A Semi-Empirical Elastic-Plastic-Visco-Damage Constitutive Model of Cortical Bone

2010 ◽  
Author(s):  
Qing Luo ◽  
Huijie Leng ◽  
Rae Acuna ◽  
Xuanliang Dong ◽  
Qiguo Rong ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Mechanical Behavior ◽  
Cortical Bone ◽  
Bone Fractures ◽  
Constitutive Models ◽  
Underlying Mechanism ◽  
Yield Behavior ◽  
Damage Constitutive Model ◽  
Semi Empirical ◽  
Further Development

Bone quality can be characterized by toughness of bone which quantifies the energy required for failure. As much of the toughness of bone occurs after yielding, elucidating the underlying mechanism of post-yield behavior of bone is critical for further development of clinical strategies to predict and prevent age and disease related bone fractures. However, the underlying mechanism of the post-yield behavior of cortical bone is so far poorly understood, which makes it difficult to establish physically sound constitutive models for cortical bone that could accurately predict the mechanical behavior of the tissue. The absence of the constitutive equations has significantly hindered the application of bone mechanics in solving biomedical problems. Besides, an accurate constitutive model is always required in numerical modeling and simulating the mechanical behavior of bone under different loading conditions. Based on the experimental results obtained in our lab, the objective of this study was to develop and verify a constitutive model of cortical bone under compression, which accounted for damage accumulation, plastic deformation and viscoelastic properties.

A Semi-Empirical Constitutive Model for Post Yield Behavior of Bone in Tension

2007 ◽  
Author(s):  
Huijie Leng ◽  
Jeffry S. Nyman ◽  
Xuanliang Dong ◽  
Michael J. Reyes ◽  
Xiaodu Wang
Keyword(s):  
Constitutive Model ◽  
Material Properties ◽  
Bone Fractures ◽  
Experimental Studies ◽  
Underlying Mechanism ◽  
Failure Behavior ◽  
Yield Behavior ◽  
Clinical Strategies ◽  
Semi Empirical ◽  
Further Development

Among the material properties that can be assessed through mechanical testing, toughness quantifies the energy required for failure and is therefore most suited for characterizing bone quality. As much of the toughness of bone occurs after yielding, post yield behavior of bone is attracting more and more attention [1, 2]. Although a lot of experimental studies have been conducted on post yield behavior of bone, little efforts have been made to develop constitutive relation for post yield behavior of bone tissues. Elucidating the underlying mechanism of post-yield behavior of bone is critical for further development of clinical strategies to predict and prevent age and disease related bone fractures. In addition, such understanding could help bridge the gap between biology and mechanics of bone since cellular activities are directly related to the ultrastructural architecture and composition of the tissue. Moreover, an accurate constitutive model is always required in numerical modeling and simulating the mechanical behavior of bone under different loading conditions. Based on the results reported in the literature and obtained in our laboratory, this study intends to develop and verify a semi-empirical constitutive model of the post-yield and failure behavior of the cortical bone tissue in tension.

scholarly journals A Damage Constitutive Model of Rock Subjected to Freeze-Thaw Cycles Based on Lognormal Distribution

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Hang Lin ◽  
Linyuan Liang ◽  
Yifan Chen ◽  
Rihong Cao
Keyword(s):  
Mechanical Properties ◽  
Constitutive Model ◽  
Lognormal Distribution ◽  
Constitutive Models ◽  
Strain Curve ◽  
Statistical Distribution ◽  
Freeze Thaw ◽  
Accurate Quantitative Analysis ◽  
Distribution Parameters ◽  
Damage Constitutive Model

The constitutive model of rock is closely connected with the mechanical properties of rock. To achieve a more accurate quantitative analysis of the mechanical properties of rock after the action of freeze-thaw cycles, it is necessary to establish the constitutive models of rock subjected to freeze-thaw cycles from the view of rock damage. Based on the assumption of rock couple damage, this study established a statistical damage constitutive model of rock subjected to freeze-thaw cycles by combining the lognormal distribution, which is commonly used in engineering reliability analysis, and the strain strength theory. Then, the coordinates and derivative at the peak of the stress-strain curve of the rock after the action of freeze-thaw cycles were obtained through experiments to solve the statistical distribution parameters με and S of the model, whereafter, the theoretical curves by the established model were compared with the experimental curves to verify the validity of it, which shows a great agreement. Finally, the sensitivity analysis of the statistical distribution parameters was implemented. The results indicate that με reflects the strength of the rock, which shows a positive relation, and S stands for the brittleness of the rock, which shows a negative relation.

scholarly journals A Statistical Damage Constitutive Model for Geomaterials under Plane-Strain Biaxial Stress State

