Uniaxial Extension Tests Research Articles

A granular micromechanic-based model for Ultra High Performance Fiber-Reinforced Concrete (UHP FRC)

There is a growing interest in the application of UHP FRC (Ultra-High Performance Fiber-Reinforced Concrete) which has been under vigorous development since its inception over two decades ago. The advantages of these advanced materials is that they overcome the problems that plague conventional concrete, these include among others low residual strength and low tensile strength, poor crack control and resistance to crack propagation, which leads corrosion of the rebars and spalling. The aim of this paper is to provide a granular micromechanics-based model to describe the deformation behavior of UHP FRC material as it gives a robust method to link the micro-scale mechanisms with the macro-scale performance of materials with granular textures. In this model, the micro-scale is described by damage-elasto-plastic spring elements that represent the effective grain pair interactions decomposed into the so-called normal and tangential directions. Since the grain-pairs are variously oriented, the macro-scale response is obtained by integrating these interactions over the orientational space. Here we specialize the granular micromechanic model for UHP FRC by introducing a novel expression for the parameterized dissipation energy at the micro or the grain-pair scale. The newly introduced constitutive parameters are identified using experimental results for uniaxial extension and compression tests. The model is then applied to simulate the case of homogeneous compression, extension and shear to show the directional evolution of damage and plasticity and the consequent emergent anisotropy.

A Comparative Study of Machine Learning and Algorithmic Approaches to Automatically Identify the Yield Point in Normal and Aneurysmal Human Aortic Tissues.

The stress-strain curve of biological soft tissues helps characterize their mechanical behavior. The yield point on this curve is when a specimen breaches its elastic range due to irreversible microstructural damage. The yield point is easily found using the offset yield method in traditional engineering materials. However, correctly identifying the yield point in soft tissues can be subjective due to its nonlinear material behavior. The typical method for yield point identification is visual inspection, which is investigator-dependent and does not lend itself to automation of the analysis pipeline. An automated algorithm to identify the yield point objectively assesses soft tissues' biomechanical properties. This study aimed to analyze data from uniaxial extension testing on biological soft tissue specimens and create a machine learning (ML) model to determine a tissue sample's yield point. We present a trained machine learning model from 279 uniaxial extension curves from testing aneurysmal/nonaneurysmal and longitudinal/circumferential oriented tissue specimens that multiple experts labeled through an adjudication process. The ML model showed a median error of 5% in its estimated yield stress compared to the expert picks. The study found that an ML model could accurately identify the yield point (as defined) in various aortic tissues. Future studies will be performed to validate this approach by visually inspecting when damage occurs and adjusting the model using the ML-based approach.

Morpho-mechanical mapping of human dura mater microstructure

The human dura mater is known to impact vastly traumatic brain injury mechanopathology. In spite of this involvement, dura mater is typically neglected in computational and physical human head models. The lack of location-dependent microstructural and related mechanical data of dura mater may be considered a rationale behind this simplification. The anisotropic nature of dura mater under various loading conditions so far remains unelucidated. Furthermore, principal collagen fiber orientation is yet to be quantified for a morpho-mechanically-informed material model on the dura mater. This study aims to assess how location-dependent mechanical anisotropy is linked to principal collagen fiber orientation. Uniaxial extension tests were performed in a heated tissue bath for 60 samples from six individuals and correlated to the three-dimensional collagen structure in four individuals using second-harmonic generation (SHG) imaging. Failure stress and stretch at failure, elastic modulus, and a microstructurally motivated material model were integrated to examine local differences in dura mater morpho-mechanics. The quantitative observation of collagen fiber orientation and dispersion confirmed that collagen is highly aligned in the human dura mater and that both fiber orientation and dispersion differ depending on the location investigated. This observation provides a possible explanation for the previously observed isotropic mechanical behavior, as the main collagen fiber direction is not oriented along the anterior-posterior or medial-lateral direction at most of the mapped locations. Additionally, these site-dependent structural properties have implications for the mechanical load response and therefore potentially for the regional functions dura mater has to fulfill. The here chosen non-symmetrical fiber dispersion material model fits the data well and provides a comprehensive parameter base for further studies and future finite element models. Statement of significanceThe human dura mater greatly affects traumatic brain injury mechanisms, but it is often ignored in computational and physical head models. This is because there is a lack of detailed microstructural and mechanical data specific to the dura mater. Its anisotropic nature and collagen fiber orientation have not been fully understood, hindering the development of an accurate material model. Hence, this study combines morphological data on collagen fiber orientation and dispersion at multiple locations of human cranial dura mater, and links microstructure to location-specific load-displacement behavior. It provides microstructurally informed mechanical information towards realistic head models for predicting location-dependent tissue behavior and failure for assessing brain injury and graft material development.

