Effect of frictional anisotropy on the quasistatic motion of a deformable solid sliding on a planar surface

Feng, Zhaosheng; Hjiaj, Mohammed; Saxcé, Géry de; Mróz, Z.

doi:10.1007/s00466-005-0674-5

Cited by 23 publications

(23 citation statements)

References 3 publications

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“…Non-homogeneity means that there are distinguished points at the contact surface, and the frictional resistance depends on a sliding path in the contact surface. The physical nature of materials and specific technologies of manufacture and machining are responsible for the observed non-isotropy and non-homogeneity of friction, see recent publications of Argatov and Dmitriev [42], Hjiaj et al [43], Feng et al [44,45], Jones and Papadopoulos [46], Konyukhov and Schweizerhof [47], Antoni et al [48], Dunn et al [49], Konyukhov et al [50], Pabst et al [51].…”

Section: The Continuum Thermodynamics Approachmentioning

confidence: 98%

“…The smoothed friction characteristic is more or less the viscous friction model. To remove the difficulty of Coulomb friction description, an elasto-plastic analogy of friction has been utilized in the literature, see Wriggers [7], Hjiaj et al [43] and Feng et al [44,45]. The tangential slip is divided into an elastic (stick) and a plastic (slip) part.…”

Section: The Multi-valued Friction Characteristic At Zero Sliding Velmentioning

confidence: 99%

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Contact stresses: a short survey of models and methods of computations

Zmitrowicz

2009

Arch Appl Mech

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Contact stresses are identified as normal and tangential forces between contacting solids. The normal stresses are modeled using unilateral and complementary conditions, elastic response and normal compliance. Friction laws describe the tangential traction. Friction of materials depends on pressure, sliding velocity, surface temperature, time of contact, surface roughness and presence of wear debris. Phenomenological, micromechanical and atomic-scale models as well as non-classical models of anisotropic and heterogeneous friction are important steps in the development of friction modeling. Sophisticated friction models are desirable in vibrating systems, materials processing, rolling contacts, rubber and polymers, geomechanics, bioengineering and living systems. Main numerical methods in contact mechanics are: finite element method, boundary element method and discrete element method. To include specific contact constraints, the following computing techniques are applied: Lagrange multipliers, penalty function, perturbated and augmented Lagrangian methods, mathematical programming methods. The advances of adhesion and impact modeling are outlined in this paper.

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Section: The Continuum Thermodynamics Approachmentioning

confidence: 98%

Section: The Multi-valued Friction Characteristic At Zero Sliding Velmentioning

confidence: 99%

Contact stresses: a short survey of models and methods of computations

Zmitrowicz

2009

Arch Appl Mech

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“…The three dimensional case has applications in contact problems with orthotropic friction law [3,17] and in electromagnetic scattering [16], just to mention two concrete examples. General background on higher dimensional elliptic cones can be found in [4,7] among other references.…”

Section: Angular Analysis Of Elliptic Conesmentioning

confidence: 99%

Angular analysis of two classes of non-polyhedral convex cones: the point of view of optimization theory

Iusem¹,

Seeger²

2007

Mat. apl. comput.

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Abstract. There are three related concepts that arise in connection with the angular analysis of a convex cone: antipodality, criticality, and Nash equilibria. These concepts are geometric in nature but they can also be approached from the perspective of optimization theory. A detailed angular analysis of polyhedral convex cones has been carried out in a recent work of ours. This note focus on two important classes of non-polyhedral convex cones: elliptic cones in an Euclidean vector space and spectral cones in a space of symmetric matrices.Mathematical subject classification: 52A40, 90C26.

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“…However, to model and implement friction models is a difficult task and it is the next step. The work of [13] shows some contact laws and it will be studied in order to implement in analysis limit problems. Also, [14] proposed a formulation for friction problems based on [15].…”

Section: Discussionmentioning

confidence: 99%

Limit Analysis on Scratch Test Problem

Figueiredo¹,

Borges²

2014

Proceedings of 10th World Congress on Computational Mechanics

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Abstract. Scratch test is one of the oldest method to determine mechanical properties in materials. The technique has gained interest due to the properties implied during test, such as adherence, hardness, cohesion and elasticity. On this test a rigid indenter is dragged on the material test surface at a constant depth and controlled forces. This problem is modeled by finite elements method and limit analysis theory, which is is a direct method and there is no need to calculate stresses during each load step in order to compute critical states and collapse mechanisms. From virtual power principle, the internal power is related to the external power, which is amplified by load factor so that the body achieves a plastic collapse. The solution of a limit analysis problem is to find this load factor, the plastically admissible stresses fields that are in equilibrium with the given forces system, the kinematically admissible velocity fields, the strain rate field , which is related to the velocity field by means of a deformation operator, and the plastic multiplier. The solution of a limit analysis problem closely depends on the yield function that describes the behavior of a material, such as von Mises for metals and Drucker-Prager for rocks. However, traditional criteria for rocks and soils such as MohrCoulomb and Drucker-Prager do not consider material porosity. Therefore, an yield criterion that includes porosity effect is applied in this work. This function is applied to the discretized limit analysis model. A semi-analytical solution based on limit analysis lower bound method is developed and the proposed yield function is also applied. Then, the results between both methods are compared.

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Effect of frictional anisotropy on the quasistatic motion of a deformable solid sliding on a planar surface

Cited by 23 publications

References 3 publications

Contact stresses: a short survey of models and methods of computations

Contact stresses: a short survey of models and methods of computations

Angular analysis of two classes of non-polyhedral convex cones: the point of view of optimization theory

Limit Analysis on Scratch Test Problem

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