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arXiv · 2303.05902

Eringen's model via linearization of nonlocal hyperelasticity

J. C. Bellido·J. Cueto·C. Mora-Corral
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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.

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J. C. Bellido, J. Cueto, C. Mora-Corral. 2023-03-10. Eringen's model via linearization of nonlocal hyperelasticity. https://arxiv.org/abs/2303.05902

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