Characterising the shear resistance of a unidirectional non-crimp glass fabric using modified picture frame and uniaxial bias extension test methods

The forming behaviour of a unidirectional non-crimp fabric (UD-NCF) consisting of polyamide stitches with a tricot-chain stitching pattern is explored. Notably, there are no stabilising tows orientated transverse to the main tow direction in this fabric, a common feature in many ‘quasi’ UD-NCFs, this allows extension of the stitch in the transverse direction under certain loading conditions. The lack of stabilising tows introduces a possible low-energy deformation mode to the UD-NCF, which is absent in biaxial fabrics and to a large extent in ‘quasi’ UD-NCFs. The in-plane shear behaviour is initially investigated using both standard ‘tightly-clamped’ picture frame tests and uniaxial bias extension tests. Preliminary results show a dramatic difference in results produced by the two test methods. During the picture frame test, fibres can be subjected to unintended tension due to sample misalignment in the picture frame rig. To mitigate error arising from this effect, the picture frame test procedure is modified in two different ways: by using an intentional pre-displacement of the picture frame rig, and by changing the clamping condition of test specimen. Results show that the modified picture frame test data contain less error than the standard ‘tightly-clamped’ test but also that the shear stiffness of the UD-NCF is notably lower when measured in the bias extension test compared to the picture frame test, mainly due to the difference in loading conditions imposed during the two tests.

Aortic Remodeling Kinetics in Response to Coarctation-Induced Mechanical Perturbations.

Background: Coarctation of the aorta (CoA; constriction of the proximal descending thoracic aorta) is among the most common congenital cardiovascular defects. Coarctation-induced mechanical perturbations trigger a cycle of mechano-transduction events leading to irreversible precursors of hypertension including arterial thickening, stiffening, and vasoactive dysfunction in proximal conduit arteries. This study sought to identify kinetics of the stress-mediated compensatory response leading to these alterations using a preclinical rabbit model of CoA. Methods: A prior growth and remodeling (G&R) framework was reformulated and fit to empirical measurements from CoA rabbits classified into one control and nine CoA groups of various severities and durations (n = 63, 5-11/group). Empirical measurements included Doppler ultrasound imaging, uniaxial extension testing, catheter-based blood pressure, and wire myography, yielding the time evolution of arterial thickening, stiffening, and vasoactive dysfunction required to fit G&R constitutive parameters. Results: Excellent agreement was observed between model predictions and observed patterns of arterial thickening, stiffening, and dysfunction among all CoA groups. For example, predicted vascular impairment was not significantly different from empirical observations via wire myography (p-value > 0.13). Specifically, 48% and 45% impairment was observed in smooth muscle contraction and endothelial-dependent relaxation, respectively, which were accurately predicted using the G&R model. Conclusions: The resulting G&R model, for the first time, allows for prediction of hypertension precursors at neonatal ages that is currently challenging to examine in preclinical models. These findings provide a validated computational tool for prediction of persistent arterial dysfunction and identification of revised severity-duration thresholds that may ultimately avoid hypertension from CoA.

Simulating hyperelasticity and fractional viscoelasticity in the human heart

Biomechanics plays an important role in the diagnosis and treatment of pathological conditions of the heart. Computational models are paving the way for personalized therapeutic treatment but they rely on accurate constitutive equations for predicting their biomechanical behavior. Even so, viscoelasticity remains under-explored in computational modeling despite experimental observations. To facilitate the viscoelastic modeling of cardiovascular soft tissues, we previously developed a fractional viscoelastic modeling approach, which extends existing hyperelastic models. This has comparable computational costs to the conventional hyperelastic model and only requires two additional material parameters for the viscoelastic response. This approach was demonstrated to be able to accurately capture the viscoelastic response of the human myocardium. However, the numerical properties of this fractional viscoelastic approach have not yet been examined. In this work, we present its implementation in Finite Element Analysis, examine its numerical properties in uniaxial extension and 2D inflation test examples, and examine its physiological implication in a computational model of an idealized left ventricle in a fully idealized circulatory system. Optimal convergence properties were observed and the importance of viscoelasticity during passive filling, ventricular motion, and regional fiber strain and stresses were explained.

