Structural Constitutive Model Research Articles

Neutron diffraction study on strain rate dependent mechanical response in superelastic NiTi alloy: Bulk structural evolution and constitutive model

As expanded service environments, it is necessary to investigate the deformation behavior of NiTi shape memory alloy under dynamic and impact loadings. In this paper, we study bulk structural responses of a superelastic NiTi alloy in strain rates from 10−5 s−1 to 3 × 103 s−1 by neutron diffraction method. The objective is to quantify structural parameters of NiTi alloy at various strain rates, and compare the differences in deformation mechanisms. Further, we derive a phenomenological model based on experimental cognition to describe the strain rate dependent mechanical responses. The results demonstrate that impact loading obviously prevents stress-induced martensitic transformation in NiTi alloy. The austenite parent phase undergoes more significant slip deformation during high-speed deformation, which is hardly observed in quasi-static compression. Meanwhile, the austenitic crystal orientation during impact loading is not essentially different from that of quasi-static condition. Through an estimation of temperature effect, the strain rate effect is caused by adiabatic temperature rise. In validation of the phenomenological model, it is proved that the model well reproduces not only stress-strain curves but also structural parameters obtained from the neutron diffraction experiments.

Data‐driven probabilistic curvature capacity modeling of circular RC columns facilitating seismic fragility analyses of highway bridges

AbstractThe availability of reliable probabilistic capacity models of reinforced concrete (RC) columns is a cornerstone for high‐confidence seismic fragility and risk analyses of highway bridges. Existing studies often perform physics‐based pushover or moment–curvature analyses for the capacity modeling of RC columns, which may encounter nonconvergent problems under high levels of nonlinearities in structural material constitutive models and elements, and become computationally inefficient especially when the analysis model contains plenty of cases involving multisource uncertainties. To mitigate the nonconvergent issues as well as release the computational burden of RC column capacity estimates, this study explores the potency of artificial neural network for data‐driven probabilistic curvature capacity modeling of circular RC columns, which can facilitate seismic fragility assessment of highway bridges. To this end, a large database is developed by fiber‐section‐based moment–curvature analyses covering major ranges of concrete and steel strengths, reinforcement ratios, vertical loads, and geometries of RC columns in engineering practices. To obtain an accurate data‐driven model, a fivefold cross‐validation training and test process is performed to optimize the neural network architecture. The optimized neural network leads to a reliable data‐driven model for estimating multilevel curvature capacity indices with percentage errors less than 15%. Finally, a typical highway bridge is taken as a case study to demonstrate the applicability of the developed data‐driven capacity model for the expediency of seismic fragility analysis. For ease of implementation, the database and associated codes are available at https://bit.ly/3A1dh1V.

Strain rate induced toughening of individual collagen fibrils.

The nonlinear mechanical behavior of individual nanoscale collagen fibrils is governed by molecular stretching and sliding that result in a viscous response, which is still not fully understood. Toward this goal, the in vitro mechanical behavior of individual reconstituted mammalian collagen fibrils was quantified in a broad range of strain-rates, spanning roughly six orders of magnitude, from 10-4 to 35 s-1. It is shown that the nonlinear mechanical response is strain rate sensitive with the tangent modulus in the linear deformation regime increasing monotonically from 214 ± 8 to 358 ± 11 MPa. More pronounced is the effect of the strain rate on the ultimate tensile strength that is found to increase monotonically by a factor of four, from 42 ± 6 to 160 ± 14 MPa. Importantly, fibril strengthening takes place without a reduction in ductility, which results in equivalently large increase in toughness with the increasing strain rate. This experimental strain rate dependent mechanical response is captured well by a structural constitutive model that incorporates the salient features of the collagen microstructure via a process of gradual recruitment of kinked tropocollagen molecules, thus giving rise to the initial "toe-heel" mechanical behavior, followed by molecular stretching and sustained intermolecular slip that is initiated at a strain rate dependent stress threshold. The model shows that the fraction of tropocollagen molecules undergoing straightening increases continuously during loading, whereas molecular sliding is initiated after a small fibril strain (1%-2%) and progressively increases with applied strain.

