Constitutive Formulation for Numerical Analysis of Visco-Hyperelastic Damage Phenomena in Soft Biological Tissues

2006 ◽  
Author(s):  
Arturo N. Natali ◽  
Emanuele L. Carniel ◽  
Piero G. Pavan ◽  
Alessio Gasparetto ◽  
Franz G. Sander ◽  
...  
Keyword(s):  
Strain Rate ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Constitutive Models ◽  
Experimental Tests ◽  
Biological Tissues ◽  
Tissue Response ◽  
Time Dependent ◽  
Soft Biological Tissues ◽  
Constitutive Formulation

Soft biological tissues show a strongly non linear and time-dependent mechanical response and undergo large strains under physiological loads. The microstructural arrangement determines specific anisotropic macroscopic properties that must be considered within a constitutive formulation. The characterization of the mechanical behaviour of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non linearity. In the model presented here a hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for soft tissues and can be properly arranged for the investigation of viscous and damage phenomena as well to interpret significant aspects pertaining to ordinary and degenerative conditions. Visco-hyperelastic models are used to analyze the time-dependent mechanical response, while elasto-damage models account for the stiffness and strength decrease that can develop under significant loading or degenerative conditions. Experimental testing points out that damage response is affected by the strain rate associated with loading, showing a decrease in the damage limits as the strain rate increases. This phenomena can be investigated by means of a model capable of accounting for damage phenomena in relation to viscous effects. The visco-hyperelastic damage model developed is defined on the basis of a Helmholtz free energy function depending on the strain-damage history. In particular, a specific damage criterion is formulated in order to evaluate the influence of the strain rate on damage. The model can be implemented in a general purpose finite element code. This makes it possible to perform numerical analyses of the mechanical response considering time-dependent effects and damage phenomena. The experimental tests develop investigated tissue response for different strain rate conditions, accounting for stretch situations capable of inducing damage phenomena. The reliability of the formulation is evaluated by a comparison with the results of experimental tests performed on pig periodontal ligament.

A Visco-Hyperelastic-Damage Constitutive Model for the Analysis of the Biomechanical Response of the Periodontal Ligament

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Arturo N. Natali ◽  
Emanuele L. Carniel ◽  
Piero G. Pavan ◽  
Franz G. Sander ◽  
Christina Dorow ◽  
...  
Keyword(s):  
Strain Rate ◽  
Periodontal Ligament ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Experimental Testing ◽  
Constitutive Models ◽  
Biological Tissues ◽  
Time Dependent ◽  
Large Strains ◽  
Free Energy Function

The periodontal ligament (PDL), as other soft biological tissues, shows a strongly non-linear and time-dependent mechanical response and can undergo large strains under physiological loads. Therefore, the characterization of the mechanical behavior of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non-linearity. The microstructural arrangement determines specific anisotropic properties. A hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for the PDL and properly arranged for investigating the viscous and damage phenomena as well to interpret significant aspects pertaining to ordinary and degenerative conditions. Visco-hyperelastic models are used to analyze the time-dependent mechanical response, while elasto-damage models account for the stiffness and strength decrease that can develop under significant loading or degenerative conditions. Experimental testing points out that damage response is affected by the strain rate associated with loading, showing a decrease in the damage limits as the strain rate increases. These phenomena can be investigated by means of a model capable of accounting for damage phenomena in relation to viscous effects. The visco-hyperelastic-damage model developed is defined on the basis of a Helmholtz free energy function depending on the strain-damage history. In particular, a specific damage criterion is formulated in order to evaluate the influence of the strain rate on damage. The model can be implemented in a general purpose finite element code. The accuracy of the formulation is evaluated by using results of experimental tests performed on animal model, accounting for different strain rates and for strain states capable of inducing damage phenomena. The comparison shows a good agreement between numerical results and experimental data.

A STUDY ON THE EFFECT OF COLLAGEN FIBER ORIENTATION ON MECHANICAL RESPONSE OF SOFT BIOLOGICAL TISSUES

2015 ◽  
Vol 76 (7) ◽  
Author(s):  
Farshid Fathi ◽  
Shahrokh Shahi ◽  
Soheil Mohammadi
Keyword(s):  
Finite Element ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Strain Energy Function ◽  
Soft Materials ◽  
Biological Tissues ◽  
Soft Biological Tissues ◽  
Proposed Model ◽  
The Matrix ◽  
Element Approach

Extensive research has been performed in the past decades to study the behavior of soft biological tissues in order to reduce the need for practical experiments. The applicability of these researches, particularly for skin, ligament, muscles and the heart, brings up its importance in various biological science and technology disciplines such as surgery and medicine. Softness and large deformation govern the behavior of soft materials and prohibit the use of small strains solutions in finite element method.In this work, the focus is set on a strain energy function which has the advantage of accurately representing the behavior of a variety of soft tissues with only a few parameters in a finite element approach. The numerical results are verified with a set of tensile experiments to demonstrate the performance of the proposed model. The parameters include the matrix and collagen bundles and their orientation. Different cases are analyzed and discussed for better prediction of different soft tissue responses.  

