Comparison of Analytical and Finite Element Implementation of Exponential Constitutive Models for Valve Tissue Under Micropipette Aspiration

Author(s):  
Ruogang Zhao ◽  
Krista Lynn Sider ◽  
Craig A. Simmons

Micropipette aspiration (MA) has been widely used to measure the biomechanical properties of cells and biomaterials [1]. Typically a linear elastic half-space model is used to fit the experimental load-deformation data [1]. However, load-deformation relationships for most biological tissues are highly nonlinear, suggesting alternative constitutive models are necessary. In the case of aortic heart valve tissue, exponential-type constitutive models have been found to fit the biaxial stress-strain behavior well [2]. Based on these studies, Butcher et al. used an exponential constitutive model to characterize the response of chicken embryonic valve (atrioventricular cushion) under MA [3]. To do so, they implemented an analytical exponential constitutive model [2] and directly related the stress and strain to the experimentally measured pressure and aspiration length. This allowed the authors to fit the tissue MA data without accounting for the complexities of the boundary conditions and multicomponent strain field inherent in MA. However, it is unclear whether the material parameters estimated using this approach are different from those estimated by solving the more complex boundary value problem, which presumably more faithfully simulates the physical process of tissue aspiration.

2019 ◽  
Author(s):  
Mazin S. Sirry ◽  
Laura Dubuis ◽  
Neil H. Davies ◽  
Jun Liao ◽  
Thomas Franz

AbstractFinite element (FE) models have been effectively utilized in studying biomechanical aspects of myocardial infarction (MI). Although the rat is a widely used animal model for MI, there is a lack of material parameters based on anisotropic constitutive models for rat myocardial infarcts in literature. This study aimed at employing inverse methods to identify the parameters of an orthotropic constitutive model for myocardial infarcts in the acute, necrotic, fibrotic and remodelling phases utilizing the biaxial mechanical data developed in a previous study. FE model was developed mimicking the setup of the biaxial tensile experiment. The orthotropic case of the generalized Fung constitutive model was utilized to model the material properties of the infarct. The parameters of Fung model were optimized so that the FE solution best fitted the biaxial experimental stress-strain data. A genetic algorithm was used to minimize the objective function. Fung orthotropic material parameters for different infarct stages were identified. The FE model predictions best approximated the experimental data of the 28 days infarct stage with 3.0% mean absolute percentage error. The worst approximation was for the 7 days stage with 3.6% error. This study demonstrated that the experimental biaxial stress-strain data of healing rat infarcts could be successfully approximated using inverse FE methods and genetic algorithms. The material parameters identified in this study will provide an essential platform for FE investigations of biomechanical aspects of MI and the development of therapies.


2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Keyvan Amini Khoiy ◽  
Rouzbeh Amini

Located on the right side of the heart, the tricuspid valve (TV) prevents blood backflow from the right ventricle to the right atrium. Similar to other cardiac valves, quantification of TV biaxial mechanical properties is essential in developing accurate computational models. In the current study, for the first time, the biaxial stress–strain behavior of porcine TV was measured ex vivo under different loading protocols using biaxial tensile testing equipment. The results showed a highly nonlinear response including a compliant region followed by a rapid transition to a stiff region for all of the TV leaflets both in the circumferential and in the radial directions. Based on the data analysis, all three leaflets were found to be anisotropic, and they were stiffer in the circumferential direction in comparison to the radial direction. It was also concluded that the posterior leaflet was the most anisotropic leaflet.


2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Maureen L. Dreher ◽  
Srinidhi Nagaraja ◽  
Jorgen Bergstrom ◽  
Danika Hayman

Computational modeling is critical to medical device development and has grown in its utility for predicting device performance. Additionally, there is an increasing trend to use absorbable polymers for the manufacturing of medical devices. However, computational modeling of absorbable devices is hampered by a lack of appropriate constitutive models that capture their viscoelasticity and postyield behavior. The objective of this study was to develop a constitutive model that incorporated viscoplasticity for a common medical absorbable polymer. Microtensile bars of poly(L-lactide) (PLLA) were studied experimentally to evaluate their monotonic, cyclic, unloading, and relaxation behavior as well as rate dependencies under physiological conditions. The data were then fit to a viscoplastic flow evolution network (FEN) constitutive model. PLLA exhibited rate-dependent stress–strain behavior with significant postyield softening and stress relaxation. The FEN model was able to capture these relevant mechanical behaviors well with high accuracy. In addition, the suitability of the FEN model for predicting the stress–strain behavior of PLLA medical devices was investigated using finite element (FE) simulations of nonstandard geometries. The nonstandard geometries chosen were representative of generic PLLA cardiovascular stent subunits. These finite element simulations demonstrated that modeling PLLA using the FEN constitutive relationship accurately reproduced the specimen’s force–displacement curve, and therefore, is a suitable relationship to use when simulating stress distribution in PLLA medical devices. This study demonstrates the utility of an advanced constitutive model that incorporates viscoplasticity for simulating PLLA mechanical behavior.