Neutron Diffraction Study on Strain Rate Dependent Mechanical Response in Superelastic Niti Alloy: Bulk Structural Evolution and Constitutive Model

Neutron Diffraction Study on Strain Rate Dependent Mechanical Response in Superelastic Niti Alloy: Bulk Structural Evolution and Constitutive Model

Modelling the Triaxial Compression Behavior of Loess Using the Disturbed State Concept

This paper investigates the triaxial compression behaviour of Q3 loess soil and the construction of a constitutive model accounting for the structural effect of loess on the basis of the disturbed state concept. By analyzing the triaxial compression testing results, we have established a new disturbing function with respect to the volumetric and shear moduli parameters. A research into the evolution laws of the disturbing function was also conducted, followed by the construction of a constitutive model for loess soil as well as the verification of the constitutive model with model test results. The results indicate that the double-parameter disturbing function evolves in an exponential form, capturing well the effect of moisture content and confining pressure on the loess structural behavior. The parameters of the constructed constitutive model based on the disturbed state are easy to be obtained and have clarified physical meanings. Considering the effectiveness in capturing the structural behavior of the loess, the constructed constitutive model has a great potential to be applied in the engineering practice in the loess area. The constructed constitutive model based on the disturbed state concept provides new ideas for the study of the structural constitutive model of loess, which is theoretically significant.

Structural kinetics constitutive models for characterizing the time-dependent rheologic behaviors of fresh cement paste

The development of microstructure of cement-based materials should be mainly responsible for the time dependences of their rheological properties. In this paper, a series of structural kinetics constitutive models were established to predict the time-evolutions of the rheological properties of fresh cement paste under different working conditions. The models were developed from the Hershel-Bulkley model by combining a kinetic equation of the structural parameter λ and the relationships between rheological parameters and the structural parameter. The effects of shear rate, thixotropy and cement hydration on the structural breakdown and structural build-up were considered in the kinetic equation. Meanwhile, the specific parameters of Portland cement paste in the kinetic equation were estimated according to the experimental data of published literatures. Moreover, the reliability of the new models was further validated by comparing the experimental results with the predicted value of dynamic and static yield stresses of cement pastes under mixing and rest. Thus, the relationship for Portland cement between the development of microstructure and the rheological properties had been established.

Load Characteristics of Tunnel Lining in Flooded Loess Strata considering Loess Structure

Loess has a unique structure and water sensitivity, and the immersion of loess leads to many tunnel lining problems in shallowly buried tunnels. Based on a tunnel in Gansu Province in China, two failure glide planes of a shallowly buried loess tunnel and their immersion modes are summarized. Finite element calculation of the structural Duncan-Chang constitutive model is realized via the secondary development of finite element software, by which the loads on the secondary lining are calculated and verified in comparison with measured results. The load characteristics of the secondary lining are studied. The load evolution is closely related to the immersion position and scope of the load. After the loess near the failure glide plane of the arch foot is flooded, the load on the arch foot sharply increases. As the immersion expands, the maximum load moves from the arch end up to the hance. After the loess near the failure glide plane of the hance is flooded, the load on the hance decreases slightly. The stability of the overlying loess decreases gradually, which causes the loads on the vault and arch shoulder to rapidly increase. Additionally, the load distribution characteristics on the secondary lining are summarized.

Mechanics of pulmonary airways: Linking structure to function through constitutive modeling, biochemistry, and histology

