Journal ArticleDOI
Linear models of dissipation in anelastic solids
Michele Caputo,Francesco Mainardi +1 more
- Vol. 1, Iss: 2, pp 161-198
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The article was published on 1971-04-01. It has received 726 citations till now. The article focuses on the topics: Dissipation.read more
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Application of Fractional Order Theory of Thermoelasticity in a Thick Plate Under Axisymmetric Temperature Distribution
TL;DR: In this article, the fractional order theory of thermoelasticity is applied to the two-dimensional problem of a thick plate whose lower and upper surfaces are traction free and subjected to a given axisymmetric temperature distribution.
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Fractional Noether’s theorem with classical and Caputo derivatives: constants of motion for non-conservative systems
TL;DR: In this article, a generalization of the Noether's theorem for Lagrangians depending on mixed classical and Caputo derivatives is presented, which can be used to obtain constants of motion for dissipative systems.
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The benefit of fractional derivatives in modelling the dynamics of filler-reinforced rubber under large strains: a comparison with the Maxwell-element approach
D. Wollscheid,Alexander Lion +1 more
TL;DR: In this article, a constitutive approach of finite fractional viscoelasticity is proposed to approximate the dynamic material properties with respect to the storage and the loss modulus of carbon-black filled SBR rubber.
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New approximate solutions to fractional nonlinear systems of partial differential equations using the FNDM
TL;DR: In this paper, the authors apply the FNDM to obtain approximate numerical solutions for two different types of nonlinear time-fractional systems of partial differential equations, and show that their analytical solutions converge very rapidly to the exact solutions.
Journal ArticleDOI
Towards a consensus on rheological models for shear waves in soft tissues
TL;DR: This paper argued that the long history of biomechanics, including the concept of the extended relaxation spectrum, along with data collected from viscoelastic soft tissues over an extended range of times and frequencies, and the theoretical framework of multiple relaxation models which model the multi-scale nature of physical tissues, all lead to the conclusion that fractional derivative models represent the most succinct and meaningful models of soft tissue visco-elastic behavior.
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Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
Book
Stress Waves in Solids
TL;DR: A large and growing number of original papers on both the experimental and the theoretical aspects of stress wave propagation is appearing in the scientific literature, and two international conferences solely concerned with the subject have been held during the last five years as mentioned in this paper.