Niclas Strömberg

Formulation and Comparison of Algorithms for Frictional Contact Problems

This paper presents two algorithms for solving the discrete, quasi-static, small-displacement, linear elastic, contact problem with Coulomb friction. The algorithms are adoptions of a Newton method for solving B-differentiable equations and an interior point method for solving smooth, constrained equations. For the application of the former method, the contact problem is formulated as a system of B-differentiable equations involving the projection operator onto sets with simple structure; for the application of the latter method, the contact problem is formulated as a system of smooth equations involving complementarity conditions and with the non-negativity of variables treated as constraints. The two algorithms are numerically tested for two-dimensional problems containing up to 100 contact nodes and up to 100 time increments. Results show that at the present stage of development, the Newton method is superior both in robustness and speed. Additional comparison is made with a commercial finite element code.

Derivation and analysis of a generalized standard model for contact, friction and wear

A model for mechanical contact including friction, wear and heat generation is proposed. By defining an internal state variable for the wear process, a generalized standard model for contact, friction and wear is derived from the principle of virtual power and the fundamental laws of thermodynamics. Within the frame of the generalized standard model some specific constitutive models are presented. For instance, a free energy corresponding to an extension of Signorinis unilateral contact conditions to include the wear process at the interface and having a linear tangential compliance between the relative tangential displacement and the tangential contact traction is suggested. Furthermore, a dual pseudo-potential with a friction and wear limit criterion in agreement with Coulombs law of friction and Archards law of wear is given. In order to study existence and uniqueness questions, this pair of free energy and dual pseudo-potential is analysed in a one point elastic quasi-static contact problem with two degrees of freedom and thermal effects neglected. The so-called rate problem is solved.

Finite element algorithms for thermoelastic wear problems

In the present paper three algorithms are applied to a finite element model of two thermoelastic bodies in frictional wearing contact. All three algorithms utilize a modification of a Newton method for B-differentiable equations as non-linear equation solver. In the first algorithm the fully-coupled system of thermomechanical equations is solved directly using the modified method, while in the other two algorithms the equation system is decoupled in one mechanical part and another thermal part which are solved using an iterative strategy of Gauss–Seidel type. The two iterative algorithms differ in which order the parts are solved. The numerical performance of the algorithms are investigated for two two-dimensional examples. Based on these numerical results, the behaviour of the model is also discussed. It is found that the iterative approach where the thermal subproblem is solved first is slightly more efficient for both examples. Furthermore, it is shown numerically how the predicted wear gap is influenced by the bulk properties of the contacting bodies, in particular how it is influenced by thermal dilatation.

A Newton method for three-dimensional fretting problems

The present paper concerns the numerical treatment of fretting problems using a finite element analysis. The governing equations resulting from a formal finite element discretization of an elastic body with a potential contact surface are considered in a quasi-static setting. The constitutive equations of the potential contact surface are Signorinis contact conditions, Coulombs law of friction and Archards law of wear. Using a backward Euler time discretization and an approach based on projections, the governing equations are written as an augmented Lagrangian formulation which is implemented and solved using a Newton algorithm for three-dimensional fretting problems of didactic nature. Details concerning the implementation are provided.

Finite element treatment of two-dimensional thermoelastic wear problems

The present paper concerns the numerical treatment of thermoelastic wear problems. The governing equations of thermoelasticity coupled to Signorini contact, Coulombs friction and Archards wear are formulated as a system of discrete equations. This equation system is solved, using a Bouligand differentiable Newton method, for five problems of didactic nature.

A model of damage coupled to wear

Abstract The present paper presents a model of damage coupled to wear. The damage model is based on a continuum model including the gradient of the damage variable. Such a model is non-local in the sense that the evolution of damage is governed by a boundary-value problem instead of a local evolution law. Thereby, the well-known mesh-dependency observed for local damage models is removed. Another feature is that the boundary conditions can be used to introduce couplings between bulk damage and processes at the boundary. In this work such a coupling is suggested between bulk damage and wear at the contact interface. The model is regarded as a first attempt to formulate a continuum damage model for studying crack initiation in fretting fatigue. The model is given within a thermodynamic framework, where it is assured that the principles of thermodynamics are satisfied. Furthermore, two variational formulations of the full initial boundary value problem, serving as starting points for finite element discretization, are presented. Finally, preliminary numerical results for a simple one-dimensional example are presented and discussed. It is qualitatively shown how the evolution of damage may influence the wear behaviour and how damage may be initiated by the wear process.

Multi-Objective Optimization of a Disc Brake System by using SPEA2 and RBFN

Many engineering design optimization problems involve multiple conflicting objectives, which today often are obtained by computational expensive finite element simulations. Evolutionary multi-objec ...

A generalized standard model for contact, friction and wear

In this paper a continuum thermodynamic model for interfacial phenomena including contact, friction and wear is proposed. The framework is that of small displacements, implying small slip. Consequently the model is mainly one for fretting, which is a wear phenomenon arising when contacting surfaces undergo oscillatory displacements with small amplitudes.

Sequential simulation of thermal stresses in disc brakes for repeated braking

In this paper, an efficient sequential approach for simulating thermal stresses in brake discs for repeated braking is presented. First, a frictional heat analysis is performed by using an Eulerian formulation of the disc. Then, by using the temperature history from the first step of the sequence, a plasticity analysis with temperature dependent material data is performed in order to determine the corresponding thermal stresses. Three-dimensional geometries of a disc and a pad to a heavy truck are considered in the numerical simulations. The contact forces are computed at each time step taking the thermal deformations of the disc and pad into account. In such manner, the frictional heat power distribution will also be updated in each time step, which in turn will influence the development of heat bands. The plasticity model is taken to be the von Mises yield criterion with linear kinematic hardening, where both the hardening and the yield limit are temperature dependent. The results show that during hard braking, high compressive stresses are generated on the disc surface in the circumferential direction which cause yielding. But when the disc cools down, these compressive stresses transform to tensile residual stresses. For repeated hard braking when this kind of stress history is repeated, we also show that stress cycles with high amplitudes are developed which might generate low cycle fatigue cracks after a few braking cycles.

An approach towards generating surrogate models by using RBFN with a priori bias

In this paper, an approach to generate surrogate modelsconstructed by radial basis function networks (RBFN) with a prioribias is presented. RBFN as a weighted combination of radialbasis functions o ...