Breathing involves fluid-solid interactions in the lung; however, the lack of experimental data inhibits combining the mechanics of air flow to airway deformation, challenging the understanding of how biomaterial constituents contribute to tissue response. As such, lung mechanics research is increasingly focused on exploring the relationship between structure and function. To address these needs, we characterize mechanical properties of porcine airways using uniaxial tensile experiments, accounting for bronchial orientation- and location- dependency. Structurally-reinforced constitutive models are developed to incorporate the role of collagen and elastin fibers embedded within the extrafibrillar matrix. The strain-energy function combines a matrix description (evaluating six models: compressible NeoHookean, unconstrained Ogden, uncoupled Mooney-Rivlin, incompressible Ogden, incompressible Demiray and incompressible NeoHookean), superimposed with non-linear fibers (evaluating two models: exponential and polynomial). The best constitutive formulation representative of all bronchial regions is determined based on curve-fit results to experimental data, accounting for uniqueness and sensitivity. Glycosaminoglycan and collagen composition, alongside tissue architecture, indicate fiber form to be primarily responsible for observed airway anisotropy and heterogeneous mechanical behavior. To the authors’ best knowledge, this study is the first to formulate a structurally-motivated constitutive model, augmented with biochemical analysis and microstructural observations, to investigate the mechanical function of proximal and distal bronchi. Our systematic pulmonary tissue characterization provides a necessary foundation for understanding pulmonary mechanics; furthermore, these results enable clinical translation through simulations of airway obstruction in disease, fluid-structure interaction insights during breathing, and potentially, predictive capabilities for medical interventions. Statement of SignificanceThe advancement of pulmonary research relies on investigating the biomechanical response of the bronchial tree. Experiments demonstrating the non-linear, heterogeneous, and anisotropic material behavior of porcine airways are used to develop a structural constitutive model representative of proximal and distal bronchial behavior. Calibrated material parameters exhibit regional variation in biomaterial properties, initially hypothesized to originate from tissue constituents. Further exploration through biochemical and histological analysis indicates mechanical function is primarily governed by microstructural form. The results of this study can be directly used in finite element and fluid-structure interaction models to enable physiologically relevant and more accurate computational simulations aimed to help diagnose and monitor pulmonary disease.

Structural constitutive modeling of the anisotropic mechanical properties of human vocal fold lamina propria.

The anisotropic mechanical properties of the vocal fold lamina propria play an important role in voice production and control. The goal of this study is to develop a constitutive model capable of predicting lamina propria elastic moduli along both the longitudinal and transverse directions under different conditions of vocal fold elongation, which can be used as input to reduced-order phonation models based on linear elasticity. A structurally-based constitutive model that links microstructural characteristics of the lamina propria to its macromechanical properties is proposed. The model prediction has been shown to agree reasonably well with recent biaxial tensile testing results.

An open-source plugin for OpenSim® to model the non-linear behaviour of dense connective tissues of the human knee at variable strain rates

The force-length characteristics of dense connective tissues (DCTs) vary non-linearly as a function of strain rate. However, there is no class of OpenSim® available to incorporate the effect of strain rate into the OpenSim® model. In this work, a new plugin for OpenSim® was developed to incorporate the non-linear strain rate behaviour of dense connective tissues (DCTs) of the human knee. Experimental force-length plots from the literature were used to extract the shape factor, scale factor, the coefficient of viscosity and elastic stiffness corresponding to specific strain rates. A new class object termed as NonLinearLigament was formulated using a customized plugin based on a structural constitutive model. A test platform was created to evaluate the force-length patterns at multiple strain rates ranging from 0.0001 s−1 to 100 s−1 for the DCT bundles. Knee kinematics of 25 DCT bundles were subjected to forward simulation at various strain rates. To understand the significance, the force-length characteristics of each of the DCTs were simulated as a function of strain rate for both existing Ligament class of OpenSim® and the proposed NonLinearLigament class. In the proposed ligament class, higher forces were observed with an increase of strain rate in DCTs. Existing Ligament class in OpenSim® was devoid of any changes at different strain rates. In summary, the developed plugin takes into account the short term viscoelastic behaviour of DCTs and hence, would help in accurate modelling of tissue behaviour specifically for dynamic situations.

Evaluation of transcatheter heart valve biomaterials: Computational modeling using bovine and porcine pericardium

ObjectiveThe durability of bioprosthetic heart valve (BHV) devices, commonly made of bovine (BP) and porcine (PP) pericardium tissue, is partly limited by device calcification and tissue degeneration, which has been associated with pathological levels of mechanical stress. This study investigated the impacts of BP and PP tissues with different thicknesses and tissue mechanical properties in BHV applications. MethodsSecond Harmonic Generation (SHG) imaging was employed to visualize the collagen fibers on each side of the pericardium. Structural constitutive modeling that incorporates collagen fiber distribution obtained from multiphoton microscopy for each tissue type were derived to characterize the corresponding biaxial mechanical testing data collected in a previous study. The models were verified through finite element (FE) simulations of the biaxial test and implemented in valve closing simulations. ResultsSmooth side collagen fibers were found to correlate with the mechanical response. BHVs with adult (ABP) and calf (CBP) BP tissues had lower maximum principal stresses than those with PP and fetal (FBP) BP tissues. Collagen fiber orientation along the circumferential axis resulted in lower maximum principal stresses and more uniform and symmetric stress distributions throughout the valve. ConclusionsThe use of PP and FBP tissue resulted in higher peak stresses than ABP and CBP tissues in the given valve design. Additionally, ensuring collagen fiber orientation along the circumferential axis led to lower maximum stresses felt by the valve leaflets, which could also improve BHV durability.

