A Note on Gradient/Fractional One-Dimensional Elasticity and Viscoelasticity

Abstract

An introductory discussion on a (weakly non-local) gradient generalization of some one-dimensional elastic and viscoelastic models, and their fractional extension is provided. Emphasis is placed on the possible implications of micro- and nano- engineering problems, including small-scale structural mechanics and composite materials, as well as collagen biomechanics and nanomaterials.

Nonlocal continuum mechanics structures: The virtual powers method vs the extra fluxes topic

“…Finally we observe that, for a better description of memory behaviors, a generalization of these nonlocal gradient theories to involve the Caputo-Fabrizio fractional calculus [31] is also desirable, see e.g. [32,33].…”

Sliding Mode Control for a Class of Nonlinear Fractional Order Systems with a Fractional Fixed-Time Reaching Law

“…Recently, fractional calculus (an extension of integer order calculus) has played an important role in solving all kinds of science and engineering problems. Fractional calculus aids the precision and conciseness of modeling, and many practical plants have been validated to have fractional order properties, such as memristor [1], viscoelasticity [2], psoriasis [3], and abnormal diffusion process [4,5]. In addition, fractional order controllers have been shown to achieve better control performance, such as strong robustness and rapid convergence speed, compared with classical integer order controllers [6][7][8].…”