Eringen's model via linearization of nonlocal hyperelasticity
Analysis of PDEs
2023-03-13 v1 Mathematical Physics
math.MP
Abstract
We consider Riesz' fractional gradient and a truncated version of it. The equations of nonlocal nonlinear elasticity based on those gradients are known. We perform a formal linearization and arrive at the equations of linear elasticity based on those nonlocal operators. We prove the existence of solutions of the linear equations, notably, by a nonlocal version of Korn's inequality. Finally, we show that the linearizations obtained are particular cases of Eringen's model with singular kernels.
Keywords
Cite
@article{arxiv.2303.05902,
title = {Eringen's model via linearization of nonlocal hyperelasticity},
author = {J. C. Bellido and J. Cueto and C. Mora-Corral},
journal= {arXiv preprint arXiv:2303.05902},
year = {2023}
}