Hyperelastic Anisotropic Microplane Constitutive Model for Annulus Fibrosus

2007 ◽  
Vol 129 (5) ◽  
pp. 632-641 ◽  
Author(s):  
Ferhun C. Caner ◽  
Zaoyang Guo ◽  
Brian Moran ◽  
Zdeněk P. Bažant ◽  
Ignacio Carol
Keyword(s):  
Experimental Data ◽  
Soft Tissue ◽  
Constitutive Model ◽  
Annulus Fibrosus ◽  
Constitutive Models ◽  
Coupling Model ◽  
Microplane Model ◽  
Composite Effect ◽  
Matrix Interaction ◽  
Fiber Matrix

In a recent paper, Peng et al. (2006, “An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Interaction for the Human Annulus Fibrosis,” ASME J. Appl. Mech., 73(5), pp. 815–824) developed an anisotropic hyperelastic constitutive model for the human annulus fibrosus in which fiber-matrix interaction plays a crucial role in simulating experimental observations reported in the literature. Later, Guo et al. (2006, “A Composites-Based Hyperelastic Constitutive Model for Soft Tissue With Application to the Human Fibrosis,” J. Mech. Phys. Solids, 54(9), pp. 1952–1971) used fiber reinforced continuum mechanics theory to formulate a model in which the fiber-matrix interaction was simulated using only composite effect. It was shown in these studies that the classical anisotropic hyperelastic constitutive models for soft tissue, which do not account for this shear interaction, cannot accurately simulate the test data on human annulus fibrosus. In this study, we show that the microplane model for soft tissue developed by Caner and Carol (2006, “Microplane Constitutive Model and Computational Framework for Blood Vessel Tissue,” ASME J. Biomech. Eng., 128(3), pp. 419–427) can be adjusted for human annulus fibrosus and the resulting model can accurately simulate the experimental observations without explicit fiber-matrix interaction because, in microplane model, the shear interaction between the individual fibers distributed in the tissue provides the required additional rigidity to explain these experimental facts. The intensity of the shear interaction between the fibers can be adjusted by adjusting the spread in the distribution while keeping the total amount of the fiber constant. A comparison of results obtained from (i) a fiber-matrix parallel coupling model, which does not account for the fiber-matrix interaction, (ii) the same model but enriched with fiber-matrix interaction, and (iii) microplane model for soft tissue adapted to annulus fibrosus with two families of fiber distributions is presented. The conclusions are (i) that varying degrees of fiber-fiber and fiber-matrix shear interaction must be taking place in the human annulus fibrosus, (ii) that this shear interaction is essential to be able to explain the mechanical behavior of human annulus fibrosus, and (iii) that microplane model can be fortified with fiber-matrix interaction in a straightforward manner provided that there are new experimental data on distribution of fibers, which indicate a spread so small that it requires an explicit fiber-matrix interaction to be able to simulate the experimental data.

scholarly journals Microplane Constitutive Model and Metal Plasticity

2000 ◽  
Vol 53 (10) ◽  
pp. 265-281 ◽  
Author(s):  
Michele Brocca ◽  
Zdeneˇk P. Bazˇant
Keyword(s):  
Constitutive Model ◽  
Plastic Region ◽  
Constitutive Models ◽  
Flow Theory ◽  
Basic Structure ◽  
Steel Tube ◽  
Loading Path ◽  
Microplane Model ◽  
Metal Plasticity ◽  
Path Direction

