PreprintarXiv licencearXiv
Global Solution Branches of Forced Nonlinearly Elastic Single-Director Surfaces
Abstract
We prove the existence of classical solutions for nonlinearly elastic, single-director surfaces or shells characterized by finite mid-plane strains and curvature. We employ topological methods, yielding solution continua far (in norm) from an unloaded, stress-free reference configuration, i.e., a global implicit function theorem of sorts. We first establish the existence of a local solution path, which is subsequently shown to be part of a global solution branch, viz., a maximal connected, locally compact set, emanating from the unloaded state.
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BibTeX
@misc{healey2026global,
title = {{Global Solution Branches of Forced Nonlinearly Elastic Single-Director Surfaces}},
author = {Timothy J. Healey},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.38498},
eprint = {2609.38498},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38498},
}
RIS
TY - UNPB
TI - Global Solution Branches of Forced Nonlinearly Elastic Single-Director Surfaces
AU - Timothy J. Healey
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.38498
UR - https://arxiv.org/abs/2609.38498
AB - We prove the existence of classical solutions for nonlinearly elastic, single-director surfaces or shells characterized by finite mid-plane strains and curvature. We employ topological methods, yielding solution continua far (in norm) from an unloaded, stress-free reference configuration, i.e., a global implicit function theorem of sorts. We first establish the existence of a local solution path, which is subsequently shown to be part of a global solution branch, viz., a maximal connected, locally compact set, emanating from the unloaded state.
ER -