Author(s):  
Rong Fan ◽  
Michael S. Sacks

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.


Author(s):  
Rong Fan ◽  
Michael S. Sacks

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.


2005 ◽  
Vol 05 (03) ◽  
pp. 397-413
Author(s):  
ŞEBNEM ÖZÜPEK ◽  
HENGCHU CAO

Characterization of anisotropy is studied in a bovine pericardial tissue undergoing non-homogeneous deformations. The purpose of this study is not to formulate an exact constitutive model for a particular tissue, but to develop a methodology for the measurement and representation of the stress-strain behavior of soft planar tissues, such as pericardium. Tissue samples with a central circular hole are subjected to uniaxial loading. A procedure for measuring local displacements is developed. Various constitutive models differing mainly in their representation of anisotropy are considered to simulate the test. The comparison of displacement and strain predictions with the measured values show that although the isotropic model has a good agreement with the data in the loading direction, the introduction of anisotropy is necessary to capture the essential characteristics of the test. The procedure provides a more realistic evaluation of the constitutive models, hence is more useful for stress analysis purposes.


2006 ◽  
Vol 306-308 ◽  
pp. 989-994 ◽  
Author(s):  
M. Nizar Machmud ◽  
Masaki Omiya ◽  
Hirotsugu Inoue ◽  
Kikuo Kishimoto

Based on previous available constitutive models, a phenomenological constitutive model has been constructed and is proposed to describe the strain, strain rate and temperature dependentdeformation behavior of PC/ABS blends. In this paper, four quasi-static uniaxial tension tests of a specimen tested at different strain rates and temperatures were used to identify the constitutive model constants. By using the proposed constitutive model, predicting the stress-strain behavior of the PC/ABS blend tested at certain strain rate and different temperatures compares well to the behavior exhibited from the tests. From comparison between the DSGZ and the proposed models, proposed model shows a better prediction. Evaluation of the proposed constitutive model was also presented and it has revealed that the proposed model might have a potential to be used for predicting a wide range of temperatures and high strain rates behavior of PC/ABS blends.


2005 ◽  
Vol 12 (1) ◽  
pp. 67-71 ◽  
Author(s):  
Ivan S. Sandler

The history of the development of Cap constitutive models is reviewed. The Cap family of models provides a powerful, yet adaptable way of representing many aspects of the dynamic stress-strain behavior of geological materials. These models have been extensively used for more than three decades to characterize the highly nonlinear behavior of soils, rocks and concrete, and are particularly well suited to the dynamic analysis arising in ground shock and seismic applications. The modern series of Cap Models is based on the adaptation of several earlier models, and was introduced in the early 1970’s as a result of university and corporate R&D technology development sponsored by the United States government. Dr. Eugene Sevin played a role in these activities during his tenure at the Defense Nuclear Agency. In this paper, the basic behavior of the early models is briefly discussed and compared, and the reasons for the introduction of Cap Models are outlined. Many adaptations of the Cap Model have been developed since the first model was introduced, and the salient features of some of these model extensions are also reviewed.


