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Research Papers

Three-Dimensional Finite Element Simulations on Impact Responses of Gels With Fractional Derivative Models

[+] Author and Article Information
Masataka Fukunaga

College of Engineering,
Nihon University,
1-2-35-405, Katahira, Aoba-ku,
Sendai, Miyagi 980-0812, Japan
e-mail: fukunaga@apple.ifnet.or.jp

Masaki Fujikawa

Faculty of Engineering,
University of the Ryukyus,
1, Senbaru, Nishihara-cho,
Nakagami-gun, Okinawa 903-0213, Japan

Nobuyuki Shimizu

MotionLabo, Inc.,
TSK Building 302,
9-1, Aza-Sunada, Kanari,
Onahama, Iwaki, Fukushima 971-8135, Japan

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 17, 2018; final manuscript received January 8, 2019; published online February 15, 2019. Assoc. Editor: Corina Sandu.

J. Comput. Nonlinear Dynam 14(4), 041011 (Feb 15, 2019) (10 pages) Paper No: CND-18-1367; doi: 10.1115/1.4042525 History: Received August 17, 2018; Revised January 08, 2019

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 solving dynamic problems of gel-like materials. This software is used to solve impact responses of gels, and the solutions are compared with the experimental results. The FE results reproduce well the experimental acceleration and displacement data from different types of gels whose properties are characterized by the fractional order and material parameters. Thus, the computational model presented here was validated. The fractional derivative model is compared with the Simo model (Computer Method in Applied Mechanics and Engineering, 60:153–173, 1987), which is an integer order derivative model. The response of the fractional derivative model can be approximated well when appropriate parameters of the Simo model are used. In the finite element method (FEM), compressibility is introduced artificially for simulations. Interpretations are given on the compressibility of materials in the FEM.

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Figures

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Fig. 1

Left: sketch of experiment, right: the model for FEM. The striker is just before collision.

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Fig. 2

Examples of experimental data of acceleration of θ−5. See Table 1 for the material constants of θ–5, and see Table 2 for the parameters of experiments: (a) θ5–1, and (b) θ5–2.

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Fig. 3

Examples of numerical solutions by FEM. ν is the Poisson's ratio: (a) the acceleration, and (b) the displacement of the model θ5–2.

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Fig. 4

The smoothed acceleration of the model plotted in Fig. 3. The acceleration (a) and the displacement (b).

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Fig. 5

The experimental data of θ5–2 fitted by the model: (a) the acceleration and (b) the displacement

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Fig. 6

The experimental data of θ5–1 fitted by the model: (a) the acceleration and (b) the displacement

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Fig. 7

The experimental data of θ5–3 fitted by the model: (a) the acceleration and (b) the displacement

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Fig. 8

The experimental data of θ7–1 fitted by the model: (a) the acceleration and (b) the displacement

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Fig. 9

The experimental data of θ6–2 fitted by the model: (a) the acceleration and (b) the displacement

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Fig. 10

Impulse responses of θ7–1 calculated by the Simo model and by the fractional derivative model (denoted by proposal): (a) the accelerations and (b) the displacements

Tables

Errata

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