Research Papers

Two-Way Coupled Multiscale Model for Predicting Mechanical Behavior of Bone Subjected to Viscoelastic Deformation and Fracture Damage

[+] Author and Article Information
Taesun You

Department of Civil Engineering,
362H WHIT,
2200 Vine Street,
University of Nebraska,
Lincoln, NE 68583
e-mail: tae-sun.you@unl.edu

Yong-Rak Kim

Department of Civil Engineering,
362N WHIT,
2200 Vine Street,
University of Nebraska,
Lincoln, NE 68583
e-mail: ykim3@unl.edu

Taehyo Park

Department of Civil and
Environmental Engineering,
Hanyang University,
Seoul 133-791, South Korea
e-mail: cepark@hanyang.ac.kr

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received June 2, 2016; final manuscript received December 5, 2016; published online February 9, 2017. Assoc. Editor: Xi Chen.

J. Eng. Mater. Technol 139(2), 021016 (Feb 09, 2017) (8 pages) Paper No: MATS-16-1164; doi: 10.1115/1.4035618 History: Received June 02, 2016; Revised December 05, 2016

This paper presents a two-way linked computational multiscale model and its application to predict the mechanical behavior of bone subjected to viscoelastic deformation and fracture damage. The model is based on continuum thermos-mechanics and is implemented through the finite element method (FEM). Two physical length scales (the global scale of bone and local scale of compact bone) were two-way coupled in the framework by linking a homogenized global object to heterogeneous local-scale representative volume elements (RVEs). Multiscaling accounts for microstructure heterogeneity, viscoelastic deformation, and rate-dependent fracture damage at the local scale in order to predict the overall behavior of bone by using a viscoelastic cohesive zone model incorporated with a rate-dependent damage evolution law. In particular, age-related changes in material properties and geometries in bone were considered to investigate the effect of aging, loading rate, and damage evolution characteristics on the mechanical behavior of bone. The model successfully demonstrated its capability to predict the viscoelastic response and fracture damage due to different levels of aging, loading conditions (such as rates), and microscale damage evolution characteristics with only material properties of each constituent in the RVEs.

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Fig. 1

Human bone (cross section) with two length scales (homogenous global-scale and heterogeneous local-scale RVE with fracture) [45,46]

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Fig. 2

Flowchart describing the two-way linked multiscale algorithm

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Fig. 3

Multiscale modeling of typical human bone with two length scales

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Fig. 4

Global-scale objects for: (a) young group and (b) aged group

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Fig. 5

Local scale RVEs for: (a) young group and (b) aged group

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Fig. 6

Selected local-scale RVEs for: (a) young group and (b) aged group

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Fig. 7

Stress contour of the global object for the young group at: (a) 0.2 s, (b) 0.5 s, and (c) 1.2 s

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Fig. 8

Embedded cohesive zone elements and crack development at 1.2 s for the young group in: (a) RVE-1, (b) RVE-2, and (c) RVE-3

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Fig. 9

Stress–strain plots for the young and aged groups with different loading rates

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Fig. 10

Stress–strain plots for various parameters in damage evolution law (Eq. (16)): (a) A and (b) m



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