2021 ◽  
Vol 1 ◽  
pp. 113-115
Author(s):  
Uwe Düsterloh ◽  
Svetlana Lerche

Abstract. The conceptual plans for the final underground disposal of radioactive waste in rock salt formations are based on extensive backfilling with crushed salt of the residual cavities left after waste deposition. It is therefore of particular importance for the historical and prognostic analysis of the load-bearing behavior and impermeability of a final repository in rock salt to demonstrate that compaction of the crushed salt backfill, which progresses over time, is suitable to seal the breaches in the geological barrier created during the underground excavation of the cavity in the long term such that safe containment of the waste is ensured. Relevant investigations on the thermal-hydraulic-mechanical (THM) behavior of crushed salt revealed that the constitutive models for the description of crushed salt compaction, which have regularly been based on the evaluation of oedometer tests, are not suitable for a sufficiently realistic representation of the essentially three-dimensional stress-strain behavior of crushed salt depending on the external load in space and time. Evidence for the above statement lies in particular in the fact that even when standardized mixtures of crushed salt are used, a computational reanalysis of compaction tests using a standardized set of parameters has hitherto been unsuccessful when different loading scenarios were specified for these laboratory tests. This means that deformations and porosities measured in the context of one individual laboratory tests can currently only be reanalyzed in sufficient quantity, irrespective of the choice of constitutive model, if the model parameters are determined in relation to this test. As a result, it must be stated that, on the one hand, the compaction behavior of crushed salt in space and time is not yet definitively understood, while, on the other hand, to ensure reliable, robust and sufficiently realistic statements to be made on compaction behavior, and thus to prove the safe containment of radioactive waste in rock salt, the availability of extensive systematically and sufficiently validated constitutive models is indispensable. This presentation introduces a methodological approach for the systematic and structured development and validation of multiphysical constitutive models, an approach that has meanwhile been successfully tested many times. The practical application of this methodology will be presented here using the example of a constitutive model that takes into account the triaxial stress-strain behavior of crushed salt. The individual development and validation steps are documented for the crushed salt model, EXPO-COM, newly developed at the Chair for Waste Disposal Technologies and Geomechanics. Validation of the constitutive model is performed by means of a back-analysis of triaxial long-term crushed salt compaction tests as follows: Test TK-031 of the German Federal Institute for Geosciences and Natural Resources (Bundesanstalt für Geowissenschaften und Rohstoffe, BGR) for isotropic load conditions Tests V1 (dry), V2 (w=0.1 %), and V3 (wet) of the German Society for Plant and Reactor Safety (Gesellschaft für Anlagen- und Reaktorsicherheit gGmbH, GRS) for different stresses and temperature levels as well as humidity Test TUC_V2 of the Clausthal University of Technology (TUC) for isotropic and deviatoric stress conditions. The TUC_V2 test characterizes, in the context of the methodology for the structured development and validation of multiphysical constitutive models, an innovative test method geared towards constitutive model development, in which the loading boundary conditions specified in the test guarantee the isolated analysis of individual factors influencing compaction behavior (Fig. 1). A description of the tests and test techniques that are still required for the full development and validation of the EXPO-COM constitutive model planned as part of the KOMPASS II research project is given together with a description of methodological guidelines relating to requirements on reliability, functionality, practicability, and validity ranges of the EXPO-COM constitutive model (Fig. 2). As a result of the subsequently possible comparison of experimentally validated and not yet validated dependencies or process variables, a validation status is defined for the constitutive model EXPO-COM. This validation status shows which factors influencing the THM-coupled material behavior of crushed salt are currently sufficiently realistically taken into account, and which influencing factors cannot yet be validated by the constitutive model. The main objectives of the tests to be carried out as part of the KOMPASS II research project include: Continued validation based on the systematized database to be created in KOMPASS II. Testing of the constitutive model in the context of numerical analyses of the predictive quality and numerical stability of the constitutive model for in situ relevant stress boundary conditions, prediction times and material properties.


2003 ◽  
Vol 76 (2) ◽  
pp. 419-435 ◽  
Author(s):  
H. J. Qi ◽  
K. Joyce ◽  
M. C. Boyce

Abstract The Durometer hardness test is one of the most commonly used measurements to qualitatively assess and compare the mechanical behavior of elastomeric and elastomeric-like materials. This paper presents nonlinear finite element simulations of hardness tests which act to provide a mapping of measured Durometer Shore A and D values to the stress-strain behavior of elastomers. In the simulations, the nonlinear stress-strain behavior of the elastomers is first represented using the Gaussian (neo-Hookean) constitutive model. The predictive capability of the simulations is verified by comparison of calculated conversions of Shore A to Shore D values with the guideline conversion chart in ASTM D2240. The simulation results are then used to determine the relationship between the neo-Hookean elastic modulus and Shore A and Shore D values. The simulation results show the elastomer to undergo locally large deformations during hardness testing. In order to assess the potential role of the limiting extensibility of the elastomer on the hardness measurement, simulations are conducted where the elastomer is represented by the non-Gaussian Arruda-Boyce constitutive model. The limiting extensibility is found to predict a higher hardness value for a material with a given initial modulus. This effect is pronounced as the limiting extensibility decreases to less than 5 and eliminates the one-to-one mapping of hardness to modulus. However, the durometer hardness test still can be used as a reasonable approximation of the initial neo-Hookean modulus unless the limiting extensibility is known to be small as is the case in many materials, such as some elastomers and most soft biological tissues.


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