A concise frictional contact formulation based on surface potentials and isogeometric discretization

Duong, Thang X.; Sauer, Roger A.

doi:10.1007/s00466-019-01689-0

Cited by 12 publications

(12 citation statements)

References 50 publications

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“…The resulting equations are discretized within a finite element framework to obtain a numerical solution, which is briefly summarized in Appendix A. The readers are referred to Duong and Sauer [18] and Sauer and De Lorenzis [46,47] for a more detailed derivation of the considered contact formulation.…”

Section: Models and Methodsmentioning

confidence: 99%

“…Figure 11: Frictional contact kinematics at current time t n+1 : current slave point x k , current position of the previous interacting point x (ξ n ), current interacting point x (ξ), the current elastic gap vector g e and its components, previous elastic gap g n e , and the sliding path C. Adopted and modified from Ref. [18].…”

Section: A2 Contact Kinematics and Contact Tractionmentioning

confidence: 99%

“…[27,58,47]). In the context of this work, we use another approach that is based on the surface potential-based contact formulations of Duong and Sauer [18] and Sauer and de Lorenzis [46]. The reader is referred to Corbett and Sauer [12,13] for the NURBS-enriched contact finite element discretization.…”

Section: Conflict Of Interestmentioning

confidence: 99%

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A modified Coulomb’s law for the tangential debonding of osseointegrated implants

Immel

Duong

Nguyen

et al. 2020

Biomech Model Mechanobiol

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Cementless implants are widely used in orthopedic and oral surgery. However, debonding-related failure still occurs at the bone-implant interface. It remains difficult to predict such implant failure since the underlying osseointegration phenomena are still poorly understood. Especially in terms of friction and adhesion at the macro-scale, there is a lack of data and reliable models. The aim of this work is to present a new friction formulation that can model the tangential contact behavior between osseointegrated implants and bone tissue, with focus on debonding. The classical Coulomb's law is combined with a state variable friction law to model a displacement-dependent friction coefficient. A smooth state function, based on the sliding distance, is used to model implant debonding. The formulation is implemented in a 3D nonlinear finite element framework, and it is calibrated with experimental data and compared to an analytical model for mode III cleavage of a coin-shaped, titanium implant [32]. Overall, the results show close agreement with the experimental data, especially the peak and the softening part of the torque curve with a relative error of less than 2.25 %. In addition, better estimates of the bone's shear modulus and the adhesion energy are obtained. The proposed model is particularly suitable to account for partial osseointegration, as is also shown.

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Section: Models and Methodsmentioning

confidence: 99%

Section: A2 Contact Kinematics and Contact Tractionmentioning

confidence: 99%

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A modified Coulomb’s law for the tangential debonding of osseointegrated implants

Immel

Duong

Nguyen

et al. 2020

Biomech Model Mechanobiol

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“…Apart from the tangential sticking constraint ξ · p α = 0 , there is also the normal contact constraint g n ≥ 0 . Normal and tangential contact are usually treated separately in most friction algorithms, but there are also unified approaches directly based on the gap vector g , see, e.g., [70, 71]. Such an approach is also taken in the following sections.…”

Section: Continuum Contact Kinematicsmentioning

confidence: 99%

A chemo-mechano-thermodynamical contact theory for adhesion, friction, and (de)bonding reactions

Sauer

Duong

Mandadapu

2021

Mathematics and Mechanics of Solids

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This work presents a self-contained continuum formulation for coupled chemical, mechanical, and thermal contact interactions. The formulation is very general and, hence, admits arbitrary geometry, deformation, and material behavior. All model equations are derived rigorously from the balance laws of mass, momentum, energy, and entropy in the framework of irreversible thermodynamics, thus exposing all the coupling present in the field equations and constitutive relations. In the process, the conjugated kinematic and kinetic variables for mechanical, thermal, and chemical contact are identified, and the analogies between mechanical, thermal, and chemical contact are highlighted. Particular focus is placed on the thermodynamics of chemical bonding distinguishing between exothermic and endothermic contact reactions. Distinction is also made between long-range, non-touching surface interactions and short-range, touching contact. For all constitutive relations, examples are proposed and discussed comprehensively with particular focus on their coupling. Finally, three analytical test cases are presented that illustrate the thermo-chemo-mechanical contact coupling and are useful for verifying computational models. Although the main novelty is the extension of existing contact formulations to chemical contact, the presented formulation also sheds new light on thermo-mechanical contact, because it is consistently derived from basic principles using only a few assumptions.

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“…where the later is associated with dissipative (sliding) contact and hence denoted g s . It is noted that both g e and g s have normal and tangential components as in the unified contact formulations of Wriggers and Haraldsson (2003) and Duong and Sauer (2019).…”

Section: Continuum Contact Kinematicsmentioning

confidence: 99%

A chemo-mechano-thermodynamical contact theory for adhesion, friction and (de)bonding reactions

Sauer¹,

Duong²,

Mandadapu³

2020

Preprint

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This work presents a self-contained continuum formulation for coupled chemical, mechanical and thermal contact interactions. The formulation is very general and hence admits arbitrary geometry, deformation and material behavior. All model equations are derived rigorously from the balance laws of mass, momentum, energy and entropy in the framework of irreversible thermodynamics, thus exposing all the coupling present in the field equations and constitutive relations. In the process, the conjugated kinematic and kinetic variables for mechanical, thermal and chemical contact are identified, and the analogies between mechanical, thermal and chemical contact are highlighted. Particular focus is placed on the thermodynamics of chemical bonding distinguishing between exothermic and endothermic contact reactions. Distinction is also made between long-range, non-touching surface interactions and short-range, touching contact. For all constitutive relations examples are proposed and discussed comprehensively with particular focus on their coupling. Finally, three analytical test cases are presented that illustrate the thermo-chemo-mechanical contact coupling and are useful for verifying computational models. While the main novelty is the extension of existing contact formulations to chemical contact, the presented formulation also sheds new light on thermo-mechanical contact, since it is consistently derived from basic principles using only few assumptions.

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A concise frictional contact formulation based on surface potentials and isogeometric discretization

Cited by 12 publications

References 50 publications

A modified Coulomb’s law for the tangential debonding of osseointegrated implants

A modified Coulomb’s law for the tangential debonding of osseointegrated implants

A chemo-mechano-thermodynamical contact theory for adhesion, friction, and (de)bonding reactions

A chemo-mechano-thermodynamical contact theory for adhesion, friction and (de)bonding reactions

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