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RISFractional Derivative Constitutive Models for Finite Deformation of Viscoelastic Materials
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: A methodology to derive fractional derivative constitutive models for finite deformation of viscoelastic materials is proposed in a continuum mechanics treatment. Fractional derivative models are generalizations of the ...
A Numerical Method for Caputo Differential Equations and Application of High-Speed Algorithm
Publisher: American Society of Mechanical Engineers (ASME)
Abstract: In this paper, a numerical algorithm to solve Caputo differential equations is proposed. The proposed algorithm utilizes the R2 algorithm for fractional integration based on the fact that the Caputo derivative of a function ...
Three-Dimensional Finite Element Simulations on Impact Responses of Gels With Fractional Derivative Models
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Fractional derivative constitutive models, developed by the present authors (CND, vol.10, 061002, 2015), are implemented into a commercial finite element (FE) software, abaqus (referred to as a computational model) for ...
A Fractional-Derivative Interpretation of Viscoelastic Rubbers—Part II: Application to Filled and Vulcanized Rubbers Under Large Compression
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Abstract. This paper explains the stress behavior of filled and vulcanized rubbers subject to large deformations by using the fractional derivatives proposed in a paper in this series (Fukunaga et al., 2025, “A Fractional ...