scholarly journals On fibre dispersion modelling of soft biological tissues: a review

2019 ◽  
Vol 475 (2224) ◽  
pp. 20180736 ◽  
Author(s):  
Gerhard A. Holzapfel ◽  
Ray W. Ogden ◽  
Selda Sherifova
Keyword(s):  
Heart Valves ◽  
Mechanical Response ◽  
Structural Information ◽  
Second Harmonic ◽  
Biological Tissues ◽  
Mechanical Tests ◽  
Soft Biological Tissues ◽  
Tensor Models ◽  
Continuum Modelling ◽  
Stress And Deformation

Collagen fibres within fibrous soft biological tissues such as artery walls, cartilage, myocardiums, corneas and heart valves are responsible for their anisotropic mechanical behaviour. It has recently been recognized that the dispersed orientation of these fibres has a significant effect on the mechanical response of the tissues. Modelling of the dispersed structure is important for the prediction of the stress and deformation characteristics in (patho)physiological tissues under various loading conditions. This paper provides a timely and critical review of the continuum modelling of fibre dispersion, specifically, the angular integration and the generalized structure tensor models. The models are used in representative numerical examples to fit sets of experimental data that have been obtained from mechanical tests and fibre structural information from second-harmonic imaging. In particular, patches of healthy and diseased aortic tissues are investigated, and it is shown that the predictions of the models fit very well with the data. It is straightforward to use the models described herein within a finite-element framework, which will enable more realistic (and clinically relevant) boundary-value problems to be solved. This also provides a basis for further developments of material models and points to the need for additional mechanical and microstructural data that can inform further advances in the material modelling.

Finite Elastic Deformation for a Class of Soft Biological Tissues

1977 ◽  
Vol 99 (2) ◽  
pp. 98-103
Author(s):  
Han-Chin Wu ◽  
R. Reiss
Keyword(s):  
Energy Function ◽  
Annulus Fibrosus ◽  
Strain Energy ◽  
Soft Tissues ◽  
Broad Class ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Tension Test ◽  
Soft Biological Tissues ◽  
Precise Form

The stress response of soft biological tissues is investigated theoretically. The treatment follows the approach of Wu and Yao [1] and is now extended for a broad class of soft tissues. The theory accounts for the anisotropy due to the presence of fibers and also allows for the stretching of fibers under load. As an application of the theory, a precise form for the strain energy function is proposed. This form is then shown to describe the mechanical behavior of annulus fibrosus satisfactorily. The constants in the strain energy function have also been approximately determined from only a uniaxial tension test.

Strain-Rate Sensitive Constitutive Modeling of Anisotropic Visco-Hyperelastic Materials

2012 ◽  
Author(s):  
Sahand Ahsanizadeh ◽  
LePing Li
Keyword(s):  
Strain Rate ◽  
Evolution Equations ◽  
Mechanical Response ◽  
Viscoelastic Behavior ◽  
Biological Tissues ◽  
Internal Variables ◽  
Current Configuration ◽  
Hyperelastic Materials ◽  
History Of ◽  
Viscoelastic Constitutive Model

Integral-based formulations of viscoelasticity have been widely used to describe the mechanical behavior of soft biological tissues and polymers. However, it is suggested that they are not suitable to be used under high strain rates. On the other hand, strain-rate sensitive models with an explicit dependence on the strain-rate have been developed for a certain class of materials. They predict the viscoelastic behavior during ramp loading more accurately while fail to account for the relaxation response. In order to overcome these drawbacks, a viscoelastic constitutive model has been proposed in this study based on the concept of internal variables. While the behavior of elastic materials is uniquely determined by the current state of deformation or external variables, the mechanical response of inelastic materials are regulated also by internal variables. The internal variables are associated with the dissipative mechanisms in the material and along with the evolution equations introduce the effect of history of the deformation to the current configuration. The current study employs short-term and long-term internal variables to account for the viscoelastic response during loading and relaxation respectively.

Finite Element Implementation of a Planar Soft Tissue Structural Constitutive Model for Heart Valve Simulations

2013 ◽  
Author(s):  
Rong Fan ◽  
Michael S. Sacks
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Soft Tissues ◽  
Structural Model ◽  
Mechanical Response ◽  
Biological Tissues ◽  
Biaxial Test ◽  
Tissue Microstructure ◽  
Highly Nonlinear ◽  
Insight Into

Constitutive modeling is critical for numerical simulation and analysis of soft biological tissues. The highly nonlinear and anisotropic mechanical behaviors of soft tissues are typically due to the interaction of tissue microstructure. By incorporating information of fiber orientation and distribution at tissue microscopic scale, the structural model avoids ambiguities in material characterization. Moreover, structural models produce much more information than just simple stress-strain results, but can provide much insight into how soft tissues internally reorganize to external loads by adjusting their internal microstructure. It is only through simulation of an entire organ system can such information be derived and provide insight into physiological function. However, accurate implementation and rigorous validation of these models remains very limited. In the present study we implemented a structural constitutive model into a commercial finite element package for planar soft tissues. The structural model was applied to simulate strip biaxial test for native bovine pericardium, and a single pulmonary valve leaflet deformation. In addition to prediction of the mechanical response, we demonstrate how a structural model can provide deeper insights into fiber deformation fiber reorientation and fiber recruitment.

