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.
Three-Dimensional Finite Element Simulations on Impact Responses of Gels With Fractional Derivative Models
University of the Ryukyus,
Nakagami-gun, Okinawa 903-0213, Japan
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.
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Fukunaga, M., Fujikawa, M., and Shimizu, N. (February 15, 2019). "Three-Dimensional Finite Element Simulations on Impact Responses of Gels With Fractional Derivative Models." ASME. J. Comput. Nonlinear Dynam. April 2019; 14(4): 041011. https://doi.org/10.1115/1.4042525
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