Two-dimensional framework for modeling load transfer in nanocomposites with thin, stiff, and prestressed reinforcements
Abstract
This paper presents a novel framework for simulating load-transfer mechanisms in nanocomposites reinforced by thin, stiff, and prestressed reinforcements, such as, e.g., nanosheets or nanoplatelets. The reinforcements are modeled as open material surfaces treated as membranes endowed with their own elastic properties and residual surface tension; the matrix is assumed to be isotropic elastic. In the two-dimensional plane-strain setting considered here, each material surface is represented by a sufficiently smooth curve of otherwise arbitrary shape. The theoretical part of the framework is based on the Gurtin--Murdoch theory in which the surfaces are represented by traction jumps across them. The elastic fields in the matrix are exactly expressed by the integral representations written in terms of the unknown traction jumps that are functions of the second-order derivatives of the displacements. The computational part is based on the isogeometric boundary element method (IGABEM) that utilizes non-uniform rational B-splines (NURBS). The unknown traction jumps are found from the numerical solutions of the coupled system of singular boundary integral equations, after which the elastic fields in the matrix are evaluated. The procedure of extracting the values of the stress intensity factors (SIFs) at the tips of the surfaces is described. The proposed algorithm is validated against available benchmark solutions for multiple surfaces located along either straight segments or circular arcs. Selected parametric studies are performed to examine the influence of surface curvatures, relative spacing, orientation, and interactions. An example involving a graphene nanoplatelet-reinforced epoxy is presented.
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BibTeX
@misc{patil2026twodimensional,
title = {{Two-dimensional framework for modeling load transfer in nanocomposites with thin, stiff, and prestressed reinforcements}},
author = {Rohit Satish Patil and Zhilin Han and Sofia G. Mogilevskaya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34014},
eprint = {2610.34014},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34014},
}
RIS
TY - UNPB
TI - Two-dimensional framework for modeling load transfer in nanocomposites with thin, stiff, and prestressed reinforcements
AU - Rohit Satish Patil
AU - Zhilin Han
AU - Sofia G. Mogilevskaya
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34014
UR - https://arxiv.org/abs/2610.34014
AB - This paper presents a novel framework for simulating load-transfer mechanisms in nanocomposites reinforced by thin, stiff, and prestressed reinforcements, such as, e.g., nanosheets or nanoplatelets. The reinforcements are modeled as open material surfaces treated as membranes endowed with their own elastic properties and residual surface tension; the matrix is assumed to be isotropic elastic. In the two-dimensional plane-strain setting considered here, each material surface is represented by a sufficiently smooth curve of otherwise arbitrary shape. The theoretical part of the framework is based on the Gurtin--Murdoch theory in which the surfaces are represented by traction jumps across them. The elastic fields in the matrix are exactly expressed by the integral representations written in terms of the unknown traction jumps that are functions of the second-order derivatives of the displacements. The computational part is based on the isogeometric boundary element method (IGABEM) that utilizes non-uniform rational B-splines (NURBS). The unknown traction jumps are found from the numerical solutions of the coupled system of singular boundary integral equations, after which the elastic fields in the matrix are evaluated. The procedure of extracting the values of the stress intensity factors (SIFs) at the tips of the surfaces is described. The proposed algorithm is validated against available benchmark solutions for multiple surfaces located along either straight segments or circular arcs. Selected parametric studies are performed to examine the influence of surface curvatures, relative spacing, orientation, and interactions. An example involving a graphene nanoplatelet-reinforced epoxy is presented.
ER -