Isomorphism Continuum Stored Energy Functional for Finite Thermoelastic Deformation

Continuum mechanics for isotropic finite thermoelastic deformations have been reviewed. Thermal effects on mechanical responses of rubbers have been captured by the isomorphism continuum stored energy (CSE) functional with the multiplicative decomposition of deformation gradient while preserving the structure of symmetry for finite structural deformation. The CSE finite thermoelastic model fits and predicts experimental data of SR and NR-C60 rubbers at different external temperatures. For internal temperature effects of both NR and NR-SIC rubbers, the CSE finite thermoelastic model of stored energy and entropy, along with the newly developed CTE and CI models, fits both nominal stress-stretch and temperature change-stretch experimental data in uniaxial extension tests.

Stochastic modeling of inhomogeneities in the aortic wall and uncertainty quantification using a Bayesian encoder–decoder surrogate

Inhomogeneities in the aortic wall can lead to localized stress accumulations, possibly initiating dissection. In many cases, a dissection results from pathological changes such as fragmentation or loss of elastic fibers. But it has been shown that even the healthy aortic wall has an inherent heterogeneous microstructure. Some parts of the aorta are particularly susceptible to the development of inhomogeneities due to pathological changes, however, the distribution in the aortic wall and the spatial extent, such as size, shape and type, are difficult to predict. Motivated by this observation, we describe the heterogeneous distribution of elastic fiber degradation in the dissected aortic wall using a stochastic constitutive model. For this purpose, random field realizations, which model the stochastic distribution of degraded elastic fibers, are generated over a non-equidistant grid. The random field then serves as input for a uniaxial extension test of the pathological aortic wall, solved with the finite element method. To include the microstructure of the dissected aortic wall, a constitutive model developed in a previous study is applied, which also includes an approach to model the degradation of interlamellar elastic fibers. To then assess the uncertainty in the output stress distribution due to the proposed stochastic constitutive model, a convolutional neural network, specifically a Bayesian encoder–decoder, was used as a surrogate model that maps the random input fields to the output stress distribution obtained from the finite element analysis. The results show that the neural network is able to predict the stress distribution of the finite element analysis while also significantly reducing the computational time. In addition, this provides the probability for exceeding certain rupture stresses within the aortic wall, which could allow for the prediction of delamination or fatal rupture.

Experimental Investigation of the Anisotropic Mechanical Response of the Porcine Thoracic Aorta.

Knowledge of the mechanical properties of blood vessels and determining appropriate constitutive relations are essential in developing methodologies for accurate prognosis of vascular diseases. We examine the directional variation of the mechanical properties of the porcine thoracic aorta by performing uniaxial extension tests on dumbbell-shaped specimens cut at five different orientations with respect to the circumferential direction of the aorta. Specimens in all the orientations considered exhibit a nonlinear constitutive response that is typical of collagenous soft tissues. Shear strain under uniaxial extension demonstrates clearly discernible anisotropy of the mechanical response of the porcine aorta, and samples oriented at 45[Formula: see text] and 60[Formula: see text] with respect to the circumferential direction show a peculiar crescent-shaped shear strain-nominal stretch response not displayed by axial and circumferential specimens. Failure stress indicates decreasing tensile strength of the porcine aortic wall from the circumferential direction to the longitudinal direction. Furthermore, we determine the material parameters for the four-fiber-family and Gasser-Holzapfel-Ogden models from the mechanical response data of the circumferential and longitudinal specimens. It is shown how the material parameters derived from the uniaxial tests on circumferential and longitudinal specimens are insufficient to characterize the response of off-axis specimens.