Implementation and Validation of Planar Soft Tissue Structural Constitutive Model

2013 ◽  
Author(s):  
Rong Fan ◽  
Michael S. Sacks
Keyword(s):  
Constitutive Model ◽  
Soft Tissues ◽  
Structural Model ◽  
Mechanical Response ◽  
Biological Tissues ◽  
Fetal Membrane ◽  
Tissue Microstructure ◽  
Highly Nonlinear ◽  
Finite Element Package ◽  
Insight Into

Constitutive modeling is of fundamental important for numerical simulation and analysis of soft biological tissues. The mechanical behaviors of soft tissues are usually highly nonlinear and anisotropic. The complex behavior is the results from the interaction of tissue microstructure. By incorporating information of fiber orientation and distribution at tissue microscopic scale, the structural model avoids ambiguities in material characterization. Moreover, structural models produce much more information than just simple stress-strain results, but can provide much insight into how soft tissues internally reorganize to external loads by adjusting their internal microstructure. Moreover, it is only through simulation of an entire organ system can such information be derived and provide insight into physiological function. However, accurate implementation and rigorous validation of these models remains very limited. In the present study we implemented a structural constitutive model into a commercial finite element package. The structural model was verified against experiential test data for native bovine pericardium and fetal membrane. In addition to prediction of the mechanical response, we demonstrate how a structural model can provide deeper insights into fiber reorientation and fiber recruitment.

Experimental Basis for Temperature-Dependent Viscoplastic Constitutive Equations

1990 ◽  
Vol 43 (5S) ◽  
pp. S338-S344 ◽  
Author(s):  
U. S. Lindholm
Keyword(s):  
Strain Rate ◽  
Constitutive Models ◽  
Inelastic Strain ◽  
Time Dependent ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Experimental Basis ◽  
Temperature Dependent ◽  
Evolutionary Equations ◽  
Nonproportional Loading

In this paper the author reviews experimental data which is felt to be illustrative of time-dependent, high temperature deformation of metals and, therefore, instructive for the development of constitutive models. Issues addressed are the interrelation between time (strain rate) and temperature, the development of evolutionary equations for both isotropic and directional hardening and recovery, and the orientation of the inelastic strain rate with respect to stress during nonproportional loading.

scholarly journals Variations in Hardness with Position In One Dimensionally Recovered Shock Loaded Metals

2018 ◽  
Vol 183 ◽  
pp. 02013 ◽  
Author(s):  
G. Whiteman ◽  
D.L. Higgins ◽  
B. Pang ◽  
J.C.F. Millett ◽  
Y-L. Chiu ◽  
...  
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Shock Loading ◽  
Mechanical Response ◽  
High Strain ◽  
Cold Work ◽  
Constitutive Models ◽  
Target Assembly ◽  
One Dimensional ◽  
The Impact

The microstructural and mechanical response of materials to shock loading is of the utmost importance in the development of constitutive models for high strain-rate applications. However, unlike a purely mechanical response, to ensure that the microstructure has been generated under conditions of pure one dimensional strain, the target assembly requires both a complex array of momentum traps to prevent lateral releases entering the specimen location from the edges and spall plates to prevent tensile interactions (spall) affecting the microstructure. In this paper, we examine these effects by performing microhardness profiles of shock loaded copper and tantalum samples. In general, variations in hardness both parallel and perpendicular to the shock direction were small indicating successful momentum trapping. Variations in hardness at different locations relative to the impact face are discussed in terms of the initial degree of cold work and the ability to generate and move dislocations in the samples.

Large Deformation Analysis of Some Soft Biological Tissues

1981 ◽  
Vol 103 (2) ◽  
pp. 73-78 ◽  
Author(s):  
H. Demiray
Keyword(s):  
Soft Tissues ◽  
Biological Tissues ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Soft Biological Tissues ◽  
Large Deformation Analysis ◽  
Vulcanized Rubber ◽  
Nonlinear Stress ◽  
Physiological Structure ◽  
Theoretical Results

Due to physiological structure of most of the soft biological tissues, measurable stresses develop after the specimen has been stretched to many hundreds of percent of its relaxed length. Therefore, the nonlinear stress-strain relations developed for vulcanized rubber cannot be applied to soft tissues, which are constitutionally much more nonlinear than other engineering materials. In this article, using two different elastic models proposed for elastic soft tissues, simple elongation of a cylindrical bar and the inflation of a spherical thick shell, which is deemed to be a model for a left venticle, are studied and the material coefficients characterizing the elastic model are obtained via comparing theoretical results with existing experiments on tissues. Furthermore, the elastic stiffnesses which are very important for physiologists and cardiologists are discussed and the consistency of the result with experiments are indicated.

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