Electromechanical Domain Wall Propagation in Dielectric Elastomers: An Exact Geometric Resolution via Conformal Mapping
Abstract
The localized electromechanical phase transition in dielectric elastomers involves complex moving boundaries and severe electrostatic fringe fields driven by high-curvature interfaces. Traditional phenomenological models fundamentally underestimate the configurational forces by completely ignoring the in-plane electric field components and geometric singularities. Here, we present a asymptotically exact geometric framework to resolve the domain wall propagation. By mapping the highly deformed current configuration to a regular parametric strip via conformal mapping, the field singularities are algebraically eliminated. An exact integration by parts directly translates the higher-order geometric metric into a rigorous topological mass term, projecting the global conformal electrostatics into a non-linear σ-model Lagrangian density. Incorporating the Gent strain-stiffening model, the continuous translation symmetry yields a Hamiltonian first integral. Eigenvalue analysis and Bogomol'nyi-Prasad-Sommerfield (BPS) bound calculations prove that the domain wall emerges strictly as an asymmetric heteroclinic orbit connecting two saddle points. This geometric resolution provides exact analytical scalings for the localized interface energy, domain wall thickness, and asymptotic decay lengths, eliminating all phenomenological parameters and offering a deterministic paradigm for geometric instabilities in active soft matter.
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BibTeX
@misc{xie2026electromechanical,
title = {{Electromechanical Domain Wall Propagation in Dielectric Elastomers: An Exact Geometric Resolution via Conformal Mapping}},
author = {Yu-Xin Xie},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03913},
eprint = {2609.03913},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03913},
note = {CC0},
}
RIS
TY - UNPB
TI - Electromechanical Domain Wall Propagation in Dielectric Elastomers: An Exact Geometric Resolution via Conformal Mapping
AU - Yu-Xin Xie
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03913
UR - https://arxiv.org/abs/2609.03913
AB - The localized electromechanical phase transition in dielectric elastomers involves complex moving boundaries and severe electrostatic fringe fields driven by high-curvature interfaces. Traditional phenomenological models fundamentally underestimate the configurational forces by completely ignoring the in-plane electric field components and geometric singularities. Here, we present a asymptotically exact geometric framework to resolve the domain wall propagation. By mapping the highly deformed current configuration to a regular parametric strip via conformal mapping, the field singularities are algebraically eliminated. An exact integration by parts directly translates the higher-order geometric metric into a rigorous topological mass term, projecting the global conformal electrostatics into a non-linear σ-model Lagrangian density. Incorporating the Gent strain-stiffening model, the continuous translation symmetry yields a Hamiltonian first integral. Eigenvalue analysis and Bogomol'nyi-Prasad-Sommerfield (BPS) bound calculations prove that the domain wall emerges strictly as an asymmetric heteroclinic orbit connecting two saddle points. This geometric resolution provides exact analytical scalings for the localized interface energy, domain wall thickness, and asymptotic decay lengths, eliminating all phenomenological parameters and offering a deterministic paradigm for geometric instabilities in active soft matter.
ER -