The microplane model is a versatile constitutive model in which the stress-strain relations are defined in terms of vectors rather than tensors on planes of all possible orientations, called the microplanes, representative of the microstructure of the material. The microplane model with kinematic constraint has been successfully employed in the modeling of concrete, soils, ice, rocks, fiber composites and other quasibrittle materials. The microplane model provides a powerful and efficient numerical tool for the development and implementation of constitutive models for any kind of material. The paper presents a review of the background from which the microplane model stems, highlighting differences and similarities with other approaches. The basic structure of the microplane model is then presented, together with its extension to finite strain deformation. Three microplane models for metal plasticity are introduced and discussed. They are compared mutually and with the classical J2-flow theory for incremental plasticity by means of two examples. The first is the material response to a nonproportional loading path given by uniaxial compression into the plastic region followed by shear (typical of buckling and bifurcation problems). This example is considered in order to show the capability of the microplane model to represent a vertex on the yield surface. The second example is the ‘tube-squash’ test of a highly ductile steel tube: a finite element computation is run using two microplane models and the J2-flow theory. One of the microplane models appears to predict more accurately the final shape of the deformed tube, showing an improvement compared to the J2-flow theory even when the material is not subjected to abrupt changes in the loading path direction. This review article includes 114 references.

Experimental and Numerical Study of Soft Tissue Surrogate Behavior Under Ballistic Loading

2012 ◽  
Author(s):  
Ericka K. Amborn ◽  
Karim H. Muci-Küchler ◽  
Brandon J. Hinz
Keyword(s):  
Soft Tissue ◽  
Constitutive Model ◽  
High Strain Rate ◽  
Strain Rate ◽  
High Strain ◽  
Split Hopkinson Pressure Bar ◽  
Numerical Study ◽  
Constitutive Models ◽  
Material Behavior ◽  
Good Representation

Studying the high strain rate behavior of soft tissues and soft tissue surrogates is of interest to improve the understanding of injury mechanisms during blast and impact events. Tests such as the split Hopkinson pressure bar have been successfully used to characterize material behavior at high strain rates under simple loading conditions. However, experiments involving more complex stress states are needed for the validation of constitutive models and numerical simulation techniques for fast transient events. In particular, for the case of ballistic injuries, controlled tests that can better reflect the effects induced by a penetrating projectile are of interest. This paper presents an experiment that tries to achieve that goal. The experimental setup involves a cylindrical test sample made of a translucent soft tissue surrogate that has a small pre-made cylindrical channel along its axis. A small caliber projectile is fired through the pre-made channel at representative speeds using an air rifle. High speed video is used in conjunction with specialized software to generate data for model validation. A Lagrangian Finite Element Method (FEM) model was prepared in ABAQUS/Explicit to simulate the experiments. Different hyperelastic constitutive models were explored to represent the behavior of the soft tissue surrogate and the required material properties were obtained from high strain rate test data reported in the open literature. The simulation results corresponding to each constitutive model considered were qualitatively compared against the experimental data for a single projectile speed. The constitutive model that provided the closest match was then used to perform an additional simulation at a different projectile velocity and quantitative comparisons between numerical and experimental results were made. The comparisons showed that the Marlow hyperelastic model available in ABAQUS/Explicit was able to produce a good representation of the soft tissue surrogate behavior observed experimentally at the two projectile speeds considered.

A Modified Microplane Model Using Transformation Surfaces to Consider Loading History on Phase Transition in Shape Memory Alloys

2014 ◽  
Author(s):  
Milad Shirani ◽  
Reza Mehrabi ◽  
Masood Taheri Andani ◽  
Mahmoud Kadkhodaei ◽  
Mohammad Elahinia ◽  
...  
Keyword(s):  
Free Energy ◽  
Constitutive Model ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Phenomenological Approach ◽  
Material Point ◽  
Loading History ◽  
Energy Potential ◽  
Microplane Model ◽  
Thermodynamic Driving Force

In most of the existing SMA constitutive models, it is assumed that transformation starts when a thermodynamic driving force reaches a specified amount regardless of loading history. In this work, a phenomenological approach is used to develop an enhanced one-dimensional constitutive model in which loading history is directly considered as one of the main parameters affecting the transformation start conditions. To generalize the model to three-dimensional cases, a microplane formulation based on volumetric-deviatoric is employed. A free energy potential is defined at the microplane level, integrated over all orientations at a material point to provide the macroscopic free energy. Experiments are carried out on Nitinol superelastic tubes to validate the newly proposed constitutive model. In these experiments, interruptions are applied during transformations to show the effects of loading history on transformation start conditions. Numerical results are compared with the experimental data to demonstrate the accuracy of the enhanced model.

