Stress Relaxation Data Research Articles

Direct Identification of the Continuous Relaxation Time and Frequency Spectra of Viscoelastic Materials

Relaxation time and frequency spectra are not directly available by measurement. To determine them, an ill-posed inverse problem must be solved based on relaxation stress or oscillatory shear relaxation data. Therefore, the quality of spectra models has only been assessed indirectly by examining the fit of the experiment data to the relaxation modulus or dynamic moduli models. As the measures of data fitting, the mean sum of the moduli square errors were usually used, the minimization of which was an essential step of the identification algorithms. The aim of this paper was to determine a relaxation spectrum model that best approximates the real unknown spectrum in a direct manner. It was assumed that discrete-time noise-corrupted measurements of a relaxation modulus obtained in the stress relaxation experiment are available for identification. A modified relaxation frequency spectrum was defined as a quotient of the real relaxation spectrum and relaxation frequency and expanded into a series of linearly independent exponential functions that are known to constitute a basis of the space of square-integrable functions. The spectrum model, given by a finite series of these basis functions, was assumed. An integral-square error between the real unknown modified spectrum and the spectrum model was taken as a measure of the model quality. This index was proved to be expressed in terms of the measurable relaxation modulus at uniquely defined sampling instants. Next, an empirical identification index was introduced in which the values of the real relaxation modulus are replaced by their noisy measurements. The identification consists of determining the spectrum model that minimizes this empirical index. Tikhonov regularization was applied to guarantee model smoothness and noise robustness. A simple analytical formula was derived to calculate the optimal model parameters and expressed in terms of the singular value decomposition. A complete identification algorithm was developed. The analysis of the model smoothness and model accuracy for noisy measurements was carried out. The equivalence of the direct identification of the relaxation frequency and time spectra has been demonstrated when the time spectrum is modeled by a series of functions given by the product of the relaxation frequency and its exponential function. The direct identification concept can be applied to both viscoelastic fluids and solids; however, some limitations to its applicability have been pointed out. Numerical studies have shown that the proposed identification algorithm can be successfully used to identify Gaussian-like and Kohlrausch–Williams–Watt relaxation spectra. The applicability of this approach to determining other commonly used classes of relaxation spectra was also examined.

Investigating grain-resolved evolution of lattice strains during plasticity and creep using 3DXRD and crystal plasticity modelling

Microstructure-informed crystal plasticity finite element models have shown great promise in predicting plastic and creep deformation in polycrystalline materials. These models can provide substantial insight into the design, fabrication and lifetime assessment of critical metallic components during operation, for instance, in thermal power plants. However, to correctly incorporate damage prediction into models, the microstructural strain simulated at the grain level must be accurately predicted with suitable validation. For this reason, a 3D X-ray Diffraction (3DXRD) experiment was carried out on 316H stainless steel, a material commonly used in thermal power plants, to obtain the per-grain strain response during plastic and creep deformation at 550°C. Several hundred grains within a probed X-ray volume were tracked and measured whilst loading in-situ, obtaining per-grain centre-of-mass positions, crystallographic orientations, and average lattice strain over individual grains. These data were used to calibrate a crystal plasticity model to study the plastic and creep deformation using macroscopic stress-strain and stress-relaxation data. Subsequently, the model was used to predict the average elastic strain in different grains during the cyclic creep experiment, which was validated by 3DXRD datasets. The model results reveal that {100} or {311} grain families are strongly sensitive to microstructure, thereby a polycrystal model that describes specific orientation and neighbourhood characteristics is essential to predict the local response of these grain families. Whereas, self-consistent models are suitable for {110} and {111} grain families. This study shows that only with a suitable calibration of subsurface grain behaviour, crystal plasticity models reveal grain characteristic-dependent micromechanical behaviour.

A Mechanical Model for Stress Relaxation of Polylactic Acid/Thermoplastic Polyurethane Blends

Polylactic acid (PLA) is considered a promising biodegradable polymer alternative. Due to its high brittleness, composite materials made by melt blending thermoplastic polyurethane (TPU) with PLA can enhance the toughness of PLA. To understand the forced aging caused by stress relaxation in polymer materials, this study explains the stress relaxation experiments of PLA/TPU blends with different mass ratios under applied strain through mechanical model simulations. The Kelvin representation of the standard linear solid model (SLSM) is used to analyze the stress relaxation data of TPU/PLA blends, successfully explaining that the Young’s moduli (E1 and E2) of springs decrease with increasing temperature and TPU content. The viscosity coefficient of the PLA/TPU blends decreases with increasing temperature, and its reciprocal follows the Arrhenius law. For TPU/PLA blends with increased concentration of TPU, the activation energy for stress relaxation shows a linear decrease, confirmed by the glass transition point measured by DMA, indicating that it does not involve chemical reactions.

