Fractal Viscoelastic Models
Introduction of the Hausdorff derivative, a new kind of methodology, for modeling viscoelastic behaviors.
Viscoelastic Behaviors of Materials
A wide range of materials, such as rubber, soft soil, blood, colloid, and polymer in the real world, are observed to simultaneously exhibit both the elastic and viscous behaviors. It is well known that the stress, respectively, in purely elastic and viscous process is linear to the strain and the rate of strain. In contrast, the viscoelastic stress response of viscoelastic materials is dependent on time and strain rate, leading to complex behaviors of creep and relaxation in the case of certain stress or constraint. Such power-law responses are usually considered as memorial behaviors, in other words, history-dependent process.
In addition, some viscoelastic materials present certain abnormal properties in the frequency domain, such as frequency-dependent damping and energy...
- Bland DR (1960) The theory of linear viscoelasticity, international series of monographs on pure and applied mathematics, vol 10. Pergamon, OxfordGoogle Scholar
- Chen W (2016) Non-power-function metric: a generalized fractal. viXra Preprint. http://viXra.org/abs/1612.0409
- Chen W (2017) Fractal geometric theory of Hausdorff calculus and fractional calculus models. Comput Aided E 27:1–6 (in Chinese)Google Scholar
- Christensen RM (1971) Theory of viscoelasticity. Academic, New YorkGoogle Scholar
- Mainardi F (2010) Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models. Imperial College Press, LondonGoogle Scholar
- Reyes-Marambio J, Moser F, Gana F, Severino B, Calderón-Muñoz WR, Palma-Behnke R, Estevez PA, Orchard M, Cortés M (2016) A fractal time thermal model for predicting the surface temperature of air-cooled cylindrical Li-ion cells based on experimental measurements. J Power Sources 306:636–645CrossRefGoogle Scholar