A bilinear structural constitutive model for strain rate-dependent behaviour of human diaphragm tissue

Diaphragmatic rupture is the tear of the diaphragm muscle result from blunt or penetrating trauma and occurs in about 5% of cases of severe blunt trauma. Both finite element (FE) modelling and experimental testing have enhanced our understanding of the injury mechanisms associated with diaphragmatic rupture. A constitutive model for human diaphragm tissue is developed and implemented via user subroutine (UMAT) in LS Dyna that accounts for the strain rate-dependent effects and bilinear behaviour observed experimentally. To better understand the material properties of the human diaphragm, 16 dynamic tensile tests were conducted at three different strain rates of 65/s, 130/s and 190/s from six whole human diaphragms. The engineering stress–strain relationship obtained from these tests showed a bilinear behaviour and strain rate dependency. A strain rate-dependent bilinear stress–strain model was developed, and its parameters were optimised using a genetic algorithm-based inverse characterization method. The results demonstrate a good correlation between experiments and the model, with an average difference of 2 ± 2.8% (mean ± SD) between the optimised FE and experimental load–time curves. The material parameters found in this study can be used in dynamic simulations using FE models of diaphragm tissues.

Pregnancy-Induced Remodeling of Heart Valves

Although many cardiovascular tissues have been shown to remodel when exposed to chronic changes in hemodynamic stresses, little is known about the capacity of heart valves to adapt in a non-pathological state such as pregnancy. Pregnancy is a volume-overload state that triggers enlargement of the heart and valve orifices, thereby elevating valve leaflet stresses. The aim of this work was to (i) investigate pregnancy-induced alterations in valve leaflet biomechanics, (ii) perform structural studies defining the material basis for these changes, and (iii) link the observed structural and mechanical information using a structural constitutive model. Valve leaflets were harvested from non-pregnant heifers and pregnant cows. Gross leaflet structure was characterized by leaflet dimensions, and small-angle light scattering was used to assess changes in internal collagen fiber architecture. Tissue composition was determined using standard biochemical assays. Histological studies assessed architectural changes in cellular and matrix components. Leaflet mechanical properties were assessed using equibiaxial mechanical testing. Collagen thermal stability and crosslinking state was assessed using denaturation and hydrothermal isometric tension tests. We observed rapid and extensive heart valve remodeling in pregnancy, with alterations to leaflet geometry, fiber architecture, composition, biomechanics, and cellularity. All the valves expanded in pregnancy, via an increase in the production of collagen, with associated changes in tissue composition and structure of the collagen network (i.e. loss of crimp, crosslink maturation, and reduction in thermal stability). Our structural constitutive model suggests that there is an initial period of permanent set-like deformation where no remodeling occurs, followed by a remodeling phase that results in near-complete restoration of homeostatic tissue-level stresses and mechanical properties. Understanding the valvular adaptations to pregnancy may be fundamental both to developing interventions and treatments for valve disease and heart failure, as well as recognizing the implications of pregnancies on maternal long-term vascular risk.

Structural integrity analysis of transmission structure in flapping-wing micro aerial vehicle via 3D printing

3D printing makes the small and compact transmission system of flapping-wing micro aerial vehicle (FMAV) available for in-house designs and tests. However, the high flapping frequency requiring stringent strength integrity and fatigue longevity for the structure itself always serves as the major responsible reason for the structural failure of FMAV. In this paper, experiment as well as numerical computation efforts were acted in concert to gain an insightful understanding of the failure mechanism for the transmission structure of FMAV. Firstly, a FMAV structure was fabricated by 3D printing using Ultraviolet(UV) Cureable Resin. The isotropic constitutive behavior of the resin was evaluated and confirmed. Further, numerical computation model describing the mechanical behavior of FMAV structure was established and verified by experiments. Secondly, together with the computational structural model and constitutive model, the dynamic response of the transmission structure subject to high frequency flipping motion was described. Both simulation and experiments share the same failure mode and configuration and the dominate factor for the failure was found out to be the excessive bending deformation. Finally, design parametric study along with different boundary conditions aiming at the future ground testing were conducted to uncover the governing influences over the transmission structure integrity. Results may shed lights on the structural integrity design of FMAV and pave a new road for future advanced FMAV design, manufacturing and testing. • A finite element modeling methodology for transmission system of FMAV was presented. • The dominate factor for the failure of the transmission structure was uncovered. • Impacts of different boundary conditions on the structural strength were discussed. • Improvement design of the main components were carried out.

