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Viscoelastic modeling of brain tissue: A fractional calculus-based approach. (English) Zbl 1189.74084
Ganghoffer, Jean-François (ed.) et al., Mechanics of microstructured solids. Cellular materials, fibre-reinforced solids and soft tissues. Papers based on the presentations at the 11th EUROMECH-MECAMAT conference, Torino, Italy, March 10–14, 2008. Berlin: Springer (ISBN 978-3-642-00910-5/hbk; 978-3-642-00911-2/ebook). Lecture Notes in Applied and Computational Mechanics 46, 81-90 (2009).
Summary: In recent years, the mechanical study of the brain has become a major topic in the field of biomechanics. A global biomechanical model of the brain could find applications in neurosurgery and haptic device design. It would also be useful for car makers, who could then evaluate the possible trauma due to impact. Such a model requires the design of suitable constitutive laws for the different tissues that compose the brain (i.e. for white and for gray matters, among others).
Numerous constitutive equations have already been proposed, based on linear elasticity, hyperelasticity, viscoelasticity and poroelasticity. Regarding the strong strain-rate dependence of the brain’s mechanical behaviour, we decided to describe the brain as a viscoelastic medium. The design of the constitutive law was based on the Caputo fractional derivation operator. By definition, it is a suitable tool for modeling hereditary materials. Indeed, unlike integer order derivatives, fractional (or real order) operators are non-local, which means they take the whole history of the function into account when computing the derivative at current time $$t$$.
For the entire collection see [Zbl 1189.74006].

##### MSC:
 74L15 Biomechanical solid mechanics 74D10 Nonlinear constitutive equations for materials with memory 92C10 Biomechanics
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