An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Shear Interaction for the Human Annulus Fibrosus

2005 ◽  
Vol 73 (5) ◽  
pp. 815-824 ◽  
Author(s):  
X. Q. Peng ◽  
Z. Y. Guo ◽  
B. Moran
Keyword(s):  
Constitutive Model ◽  
Energy Function ◽  
Annulus Fibrosus ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Material Parameters ◽  
The Matrix ◽  
Fiber Matrix ◽  
Matrix Shear ◽  
Fiber Interaction

Based on fiber reinforced continuum mechanics theory, an anisotropic hyperelastic constitutive model for the human annulus fibrosus is developed. A strain energy function representing the anisotropic elastic material behavior of the annulus fibrosus is additively decomposed into three parts nominally representing the energy contributions from the matrix, fiber and fiber-matrix shear interaction, respectively. Taking advantage of the laminated structure of the annulus fibrosus with one family of aligned fibers in each lamella, interlamellar fiber-fiber interaction is eliminated, which greatly simplifies the constitutive model. A simple geometric description for the shearing between the fiber and the matrix is developed and this quantity is used in the representation of the fiber-matrix shear interaction energy. Intralamellar fiber-fiber interaction is also encompassed by this interaction term. Experimental data from the literature are used to obtain the material parameters in the constitutive model and to provide model validation. Determination of the material parameters is greatly facilitated by the partition of the strain energy function into matrix, fiber and fiber-matrix shear interaction terms. A straightforward procedure for computation of the material parameters from simple experimental tests is proposed.

NUMERICAL VALIDATION OF A FIBER-REINFORCED HYPERELASTIC CONSTITUTIVE MODEL FOR HUMAN INTERVERTEBRAL DISC ANNULUS FIBROSUS

2011 ◽  
Vol 11 (01) ◽  
pp. 163-176
Author(s):  
XIONGQI PENG ◽  
YU WANG ◽  
ZAOYANG GUO ◽  
SHAOQING SHI
Keyword(s):  
Experimental Data ◽  
Lumbar Spine ◽  
Constitutive Model ◽  
Intervertebral Disc ◽  
Numerical Simulations ◽  
Annulus Fibrosus ◽  
Fe Model ◽  
Fiber Reinforced ◽  
Cadaveric Specimen ◽  
Motion Segment

This paper validates a constitutive model for human intervertebral disc annulus fibrosus via numerical simulations on a lumber spine motion segment. This anisotropic hyperelastic fiber-reinforced constitutive model was previously developed by the authors. Based on three-dimensional (3D) lumbar spine segments that are constructed from CT scanning images, a detailed and anatomically accurate human lumbar spine finite element (FE) model for L3–L4 motion segment is developed. The FE model includes vertebral bodies, intervertebral disc, and various ligaments. Numerical simulations are carried out by using commercial CAE software package ABAQUS/Standard. The loading cases considered in the numerical analysis are set to be consistent with sets-up of cadaveric specimen testing available in the literature. Numerical results such as load–displacement curves and nucleus pressure are compared with experimental data. Simulation results show good consistency with cadaveric experimental data, and have good biomechanical fidelity. The constitutive model can be used for human intervertebral disc modeling and biomechanical analysis of human spine column.

scholarly journals Identifiability of Tissue Material Parameters from Uniaxial Tests using Multi-start Optimization

2020 ◽  
Author(s):  
Babak N. Safa ◽  
Michael H. Santare ◽  
C. Ross Ethier ◽  
Dawn M. Elliott
Keyword(s):  
Experimental Data ◽  
Constitutive Model ◽  
Constitutive Models ◽  
Data Fitting ◽  
Tissue Mechanics ◽  
Lateral Strain ◽  
Model Parameters ◽  
Fiber Reinforced ◽  
Material Parameters ◽  
Tissue Material

