Three-dimensional stress-gradient non-locality problem: Displacement field for an arbitrary and a conservative force
Abstract
In order to obtain the displacement field, both generally in the case of an arbitrary body force and specifically in the case of a conservative body force, the mechanical problem of statics of three-dimensional stress-gradient non-local medium is analytically solved on unbounded domain by considering a system of equations consisting of an equilibrium equation, infinitesimal strain, and both scalar- and tensor-type stress-gradient Eringen three-dimensional models. Since the system of equations is linear, for each model the solution is obtained in the form of a superposition of the local-type displacement field, common to each model, and the non-local-type displacement field, specific to the non-locality operator of the model. Among the three scalar-type and five tensor-type considered models, six distinct analytical displacement field expressions are obtained for an arbitrary body force: one expression specific to a scalar-type model, three specific to individual tensor-type models, while each of the remaining two expressions are common to one scalar- and one tensor-type model. The displacement vector fields are graphically represented in the case of gravitational body force, yielding five different models, since two tensor-type models become the same when the force is conservative.
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BibTeX
@misc{jelic2026threedimensional,
title = {{Three-dimensional stress-gradient non-locality problem: Displacement field for an arbitrary and a conservative force}},
author = {Slađan Jelić and Dušan Zorica},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39888},
eprint = {2610.39888},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39888},
}
RIS
TY - UNPB
TI - Three-dimensional stress-gradient non-locality problem: Displacement field for an arbitrary and a conservative force
AU - Slađan Jelić
AU - Dušan Zorica
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39888
UR - https://arxiv.org/abs/2610.39888
AB - In order to obtain the displacement field, both generally in the case of an arbitrary body force and specifically in the case of a conservative body force, the mechanical problem of statics of three-dimensional stress-gradient non-local medium is analytically solved on unbounded domain by considering a system of equations consisting of an equilibrium equation, infinitesimal strain, and both scalar- and tensor-type stress-gradient Eringen three-dimensional models. Since the system of equations is linear, for each model the solution is obtained in the form of a superposition of the local-type displacement field, common to each model, and the non-local-type displacement field, specific to the non-locality operator of the model. Among the three scalar-type and five tensor-type considered models, six distinct analytical displacement field expressions are obtained for an arbitrary body force: one expression specific to a scalar-type model, three specific to individual tensor-type models, while each of the remaining two expressions are common to one scalar- and one tensor-type model. The displacement vector fields are graphically represented in the case of gravitational body force, yielding five different models, since two tensor-type models become the same when the force is conservative.
ER -