Quasistatic Viscoelasticity with Self-Contact at Large Strains

Krömer, Stefan; Roubíček, Tomáš

doi:10.1007/s10659-020-09801-9

Cited by 13 publications

(13 citation statements)

References 23 publications

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“…But, the method is computationally intensive. Configuration space method [Hammami et al, 2016] (36) ; [Yamamoto, 2017] (37) ; [Jiang et al, 2017] (38) ; [Zeng et al, 2017] (39) ; [Mehnert et al, 2018] (40) ; [Drainville, 2019] (41) ; [Goryacheva and Miftakhova, 2019] (42) ; [Jamshidi et al, 2020] (43) ; [Kromer and Roubicek, 2020] (44) ; [Brighenti et al, 2021] (45) ;…”

Section: Review On Viscoelastic Dampingmentioning

confidence: 99%

Dynamic Modelling and Control of Flexible Link Manipulators: Methods and Scope - Part 2

Mishra¹,

Singh²

2021

IJST

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Objectives: This paper addresses two key issues in the area of flexible robotics. The issues are vibration control of flexible links and trajectory control of flexible robots. A brief, yet, significant review is provided that addresses these two issues. Methods: For vibration control of flexible links, possibilities of the use of passive and active damping methods are explored in the literature. After that, the effect of proper trajectory planning to ensure positional accuracy at the end-effector is studied. Findings: After a review of 181 research papers from the year 1970 to 2021, it has been found that the vibration suppression of flexible links can be achieved through the application of viscoelastic materials, piezoelectric materials, and optimum trajectory planning. Recent trends in research in the area of flexible manipulators show that an optimal trajectory can significantly help in reduction of link vibrations and achievement of positional accuracy simultaneously. Novelty: The novelty of the present work lies in exploring the possible application of passive and active damping control methods for vibration suppression of flexible link manipulators. Besides that, the survey also highlights how well planned trajectory may help achieve accurate tip positioning of flexible robots.

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Section: Review On Viscoelastic Dampingmentioning

confidence: 99%

Dynamic Modelling and Control of Flexible Link Manipulators: Methods and Scope - Part 2

Mishra¹,

Singh²

2021

IJST

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“…To our best knowledge, the existence of a solution has not been established up to now. On the other hand, if the stored energy is enriched by the second gradient of the deformation, existence results are available in various settings, see [8,11] in three dimensions and [3,12] in one dimension. Namely, a standard approach to obtain solutions for such evolution problems is to introduce an implicit time discretization.…”

Section: Modeling Of Nonlinear Viscoelasticitymentioning

confidence: 99%

Linearization and Computation for Large-Strain Viscoelasticity

Dondl¹,

Jesenko²,

Kružík³

et al. 2021

Preprint

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Time-discrete numerical minimization schemes for simple viscoelastic materials in the large strain Kelvin-Voigt rheology are not well-posed due to non-quasiconvexity of the dissipation functional. A possible solution is to resort into non-simple material models with higher-order gradients of deformations. This makes, however, numerical computations much more involved.Here we propose another approach relying on local minimizers of the simple-material model. Computational tests are provided showing a very good agreement between our model and the original one.

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“…However in order to show that this object has a meaning as a solution to the given contact-problem, further work needs to be done.Even for the case of an elastic solid deformations alone the understanding of self-touching of the solid (or alternatively touching the container) is still unclear from a mathematical point of view; in particular understanding the contact force on the solid that is preventing the self-penetration. Some contact-forces have been identified in the fully static problem only recently in [PH17] and a generalization to the quasi-static situation is due to [KR19a]. Generalizations to fluid-structure interaction or even hyperbolic evolution, however, remain widely open.…”

Section: Contact Conditionsmentioning

confidence: 99%

“…It should also be noted that recent progress into the quasi-stationary analogue of this has been made by [KR19a] with a different approach, where instead of a variational inequality, they consider the associated Lagrange-multiplyier and its physical significance.…”

Section: 3mentioning

confidence: 99%

A variational approach to hyperbolic evolutions and fluid-structure interactions

Benešová¹,

Kampschulte²,

Schwarzacher³

2020

Preprint

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We introduce a two time-scale scheme which allows to extend the method of minimizing movements to hyperbolic problems. This method is used to show the existence of weak solutions to a fluid-structure interaction problem between a nonlinear, visco-elastic, ndimensional bulk solid governed by a hyperbolic evolution and an incompressible fluid governed by the (n-dimensional) Navier-Stokes equations for n ≥ 2. Contents 1. Introduction 1 1.1. Setup 3 1.2. Main result 5 1.3. Mechanical and analytical restrictions on the energy/dissipation functional 9 1.4. Outlook and further applicability 11 1.5. Notation 12 2. Minimizing movements for fluid-structure interactions. 13 2.1. Preliminary analysis 14 2.2. Proof of Theorem 2.2 16 2.3. The example Energy-Dissipation pair 26 3. Minimizing movements for hyperbolic evolutions 28 3.1. The time-delayed problem 30 3.2. Proof of Theorem 3.2 33 3.3. Remarks 37 4. The unsteady fluid-structure interaction problem 39 4.1. An intermediate, time delayed model 40 4.2. Proof of Theorem 1.2 46 4.3. Remarks on the full problem 56 Appendix A. 57 A.1. Some technical lemmata 57 A.2. Proof of Proposition 2.22 59 Acknowledgments 62 References 62

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Quasistatic Viscoelasticity with Self-Contact at Large Strains

Cited by 13 publications

References 23 publications

Dynamic Modelling and Control of Flexible Link Manipulators: Methods and Scope - Part 2

Dynamic Modelling and Control of Flexible Link Manipulators: Methods and Scope - Part 2

Linearization and Computation for Large-Strain Viscoelasticity

A variational approach to hyperbolic evolutions and fluid-structure interactions

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