Characterization of mechanical properties of pericardium tissue using planar biaxial tension and flexural deformation.

Flexure is an important mode of deformation for native and bioprosthetic heart valves. However, mechanical characterization of bioprosthetic leaflet materials has been done primarily through planar tensile testing. In this study, an integrated experimental and computational cantilever beam bending test was performed to characterize the flexural properties of glutaraldehyde-treated bovine and porcine pericardium of different thicknesses. A strain-invariant based structural constitutive model was used to model the pericardial mechanical behavior quantified through the bending tests of this study and the planar biaxial tests previously performed. The model parameters were optimized through an inverse finite element (FE) procedure in order to describe both sets of experimental data. The optimized material properties were implemented in FE simulations of transcatheter aortic valve (TAV) deformation. It was observed that porcine pericardium TAV leaflets experienced significantly more flexure than bovine when subjected to opening pressurization, and that the flexure may be overestimated using a constitutive model derived from purely planar tensile experimental data. Thus, modeling of a combination of flexural and biaxial tensile testing data may be necessary to more accurately describe the mechanical properties of pericardium, and to computationally investigate bioprosthetic leaflet function and design.

Constitutive modeling of the passive inflation-extension behavior of the swine colon.

In the present work, we propose the first structural constitutive model of the passive mechanical behavior of the swine colon that is validated against physiological inflation-extension tests, and accounts for residual strains. Sections from the spiral colon and the descending colon were considered to investigate potential regional variability. We found that the proposed constitutive model accurately captures the passive inflation-extension behavior of both regions of the swine colon (coefficient of determination R2=0.94±0.02). The model revealed that the circumferential muscle layer does not provide significant mechanical support under passive conditions and the circumferential load is actually carried by the submucosa layer. The stress analysis permitted by the model showed that the colon tissue can distend up to 30% radially without significant increase in the wall stresses suggesting a highly compliant behavior of the tissue. This is in-line with the requirement for the tissue to easily accommodate variable quantities of fecal matter. The analysis also showed that the descending colon is significantly more compliant than the spiral colon, which is relevant to the storage function of the descending colon. Histological analysis showed that the swine colon possesses a four-layer structure similar to the human colon, where the longitudinal muscle layer is organized into bands called taeniae, a typical feature of the human colon. The model and the estimated parameters can be used in a Finite Element framework to conduct simulations with realistic geometry of the swine colon. The resulting computational model will provide a foundation for virtual assessment of safe and effective devices for the treatment of colonic diseases.

Modeling the response of exogenously crosslinked tissue to cyclic loading: The effects of permanent set.

Bioprosthetic heart valves (BHVs), fabricated from exogenously crosslinked collagenous tissues, remain the most popular heart valve replacement design. However, the life span of BHVs remains limited to 10-15 years, in part because the mechanisms that underlie BHV failure remain poorly understood. Experimental evidence indicates that BHVs undergo significant changes in geometry with in vivo operation, which lead to stress concentrations that can have significant impact on structural damage. These changes do not appear to be due to plastic deformation, as the leaflets only deform in the elastic regime. Moreover, structural damage was not detected by the 65 million cycle time point. Instead, we found that this nonrecoverable deformation is similar to the permanent set effect observed in elastomers, which allows the reference configuration of the material to evolve over time. We hypothesize that the scission-healing reaction of glutaraldehyde is the underlying mechanism responsible for permanent set in exogenously crosslinked soft tissues. The continuous scission-healing process of glutaraldehyde allows a portion of the exogenously crosslinked matrix, which is considered to be the non-fibrous part of the extra-cellular matrix, to be re-crosslinked in the loaded state. Thus, this mechanism for permanent set can be used to explain the time evolving mechanical response and geometry of BHVs in the early stage. To model the permanent set effect, we assume that the exogenously crosslinked matrix undergoes changes in reference configurations over time. The changes in the collagen fiber architecture due to dimensional changes allow us to predict subsequent changes in mechanical response. Results show that permanent set alone can explain and, more importantly, predict how the mechanical response of the biomaterial change with time. Furthermore, we found is no difference in permanent set rate constants between the strain controlled and the stress controlled cyclic loading studies. An important finding we have is that the collagen fiber architecture has a limiting effect on the maximum changes in geometry that the permanent set effect can induce. This is due to the recruitment of collagen fibers as the changes in geometry due to permanent set increase. This means we can potentially optimize the BHV geometry based on the predicted the final BHV geometry after permanent set has largely ceased. Thus, we have developed the first structural constitutive model for the permanent set effect in exogenously crosslinked soft tissue, which can help to simulate BHV designs and reduce changes in BHV geometry during cyclic loading and thus potentially increasing BHV durability.