AbstractDetermining tissue biomechanical material properties from mechanical test data is frequently required in a variety of applications, e.g. tissue engineering. However, the validity of the resulting constitutive model parameters is the subject of debate in the field. Common methods to perform fitting, such as nonlinear least-squares, are known to be subject to several limitations, most notably the uniqueness of the fitting results. Parameter optimization in tissue mechanics often comes down to the “identifiability” or “uniqueness” of constitutive model parameters; however, despite advances in formulating complex constitutive relations and many classic and creative curve-fitting approaches, there is no accessible framework to study the identifiability of tissue material parameters. Our objective was to assess the identifiability of material parameters for established constitutive models of fiber-reinforced soft tissues, biomaterials, and tissue-engineered constructs. To do so, we generated synthetic experimental data by simulating uniaxial tension and compression tests, commonly used in biomechanics. We considered tendon and sclera as example tissues, using constitutive models that describe these fiber-reinforced tissues. We demonstrated that not all of the model parameters of these constitutive models were identifiable from uniaxial mechanical tests, despite achieving virtually identical fits to the stress-stretch response. We further show that when the lateral strain was considered as an additional fitting criterion, more parameters are identifiable, but some remain unidentified. This work provides a practical approach for addressing parameter identifiability in tissue mechanics.Statement of SignificanceData fitting is a powerful technique commonly used to extract tissue material parameters from experimental data, and which thus has applications in tissue biomechanics and engineering. However, the problem of “uniqueness” or “identifiability” of the fit parameters is a significant issue, limiting the fit results’ validity. Here we provide a novel method to evaluate data fitting and assess the uniqueness of results in the tissue mechanics constitutive models. Our results indicate that the uniaxial stress-stretch experimental data are not adequate to identify all the tissue material parameters. This study is of potential interest to a wide range of readers because of its application for the characterization of other engineering materials, while addressing the problem of uniqueness of the fitted results.

An Evaluation of Several Constitutive Model Structures for Transient Nonproportional Cyclic Plasticity

1986 ◽  
Vol 108 (3) ◽  
pp. 273-279 ◽  
Author(s):  
W. Sotolongo ◽  
D. L. McDowell
Keyword(s):  
Experimental Data ◽  
Constitutive Model ◽  
Constitutive Models ◽  
Plasticity Theory ◽  
Cyclic Plasticity ◽  
Multiaxial Loading ◽  
Torsional Loading ◽  
Integration Algorithm ◽  
Surface Theory ◽  
Model Structures

Four constitutive models for cyclic plasticity of different essential structure are evaluated under conditions of nonproportional, multiaxial loading. Drucker’s one-surface theory, McDowell’s two-surface theory, Krieg’s one-surface theory with Radial-Return Integration Algorithm, and Abrahamson’s Unified Creep-Plasticity theory are the constitutive models under consideration. Their transient hardening and stable loop responses are compared to experimental data for two nonproportional axial-torsional loading histories. Their computational efficiency is also analyzed.

A transversely hyperelastic constitutive model of flexible film composite

2021 ◽  
pp. 152808372110017
Author(s):  
Zhipeng Qu ◽  
Houdi Xiao ◽  
Mingyun Lv
Keyword(s):  
Shear Stress ◽  
Constitutive Model ◽  
Strain Energy Function ◽  
Shear Stresses ◽  
Fiber Elongation ◽  
Plane Shear ◽  
Matrix Interaction ◽  
Out Of Plane ◽  
Fiber Matrix ◽  
Anisotropic Elastic

This paper presents a transversely hyperelastic constitutive model for predicting mechanical properties of flexible composites under unidirectional tension. A strain energy function which reflects the behavior of anisotropic elastic material is decomposed into three parts: matrix, fiber and fiber-matrix interaction. The fiber-matrix interaction was decomposed into in-plane shear stresses and out-of-plane shear stress, the in-plane shear stresses were related to the fiber elongation invariants, and the out-of-plane shear stress was related to the fiber elongation invariants and the matrix invariants. The fiber-matrix interaction considering shear factor was established. Based on fiber reinforced continuum mechanics, a transverse hyperelastic constitutive model including fiber, matrix and their interaction is developed. The transversely hyperelastic constitutive model is verified by the uniaxial tension tests. The constitutive model can be used to design the flexible structure of stratospheric airship.

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