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Abstract

A linear physics-based model is developed to investigate the one-dimensional impact on a viscoelastic material. A generalized model with three Maxwell elements is considered to describe the viscoelastic behavior. An analytical method based on Laplace transformation is used to solve the impact problem. To have a comprehensive understanding of viscoelastic material response, drop-weight impact is also considered in this study. For both linear impact and drop-weight cases, a maximum reduction of 15% of the impact force as well as 32% higher energy absorption can be achieved with the increase in tan δ from 0.01 to 0.8 of viscoelastic material. In addition, for linear impact, impact force decreases by 20% when tan δ = 1. With the increase in tan δ, storage modulus decreases by around 57% for maintaining a predetermined deformation. Moreover, for almost constant maximum displacement, materials with a higher storage modulus absorb more impact energy and experience higher impact force as compared to materials with a lower storage modulus.

Keywords

Viscoelastic materials impact loading mathematical modeling loss tangent energy absorption force loss

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References

Lakes

. Viscoelastic materials. 1st ed. Cambridge: Cambridge University Press, 2009.

Fung

. Biomechanics. 2nd ed. New York: Springer, 1993.

Kingston

Clarke

. Some aspects of the rheological behavior of wood. 1: the effect of stress with particular reference to creep. Aust J Basic Appl Sci 1961; 6: 211–226.

Nakai

Grossman

PUA

. Deflection of wood under intermittent loading. Wood Sci Technol 1983; 17(1): 55–67.

Mukudai

. Evaluation on non-linear viscoelastic bending deflection of wood. Wood Sci Technol 1983; 17: 39–54.

Foudjet

. Contribution à l’étude Rhéologique du Matériau Bois. Thèseès Science Engénie Civil. Lyon: Université Claude Bernard, Lyon, 1986.

Yanson

. Energy dissipation calculations for a linear viscoelastic body under impact loading. Polym Mech 1974; 10(4): 578–583.

Yang

Chen

. Stress response and energy dissipation in a linear viscoelastic material under periodic triangular strain loading. J Polym Sci Polym Phys 1982; 20: 1437–1442.

Chen

Lakes

. Design of viscoelastic impact absorbers: optimal material properties. J Solid Struct 1990; 26(12): 1313–1328.

10.

Larson

Goyal

Aloisio

. A predictive model for impact response of viscoelastic polymers in drop tests. Rheologica 1996; 35: 252–264.

11.

Funk

Hall

Crandall

, et al. Linear and quasi-linear viscoelastic characterization of ankle ligaments. J Biomech Eng 2000; 122: 15–22.

12.

Zhang

Kassab

. A bilinear stress–strain relationship for arteries. Biomaterials 2007; 28(6): 1307–1315.

13.

Zhang

Chen

Kassab

. A rate-insensitive linear viscoelastic model for soft tissues. Biomaterials 2007; 28(24): 3579–3586.

14.

Yamamoto

Minato

. Theory of energy dissipation in a viscoelastic body under time-dependent stress. Adv Space Res 2007; 39(3): 472–476.

15.

Moraveca

Letzelterb

. On the modeling of the linear viscoelastic behaviour of biological materials using COMSOL Multiphysics. Appl Comput Mech 2007; 1: 175–184.

16.

Liu

. Dissipated energy function, hysteresis and precondition of a viscoelastic solid model. Nonlinear Anal Real World 2010; 11(2): 907–912.

17.

Argatov

. Mathematical modeling of linear viscoelastic impact: application to drop impact testing of articular cartilage. Trib Int 2013; 63: 213–225.

18.

Argatov

Selyutina

Mishuris

. Impact problem for the quasi-linear viscoelastic standard solid model. J Strain Anal Eng Des 2015; 51: 294–303.

19.

Viano

. Head impact biomechanics in sport. In: Gilchrist

(ed.) Solid mechanics and its applications: IUTAM symposium on impact biomechanics: from fundamental insights to applications. Dordrecht: Springer, 2005, pp.121–130.

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Mathematical modeling of viscoelastic material under impact load

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