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pith:OFH2LNM7

pith:2026:OFH2LNM7EQX22XRS7XF7TKHO6X

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Variational derivation of the Flamant solution for a nonlinear elastic wedge

Dominik Engl, Ian Tobasco, Paul Plucinsky

The Flamant solution from linear elasticity is the leading-order response of a nonlinear elastic wedge to small tip loads or displacements.

arxiv:2605.17485 v1 · 2026-05-17 · math.AP · cond-mat.soft

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Claims

C1strongest claim

We prove that the Flamant solution gives the leading order response of a slightly truncated wedge to small boundary displacements or loads. This asymptotic result holds for general hyperelastic energies with super-quadratic growth at infinity; it also holds in the borderline case of quadratic growth at infinity, so long as the tip of the wedge is subjected to small enough displacements or loads.

C2weakest assumption

The hyperelastic energy has at least super-quadratic growth at infinity (or quadratic growth with sufficiently small loads), which is required to apply the uniform geometric rigidity inequality and restore compactness after the logarithmic change of variables.

C3one line summary

The Flamant solution is the leading-order asymptotic response of a slightly truncated nonlinear elastic wedge to small loads, derived via a variational principle after a logarithmic change of variables.

References

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[1] iMechanica, October 19 2006 2006

[2] V. Agostiniani, G. Dal Maso, and A. DeSimone. Linear elasticity obtained from finite elasticity byΓ-convergence under weak coerciveness conditions.Ann. Inst. H. Poincaré C Anal. Non Linéaire, 29(5):71 2012

[3] R. Alicandro, G. Lazzaroni, M. Palombaro, and P. Wozniak. Derivation of linear elasticity from energy functionals with infinitely many wells, 2026. cvgmt preprint 2026

[4] S. Almi, E. Davoli, and M. Friedrich. Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture.J. Math. Pures Appl. (9), 175:1–36, 2023 2023

[5] J. R. Barber.Elasticity, volume 172 ofSolid Mechanics and Its Applications. Springer Cham, Cham, 4th edition, 2023 2023

Receipt and verification

First computed	2026-05-20T00:04:41.437346Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

714fa5b59f242fad5e32fdcbf9a8eef5f820538f5417e869135a32692e5ed73f

Aliases

arxiv: 2605.17485 · arxiv_version: 2605.17485v1 · doi: 10.48550/arxiv.2605.17485 · pith_short_12: OFH2LNM7EQX2 · pith_short_16: OFH2LNM7EQX22XRS · pith_short_8: OFH2LNM7

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OFH2LNM7EQX22XRS7XF7TKHO6X \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 714fa5b59f242fad5e32fdcbf9a8eef5f820538f5417e869135a32692e5ed73f

Canonical record JSON

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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-17T14:53:14Z",
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