On the dynamics of grounded shallow ice sheets: Modeling and analysis

Piersanti, Paolo; Témam, Roger

doi:10.1515/anona-2022-0280

Cited by 3 publications

(5 citation statements)

References 42 publications

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“…It can be shown, in the same fashion as [8,21], that the operator β is monotone, bounded and non-expansive. Lemma 2.1.…”

Section: Penalty Methods For Flexural Shell Modelmentioning

confidence: 89%

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On the numerical corroboration of an obstacle problem for linearly elastic flexural shells

Peng,

Piersanti,

Shen

2024

Phil. Trans. R. Soc. A.

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In this article, we study the numerical corroboration of a variational model governed by a fourth-order elliptic operator that describes the deformation of a linearly elastic flexural shell subjected not to cross a prescribed flat obstacle. The problem under consideration is modelled by means of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable Sobolev space and is known to admit a unique solution. Qualitative and quantitative numerical experiments corroborating the validity of the model and its asymptotic similarity with Koiter’s model are also presented. This article is part of the theme issue ‘Non-smooth variational problems with applications in mechanics’.

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“…It can be shown, in the same fashion as [8,21], that the operator β is monotone, bounded and non-expansive. Lemma 2.1.…”

Section: Penalty Methods For Flexural Shell Modelmentioning

confidence: 89%

“…Examples of frictionless contact problems in virus mechanics were recently considered in the papers [17,18]. Frictionless contact problems were also studied in the context of glaciology in the papers [19][20][21].…”

Section: Penalty Methods For Flexural Shell Modelmentioning

confidence: 99%

On the numerical corroboration of an obstacle problem for linearly elastic flexural shells

Peng,

Piersanti,

Shen

2024

Phil. Trans. R. Soc. A.

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“…surrounding bodies: this idea is especially encouraged by the recent progress on nonlinear problems of constrained shells (e.g. [56][57][58][59]). The research in this direction is ongoing.…”

Section: Conflict Of Interestmentioning

confidence: 99%

“…An even more ambitious target would be the analysis of sophisticated thin deformable inclusions and surrounding bodies: this idea is especially encouraged by the recent progress on nonlinear problems of constrained shells (e.g. [56–59]). The research in this direction is ongoing.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

On hyperelastic solid with thin rigid inclusion and crack subjected to global injectivity condition

Furtsev,

Rudoy,

Sazhenkov

2024

Phil. Trans. R. Soc. A.

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The paper investigates a problem concerning the equilibrium of a solid body containing a thin rigid inclusion and a crack. It is assumed that the body is hyperelastic, therefore, it is described within the framework of finite strain theory. One of the peculiarities of this problem is a global injectivity constraint, which prevents the body, the crack faces and the inclusion from both mutual and self penetration. First, the paper deals with the differential formulation of the problem. Next, we consider energy minimization, showing that the latter provides the weak formulation of the former. Finally, the existence of the weak solution is demonstrated through the use of the variational technique. This article is part of the theme issue ‘Non-smooth variational problems with applications in mechanics’.

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“…A different model describing the evolution of the thickness of shallow ice sheets was proposed and studied very recently by Piersanti and Temam [26].…”

Section: Introductionmentioning

confidence: 99%