A model-adaptivity method for the solution of Lennard-Jones based adhesive contact problems

Dhia, Hachmi Ben; Du, Shuimiao

doi:10.1007/s00466-018-1578-5

Cited by 2 publications

(5 citation statements)

References 40 publications

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“…21b). A rough comparison with results reported in [6] where the Newton-Raphson method was used to solve the contact between an elastic cylinder and a rigid flat surface in absence of contact instabilities, could show the gap between the two approaches in terms of efficiency.…”

Section: Attachment and Detachment Of A Rigid Sphere From An Elastic mentioning

confidence: 89%

“…As discussed in our previous work [6], due to the very localized zones of interest and their evolution with respect to the external load, multiscale methods are highly demanded to solve the LJ-based adhesive contact problems with a reasonable computational cost. In this work, we employ again the flexible multiscale Arlequin framework (see [4,5]) to achieve this task.…”

Section: : End Loopmentioning

confidence: 99%

“…However, for most of the contact problems in both academic and engineering practice, the analytical solutions cannot been obtained in closed form due to various complexities. Therefore, one should resort to numerical computational methods among which the most commonly used is the Finite Element Method (FEM) in the framework of continuum mechanics combined with numerical algorithms applied for the solution of Lennard-Jones (LJ) based contact problems (see [29,15,26,35,24,6]). For an enlarged review of the numerical modeling methods, readers are referred to the recent survey by Sauer [28].…”

Section: Introductionmentioning

confidence: 99%

“…From a theoretical and numerical points of view, four difficulties have been pointed out in [6] regarding the resolution of the LJ-based adhesive contact problem. They are directly related to the intrinsic multi-scale, unbounded, undefined (in presence of interpenetrations) and non-convex natures of the LJ potential.…”

Section: Introductionmentioning

confidence: 99%

“…They are directly related to the intrinsic multi-scale, unbounded, undefined (in presence of interpenetrations) and non-convex natures of the LJ potential. The first three difficulties have been dealt with in [6] where the multiscale aspect was addressed by using the Arlequin method (see [4,5]) and the unbounded and undefined aspects were addressed by a convergent model-adaptivity method. The fourth difficulty is addressed in this work.…”

Section: Introductionmentioning

confidence: 99%

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An asymptotic numerical method to solve compliant Lennard-Jones-based contact problems involving adhesive instabilities

Dhia

2018

Comput Mech

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For compliant adhesive contact problems based on the Lennard-Jones (LJ) potential, the non-convexity of the latter leads to jump-in and jump-off instabilities which can hardly be traced by using classical algorithms. In this work, we combine an adapted Asymptotic Numerical Method (ANM) and the multiscale Arlequin method to trace efficiently these instabilities. The ANM is used to trace the entire unstable solution path in a branch-by-branch manner. The Arlequin method is used to achieve a refined resolution in the vicinity of the contact surface and to reduce possible spurious numerical oscillations due to coarse surface discretizations. Numerical results, validated by comparison with available ones, reveal the accuracy, efficiency and robustness of the proposed global methodology.

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Section: Attachment and Detachment Of A Rigid Sphere From An Elastic mentioning

confidence: 89%

Section: : End Loopmentioning

confidence: 99%