Predictive Continuum Constitutive Modeling of Unfilled and Filled Rubbers

The general CSE model fits Treloar’s uniaxial extension test and predicts unfitted uniaxial compression, equibiaxial extension, biaxial extension, pure shear, and simple shear tests. As a newly proposed method, the general CSE model, along with the stress-softening ratio, the residualstretch ratio, and the weighted piecewise two-point interpolation function, fits the Cheng–Chen’s test and the Diani–Fayolle–Gilormini’s test in cyclic uniaxial extension at different pre-stretches and predicts corresponding responses at untested pre-stretches. Physical mechanisms of the Mullins effect have also been predicted based on the evolution of constitutive parameters.

Passive mechanical properties in healthy and infarcted rat left ventricle characterised via a mixture model

During the cardiac cycle, electrical excitation is coupled with mechanical response of the myocardium. Besides the active contraction, passive mechanics plays an important role, and its behaviour differs in healthy and diseased hearts as well as among different animal species. The aim of this study is the characterisation of passive mechanical properties in healthy and infarcted rat myocardium by means of mechanical testing and subsequent parameter fitting. Elasticity assessments via uniaxial extension tests are performed on healthy and infarcted tissue samples from left ventricular rat myocardium. In order to fully characterise the orthotropic cardiac tissue, our experimental data are combined with other previously published tests in rats – shear tests on healthy myocardium and equibiaxial tests on infarcted tissue. In a first step, we calibrate the Holzapfel-Ogden strain energy function in the healthy case. Sa far, this orthotropic constitutive law for the passive myocardium has been fitted to experimental data in several species, however there is a lack of an appropriate parameter set for the rat. With our determined parameters, a finite element simulation of the end-diastolic filling is performed. In a second step, we propose a model for the infarcted tissue. It is represented as a mixture of intact myocardium and a transversely isotropic scar structure. In our mechanical experiments, the tissue after myocardial infarction shows significantly stiffer behaviour than in the healthy case, and the stiffness correlates with the amount of fibrosis. A similar relationship is observed in the computational simulation of the end-diastolic filling. We conclude that our new proposed material model can capture the behaviour of two kinds of tissues – healthy and infarcted rat myocardium, and its calibration with the fitted parameters represents the experimental data well.

Mechanical, compositional and morphological characterisation of the human male urethra for the development of a biomimetic tissue engineered urethral scaffold

This study addresses a crucial gap in the literature by characterising the relationship between urethral tissue mechanics, composition and gross structure. We then utilise these data to develop a biomimetic urethral scaffold with physical properties that more accurately mimic the native tissue than existing gold standard scaffolds; small intestinal submucosa (SIS) and urinary bladder matrix (UBM).Nine human urethra samples were mechanically characterised using pressure-diameter and uniaxial extension testing. The composition and gross structure of the tissue was determined using immunohistological staining. A pressure stiffening response is observed during the application of intraluminal pressure. The elastic and viscous tissue responses to extension are free of regional or directional variance. The elastin and collagen content of the tissue correlates significantly with tissue mechanics.Building on these data, a biomimetic urethral scaffold was fabricated from collagen and elastin in a ratio that mimics the composition of the native tissue. The resultant scaffold is comprised of a dense inner layer and a porous outer layer that structurally mimic the submucosa and corpus spongiosum layers of the native tissue, respectively. The porous outer layer facilitated more uniform cell infiltration relative to SIS and UBM when implanted subcutaneously (p < 0.05). The mechanical properties of the biomimetic scaffold better mimic the native tissue compared to SIS and UBM.The tissue characterisation data presented herein paves the way for the development of biomimetic urethral grafts, and the novel scaffold we develop demonstrates positive findings that warrant further in vivo evaluation.

A hybrid lamination model for simulation of woven fabric reinforced thermoplastic composites solid-state thermo-stamping

Solid-state thermo-stamping of fabric reinforced composites has attracted extensive attention for its efficiency and potential energy saving in recent years. In this paper, a hybrid lamination model is proposed to describe the forming behavior of woven fabric reinforced thermoplastic composites (WFRTP) during solid-state thermo-stamping process. The woven carbon fiber (CF)/ Polyetheretherketone (PEEK) sheet/prepreg is modelled as laminate structure with woven reinforcement layers (shell elements) embedded in thermoplastic resin layer (solid elements). More specifically, a hypoelastic constitutive model is used to represent the anisotropic mechanical behavior of fabric reinforcement under large deformation, while the fabric model is calibrated and validated by uniaxial bias extension (UBE) test and tensile test of woven fabric. A phenomenological model is adopted to describe the viscoelastic-plastic deformation behavior of thermoplastic resin, while the resin model is calibrated by tensile tests of PEEK. The applicability of the hybrid model is demonstrated through comparing numerical results of UBE tests and Erichsen tests with their corresponding experiment results. The hybrid lamination model provides a theoretical foundation for numerical simulation of WFRTP solid-state thermo-stamping.