Affine kinematics in planar fibrous connective tissues: an experimental investigation.

The affine transformation hypothesis is usually adopted in order to link the tissue scale with the fibers scale in structural constitutive models of fibrous tissues. Thanks to the recent advances in imaging techniques, such as multiphoton microscopy, the microstructural behavior and kinematics of fibrous tissues can now be monitored at different stretching within the same sample. Therefore, the validity of the affine hypothesis can be investigated. In this paper, the fiber reorientation predicted by the affine assumption is compared to experimental data obtained during mechanical tests on skin and liver capsule coupled with microstructural imaging using multiphoton microscopy. The values of local strains and the collagen fibers orientation measured at increasing loading levels are used to compute a theoretical estimation of the affine reorientation of collagen fibers. The experimentally measured reorientation of collagen fibers during loading could not be successfully reproduced with this simple affine model. It suggests that other phenomena occur in the stretching process of planar fibrous connective tissues, which should be included in structural constitutive modeling approaches.

A functionally graded material model for the transmural stress distribution of the aortic valve leaflet

Heterogeneities in structure and stress within heart valve leaflets are of significant concern to their functional physiology, as they affect how the tissue constituents remodel in response to pathological and non-pathological (e.g. exercise, pregnancy) alterations in cardiac function. Indeed, valve interstitial cells (VICs) are known to synthesize and degrade leaflet extracellular matrix (ECM) components in a manner specific to their local micromechanical environment. Quantifying local variations in ECM structure and stress is thus necessary to understand homeostatic valve maintenance as well as to develop predictive models of disease progression and post-surgical outcomes. In the aortic valve (AV), transmural variations in stress have previously been investigated by modeling the leaflet as a composite of contiguous but mechanically distinct layers. Based on previous findings about the bonded nature of these layers (Buchanan and Sacks, BMMB, 2014), we developed a more generalized structural constitutive model by treating the leaflet as a functionally graded material (FGM), whose properties vary continuously over the thickness. We informed the FGM model using high-resolution morphological measurements, which demonstrated that the composition and fiber structure change gradually over the thickness of the AV leaflet. For validation, we fit the model against an extensive database of whole-leaflet and individual-layer mechanical responses. The FGM model predicted large stress variations both between and within the leaflet layers at end-diastole, with low-collagen regions bearing significant radial stress. These novel results suggest that the continually varying structure of the AV leaflet has an important purpose with regard to valve function and tissue homeostasis.

A macro-structural constitutive model for partially saturated expansive soils

The mechanical behaviour of unsaturated expansive soils is an important factor in the design of barriers for nuclear waste disposal. Double structural constitutive models for expansive soil have been developed based on the distinction between micro-structure and macro-structure of the expansive soil. Nevertheless, the micro-parameters and the coupling function of these models are hard to determine. To eliminate the limitations of these models, the concept of a macro-structural neutral loading line was introduced by adopting a simple assumption concerning the plastic swelling potential of unsaturated expansive soil. A macro-structural volume change equation of unsaturated expansive soil was derived using a macro-structural neutral loading line. The model was based on an existing model for non-expansive unsaturated soils. Only one new macro-parameter was introduced into the constitutive model compared to the original model. Finally, a comparison between predicted results and experimental data indicates that the proposed model has a remarkable ability to reproduce the mechanical and hydraulic responses of unsaturated expansive soils.