Pith Number

pith:5H7ENRV2

pith:2026:5H7ENRV2ZAPRQ3BUKJMFAM2M3G

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Volumetric Growth in Linear Elasticity Driven by an Optimality Criterion

Marco Picchi Scardaoni, Roberto Paroni, Rohan Abeyaratne

Volumetric growth in linear elasticity is determined implicitly by constrained optimization rather than by prescribed evolution laws.

arxiv:2605.13609 v1 · 2026-05-13 · math-ph · math.MP

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Claims

C1strongest claim

Using linearized elasticity as a convenient mechanical framework, we show that volumetric growth can be formulated as an optimization-driven process in which the growth tensor is determined implicitly by constrained optimization rather than prescribed through phenomenological evolution laws.

C2weakest assumption

That a suitable objective functional exists which encodes the physical driving mechanism of growth and that the resulting incremental constrained minimization problem remains well-posed under the stated equilibrium, mass-balance, and irreversibility constraints.

C3one line summary

Volumetric growth in linear elasticity is cast as a constrained optimization problem that determines the growth tensor at each step while satisfying equilibrium, mass balance, and irreversibility.

References

29 extracted · 29 resolved · 0 Pith anchors

[1] Abeyaratne, R., Paroni, R., Picchi Scardaoni, M. (2026). Surface growth driven by an opti- mality criterion. Submitted 2026

[2] Ambrosi, D., Guana, F. (2007). Stress-modulated growth.Mathematics and Mechanics of Solids, 12(3), 319–342. doi:10.1177/1081286505059739 2007 · doi:10.1177/1081286505059739

[3] Ambrosi, D., Mollica, F. (2002). On the mechanics of a growing tumor.International Journal of Engineering Science, 40(12), 1297–1316 2002

[4] Ambrosi, D., Pezzuto, S., Riccobelli, D., Stylianopoulos, T., Ciarletta, P. (2017). Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth.Journal of Elasticity, 129(1–2), 107– 2017 · doi:10.1007/s10659-016-9619-9

[5] Gradient Flows: In Metric Spaces and in the Space of Probability Measures 2005 · doi:10.1007/978-3-7643-8722-8

Receipt and verification

First computed	2026-05-18T02:44:18.076055Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9fe46c6bac81f186c34525850334cd99e3b0d2c76038be210af2fb7216f800d

Aliases

arxiv: 2605.13609 · arxiv_version: 2605.13609v1 · doi: 10.48550/arxiv.2605.13609 · pith_short_12: 5H7ENRV2ZAPR · pith_short_16: 5H7ENRV2ZAPRQ3BU · pith_short_8: 5H7ENRV2

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5H7ENRV2ZAPRQ3BUKJMFAM2M3G \
  | 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: e9fe46c6bac81f186c34525850334cd99e3b0d2c76038be210af2fb7216f800d

Canonical record JSON

{
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    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-13T14:43:09Z",
    "title_canon_sha256": "da9e201cdc025ed092239cfa0e167626b2cd25abdcee434fb35dc4e753c7c43f"
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  "source": {
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    "kind": "arxiv",
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}