Analysis of the wrinkle geometry of the woven fabrics during uniaxial bias extension test using Ricker wavelet algorithm

Out-of-plane wrinkling has a significant influence on the woven fabric behavior during the shear testing. This study aimed to introduce a new methodology combining non-destructive characterization and numerical analysis techniques for the automatic creation of a number of models having controlled wrinkle geometry and predict the new ones. First, 3D geometrical parameters of the fabric deformation at different crosshead displacements were measured. Then, the Ricker Wavelet equation was selected according to wrinkle topology and the function parameter was estimated. The correlation of the geometrical measured and function estimated parameters with the crosshead displacement values were obtained. The correlated function was used to predict the wrinkle geometry in the new crosshead displacement. The validation and accuracy of the predicted wrinkle geometry was confirmed by the image processing method. Finally, the effect of wrinkle maximum depth and shear angle on Poisson’s ratio showed a decrease due to an increase of them.

An extended eight-chain model for hyperelastic and finite viscoelastic response of rubberlike materials: Theory, experiments and numerical aspects

Rubberlike materials exhibit strong rate-dependent mechanical response which manifests itself in creep and relaxation tests as well as in the hysteresis curves under cyclic loading. Unlike linear viscoelasticity, creep and relaxation response of rubber is nonlinear and amplitude-dependent. Within this context, the contribution of this work is three fold. (i) On the experimental side, the characterization of equilibrium and non-equilibrium responses are carried out by means of uniaxial and equibiaxial extension tests. Also performed are the creep and relaxation experiments at various stress and strain levels. (ii) On the theoretical side, we extend the well-known eight-chain model via incorporating a simple yet instrumental tube-constraint term composed of the second invariant into the non-affine network contribution reflecting the ground state equilibrium response. For the non-equilibrium response, we propose a new evolution equation for the creep/relaxation behavior of rubberlike materials based on a relaxation kinetics of a single polymer chain. The geometric non-linearity is incorporated via the finite deformation kinematics based on the multiplicative split of the deformation gradient into elastic and viscous parts, whereas the volumetric and isochoric split of the deformation gradient is entirely discarded. The rheology uses a nonlinear spring responsible for equilibrium elastic response in parallel to n number of Maxwell elements, leading to a generalized Maxwell-Wiechert viscoelastic solid. (iii) The algorithmic implementation of the model features the spectral decomposition of the respective terms and is demonstrated within the context of the finite element method. The developed model is validated by fitting both the elastic and viscoelastic model responses with respect to the experimental data in the sense of uniaxial, (equi)biaxial extensions, and pure shear tests. Relaxation and creep behavior of the model are thoroughly assessed. Also presented in the manuscript is the capability and the performance of the model in the face of a relevant non-homogeneous boundary value problem. The quality of the findings earns the model vast utilization areas from an engineering perspective.

Investigation of the Mechanical Properties of Parts Fabricated with Ultrasonic Micro Injection Molding Process Using Polypropylene Recycled Material.

This research focuses on investigating how physical and mechanical properties of polypropylene (PP) recycled material are modified when ultrasonic micro injection molding (UMIM) technology is used to produce material specimens. Experimental characterization by differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), Fourier transform infrared (FTIR) spectra, and rheology tests show that the fabricated PP samples were able to withstand up to five times recycled processing before some signs of mechanical and physical properties degradation are observed. Surprisingly, uniaxial extension tests show an increase of 3.07%, 10.97% and 27.33% for Young’s modulus, yield stress and ultimate stress values, respectively, and a slight reduction of 1.29% for the samples elongation at break when compared to the experimental data collected from virgin material samples. The improvement of these mechanical properties in the recycled samples suggests that ultrasonic microinjection produces a mechano-chemical material change.

