applied Sciences

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This paper is concerned with the modeling of power dissipation due to friction and its relation with wear estimation in wheel–rail contact. Wear is a complex multi-scale and multi-physical phenomenon appearing in rolling contact. Wear is generated by high contact stress and the work of friction forces. This phenomenon leads to the appearing of the worn material in the form of wear debris between contacting surfaces. In contact models, wear is usually described in terms of the wear depth function. This function modifies the gap between the contacting bodies as well as the shape of the surfaces of the wheel and rail in contact. In this paper, besides the wear depth function, the dissipated energy, rather than the contact stress, is taken into account to evaluate the wear impact on rail or wheel surfaces. The dissipated energy allows us to more precisely evaluate the wear debris amount as well as the depth of wear and its distribution along the contact interface. A two-dimensional rolling contact problem with frictional heat flow is considered. The elasto-plastic deformation of the rail is considered. This contact problem is governed by a coupled system of mechanical and thermal equations in terms of generalized stresses, displacement and temperature. The finite element method is used to discretize this problem. A discretized system of equations with nonpenetration and friction conditions is transformed and formulated as a nonlinear complementarity problem. The generalized Newton method is applied to numerically solve this mechanical subproblem. The Cholesky method is used to find the solution of the heat-conductive problem. The dissipated power is evaluated based on the resultant force and slip at a reference point. Numerical results including the distribution of slip velocity, power factor and wear rate are provided and discussed.

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Section: Discussionmentioning

confidence: 99%

“…The finite element method [32,33,36] is used to replace the system (4)-( 8) and ( 10)-( 12) with the discretized one. Due to plasticity as well as contact conditions, this mechanical subsystem consists of two coupled inequalities rather than equations.…”

Section: Numerical Solution Methodsmentioning

confidence: 99%

Power Dissipation and Wear Modeling in Wheel–Rail Contact

Myśliński,

Chudzikiewicz

2023

Applied Sciences

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“…The impact of hardening parameters, as well as temperature-dependent material parameters and creepage on the wear evolution process, requires further research. In the wear evolution process, the location of the contact zone may be also treated as the shape optimization problem [26]. Therefore, the choice of parameters ensuring the minimization of the worn material volume may be considered and formulated as the shape optimization problem where the dissipated energy is the criterion of optimization.…”

Section: Discussionmentioning

confidence: 99%

Wear modelling in wheel–rail contact problems based on energy dissipation

Myśliński

Chudzikiewicz

2020

Tribology - Materials, Surfaces & Interfaces

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This work is concerned with the numerical procedure to solve two-dimensional wheel-rail contact problem between a rigid wheel and an elastic-plastic rail lying on a rigid foundation. The contact phenomenon includes Coulomb friction, frictional heat generation as well as the wear of the contacting surfaces. The wear depth function appears as an internal variable in the non-penetration condition updating the gap between the worn surfaces of the bodies. Moreover the dissipated energy due to friction is calculated to evaluate the loss of material and to determine the shape of the contacting surfaces during the wear evolution process. This contact problem is solved numerically using the finite element method as well as the operator splitting approach and semi-smooth Newton method. The distribution of contact surface stresses and temperatures as well as the evolution of the shape of the contact surfaces and the wear depth are reported and discussed.

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“…A combined interface shape and material stiffness optimization method based on evolutionary optimization techniques was developed in [1]. The shape and topology optimization of the unilateral contact problems was conducted to minimize the normal contact stress [9,10]. A topology optimization method was developed in [11] to control the contact stress distribution directly, by simultaneously minimizing the average and variation of the contact stress of an apriori unknown contact area.…”

Section: Introductionmentioning

confidence: 99%

Simple layer potential expansion for optimization of contact interaction taking into account friction and adhesion

Shyshkanova,

Walther

2023

J. Phys.: Conf. Ser.

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Friction plays a crucial role in the formation of contact problems, particularly through adhesion. This paper focuses on a quasi-static three-dimensional problem of a punch movement along the boundary of an elastic half-space. The investigation considers friction and adhesion forces, employing a two-term friction law. The objective is to optimize the pressure distribution beneath the punch. The shape of the punch serves as the design variable, while the deviation of the pressure distribution, originating from a given one, is minimized. The optimization problem can be divided into two sequentially solvable sub-problems. The first task involves finding a pressure distribution that minimizes the performance functional, which has a known solution. The second problem entails searching for the optimal shape of the punch to achieve the previously determined pressure distribution. A numeric-analytical solution is developed based on the expansion of the simple layer potential. The coefficients characterizing friction and adhesion act as small parameters. The proposed method gives the ability to obtain closed-form formulas in each approximation, enabling convenient qualitative analysis and practical engineering applications. The calculations and analytical dependence reveal an asymmetric distribution of pressure on the contact area, during the movement of an axisymmetric punch.

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Structural optimization of contact problems using Cahn–Hilliard model

Cited by 24 publications

References 30 publications

Power Dissipation and Wear Modeling in Wheel–Rail Contact

Power Dissipation and Wear Modeling in Wheel–Rail Contact

Wear modelling in wheel–rail contact problems based on energy dissipation

Simple layer potential expansion for optimization of contact interaction taking into account friction and adhesion

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