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Hongwei Zhang ◽  
Zhijun Wan ◽  
Chaoyi Wang ◽  
Zhaoyang Ma ◽  
Yuan Zhang ◽  
...  
Keyword(s):  
Stress State ◽  
Constitutive Model ◽  
Mechanical Behavior ◽  
Plane Strain ◽  
Biaxial Stress ◽  
Statistical Parameters ◽  
Biaxial Stress State ◽  
Damage Constitutive Model ◽  
Statistical Damage Constitutive Model ◽  
Statistical Damage

The mechanical behavior of geomaterials under plane-strain biaxial stress state (PSBSS, a special case of biaxial stress state) is often considered in geotechnical structures such as highwall and longwall coal pillars. In this study, a modified statistical damage constitutive model based on Weibull distribution was established to explain the mechanical behavior of rocks under the PSBSS. The modified Wiebols-Cook criterion, Drucker-Prager criterion, and extremum method were adopted in this model to estimate the peak strength of rock, the strength level of microscopic element, and the statistical parameters of model, respectively. Besides, laboratory tests for brittle and ductile geomaterials under PSBSS were conducted using the modified surface instability detection apparatus to validate the accuracy of the proposed statistical damage model. Finally, the relationships between mechanical parameters and statistical parameters were studied and discussed.

Mechanical Behavior and Damage Constitutive Model of Rock Subjected to Water-Weakening Effect and Uniaxial Loading

2018 ◽  
Vol 52 (1) ◽  
pp. 97-106 ◽  
Author(s):  
Kang Bian ◽  
Jian Liu ◽  
Wei Zhang ◽  
Xiaoqing Zheng ◽  
Shaohu Ni ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Mechanical Behavior ◽  
Uniaxial Loading ◽  
Damage Constitutive Model

A Multistage Creep Damage Constitutive Model for Isotropic and Transversely-Isotropic Materials With Elastic Damage

2011 ◽  
Author(s):  
Calvin M. Stewart ◽  
Ali P. Gordon
Keyword(s):  
Constitutive Model ◽  
Creep Deformation ◽  
Constitutive Models ◽  
Creep Damage ◽  
Transversely Isotropic ◽  
Common Source ◽  
Isotropic Materials ◽  
Damage Constitutive Model ◽  
Transversely Isotropic Materials ◽  
Elastic Damage

In the pressure vessel and piping and power industries, creep deformation has continued to be an important design consideration. Directionally-solidified components have become commonplace. Creep deformation and damage is a common source of component failure. A considerable effort has gone into the study and development of constitutive models to account for such behavior. Creep deformation can be separated into three distinct regimes: primary, secondary, and tertiary. Most creep damage constitutive models are designed to model only one or two of these regimes. In this paper, a multistage creep damage constitutive model is developed and designed to model all three regimes of creep for isotropic materials. A rupture and critical damage prediction method follows. This constitutive model is then extended for transversely-isotropic materials. In all cases, the influence of creep damage on general elasticity (elastic damage) is included. Methods to determine material constants from experimental data are detailed. Finally, the isotropic material model is exercised on tough pitch copper tube and the anisotropic model on a Ni-base superalloy.

scholarly journals A Creep Damage Constitutive Model for a Rock Mass with Nonpersistent Joints under Uniaxial Compression

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Shuran Lv ◽  
Wanqing Wang ◽  
Hongyan Liu
Keyword(s):  
Rock Mass ◽  
Constitutive Model ◽  
Mechanical Behavior ◽  
Uniaxial Compression ◽  
Damage Model ◽  
Creep Damage ◽  
Model Parameters ◽  
Damage Constitutive Model ◽  
Set Up ◽  
Creep Damage Model

As part of the rock mass, both the mesoscopic and macroscopic flaws will affect the creep mechanical behavior of the rock mass with nonpersistent joints. This study focuses on this kind of rock mass and establishes a creep damage model to account for the effect of the joint on its creep mechanical behavior. First, on basis of analyzing the rock element creep mechanism and the typical creep deformation curve, a new creep damage constitutive model for the rock element is set up by introducing the damage theory and Kachanov damage evolution law into the classic creep constitutive model such as J body model. Second, the determination method of the proposed model parameters is studied in detail. Third, the calculation method of the macroscopic damage caused by the joint proposed by others is introduced which can consider the joint geometry, strength, and deformation parameters at the same time. Finally, the creep damage model for the rock mass with nonpersistent joints under uniaxial compression is proposed. The calculation examples indicate that it can present the effect of the joint on the rock mass creep mechanical behavior.

A Study on the Mechanical Behavior and Statistical Damage Constitutive Model of Sandstone

2017 ◽  
Vol 43 (10) ◽  
pp. 5179-5192 ◽  
Author(s):  
Junbao Wang ◽  
Zhanping Song ◽  
Baoyun Zhao ◽  
Xinrong Liu ◽  
Jun Liu ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Mechanical Behavior ◽  
Damage Constitutive Model ◽  
Statistical Damage Constitutive Model ◽  
Statistical Damage
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