On biological availability dependent bone remodeling

Modeling the evolution of bone density is relevant for understanding, simulation and possible prediction of bone response to external and internal influences. In this work we present a formulation for the bone density evolution process that takes into account not only the commonly considered mechanical stimulus, but, as novelty, also the influence of the availability of nutrients and hormones, with its implementation pursued within the finite element method. A simple uni-axial extension test is used to illustrate and compare our novel model against the classical approach. The results of the proposed modified model are promising for application to real-life problems.

On age-dependent bone remodeling

A number of previous studies have investigated the possibilities of modelling the change in density of bones. Remodeling can be formulated at the constitutive or the kinematic level. In this work we introduce a formulation for the density growth process which takes not only the mechanical stimulus into account but also the influence of age on the evolution of growth. We demonstrate the implementation in the context of the finite element method. This novel approach is illustrated for a simple uniaxial extension test and is verified against previous numerical results. Moreover, two further physiologically motivated examples are performed. The results of the proposed modified model show excellent agreement with comparable results from literature and are promising for the application to real-life problems.

Poisson's ratio and volume change accompanying deformation of randomly oriented electrospun nanofibrous membranes

ABSTRACTThe present work focuses on the determination of volume change accompanying deformation and Poisson's ratio for electrospun nanofibrous membranes. For this purpose, polyurethane (PU) is considered for the fabrication of electrospun nanofibrous membranes. Three different sample thicknesses are fabricated. Following this, surface morphology analysis and fibre orientation analysis are conducted to investigate the variation of properties between electrospun PU membranes of different thicknesses. Subsequently, PU specimens are subjected to uniaxial extension test where the changes in sample width and thickness are recorded as a function of applied strain. Volume changes are computed while further analysis on the relationship between transverse strains and axial strain provided the values of Poisson's ratio. For all three electrospun PU samples investigated, significant volume changes are observed while the in-plane Poisson's ratio is found to be around 0.55. However, the out-of-plane Poisson's ratio of electrospun PU membranes are not classical and remains undetermined.

Failure properties and microstructure of healthy and aneurysmatic human thoracic aortas subjected to uniaxial extension with a focus on the media

Current clinical practice for aneurysmatic interventions is often based on the maximum diameter of the vessel and/or on the growth rate, although rupture can occur at any diameter and growth rate, leading to fatality. For 27 medial samples obtained from 12 non-aneurysmatic (control) and 9 aneurysmatic human descending thoracic aortas we examined: the mechanical responses up to rupture using uniaxial extension tests of circumferential and longitudinal specimens; the structure of these tissues using second-harmonic imaging and histology, in particular, the content proportions of collagen, elastic fibers and smooth muscle cells in the media. It was found that the mean failure stresses were higher in the circumferential directions (Control-C 1474kPa; Aneurysmatic-C 1446kPa), than in the longitudinal directions (Aneurysmatic-L 735kPa; Control-L 579kPa). This trend was the opposite to that observed for the mean collagen fiber directions measured from the loading axis (Control-L > Aneurysmatic-L > Aneurysmatic-C > Control-C), thus suggesting that the trend in the failure stress can in part be attributed to the collagen architecture. The difference in the mean values of the out-of-plane dispersion in the radial/longitudinal plane between the control and aneurysmatic groups was significant. The difference in the mean values of the mean fiber angle from the circumferential direction was also significantly different between the two groups. Most specimens showed delamination zones near the ruptured region in addition to ruptured collagen and elastic fibers. This study provides a basis for further studies on the microstructure and the uniaxial failure properties of (aneurysmatic) arterial walls towards realistic modeling and prediction of tissue failure. Statement of SignificanceA data set relating uniaxial failure properties to the microstructure of non-aneurysmatic and aneurysmatic human thoracic aortic medias under uniaxial extension tests is presented for the first time. It was found that the mean failure stresses were higher in the circumferential directions, than in the longitudinal directions. The general trend for the failure stresses was Control-C > Aneurysmatic-C > Aneurysmatic-L > Control-L, which was the opposite of that observed for the mean collagen fiber direction relative to the loading axis (Control-L > Aneurysmatic-L > Aneurysmatic-C > Control-C) suggesting that the trend in the failure stress can in part be attributed to the collagen architecture. This study provides a first step towards more realistic modeling and prediction of tissue failure.