Quantifying the microstructural and biomechanical changes in the porcine ventricles during growth and remodelling.

Cardiac tissue growth and remodelling (G & R) occur in response to the changing physiological demands of the heart after birth. The early shift to pulmonary circulation produces an immediate increase in ventricular workload, causing microstructural and biomechanical changes that serve to maintain overall physiological homoeostasis. Such cardiac G & R continues throughout life. Quantifying the tissue's mechanical and microstructural changes because of G & R is of increasing interest, dovetailing with the emerging fields of personalised and precision solutions. This study aimed to determine equibiaxial, and non-equibiaxial extension, stress-relaxation, and the underlying microstructure of the passive porcine ventricles tissue at four time points spanning from neonatal to adulthood. The three-dimensional microstructure was investigated via two-photon excited fluorescence and second-harmonic generation microscopy on optically cleared tissues, describing the 3D orientation, rotation and dispersion of the cardiomyocytes and collagen fibrils. The results revealed that during biomechanical testing, myocardial ventricular tissue possessed non-linear, anisotropic, and viscoelastic behaviour. An increase in stiffness and viscoelasticity was noted for the left and right ventricular free walls from neonatal to adulthood. Microstructural analyses revealed concomitant increases in cardiomyocyte rotation and dispersion. This study provides baseline data, describing the biomechanical and microstructural changes in the left and right ventricular myocardial tissue during G & R, which should prove valuable to researchers in developing age-specific, constitutive models for more accurate computational simulations. STATEMENT OF SIGNIFICANCE: There is a dearth of experimental data describing the growth and remodelling of left and right ventricular tissue. The published literature is fragmented, with data reported via different experimental techniques using tissues harvested from a variety of animals, with different gender and ages. This prevents developing a continuum of data spanning birth to death, so limiting the potential that can be leveraged to aid computational modelling and simulations. In this study, equibiaxial, non-equibiaxial, and stress-relaxation data are presented, describing directional-dependent material responses. The biomechanical data is consolidated with equivalent microstructural data, an important element for the development of future material models. Combined, these data describe microstructural and biomechanical changes in the ventricles, spanning G &R from neonatal to adulthood.

Nonlinear time-dependent mechanical behavior of mammalian collagen fibrils.

The viscoelastic mechanical behavior of collagenous tissues has been studied extensively at the macroscale, yet a thorough quantitative understanding of the time-dependent mechanics of the basic building blocks of tissues, the collagen fibrils, is still missing. In order to address this knowledge gap, stress relaxation and creep tests at various stress (5-35 MPa) and strain (5-20%) levels were performed with individual collagen fibrils (average diameter of fully hydrated fibrils: 253±21 nm) in phosphate buffered saline (PBS). The experimental results showed that the time-dependent mechanical behavior of fully hydrated individual collagen fibrils reconstituted from Type I calf skin collagen, is described by strain-dependent stress relaxation and stress-dependent creep functions in both the heel-toe and the linear regimes of deformation in monotonic stress-strain curves. The adaptive quasilinear viscoelastic (QLV) model, originally developed to capture the nonlinear viscoelastic response of collagenous tissues, provided a very good description of the nonlinear stress relaxation and creep behavior of the collagen fibrils. On the other hand, the nonlinear superposition (NSP) model fitted well the creep but not the stress relaxation data. The time constants and rates extracted from the adaptive QLV and the NSP models, respectively, pointed to a faster rate for stress relaxation than creep. This nonlinear viscoelastic behavior of individual collagen fibrils agrees with prior studies of macroscale collagenous tissues, thus demonstrating consistent time-dependent behavior across length scales and tissue hierarchies. STATEMENT OF SIGNIFICANCE: Pure stress relaxation and creep experiments were conducted for the first time with fully hydrated individual collagen fibrils. It is shown that collagen nanofibrils have a nonlinear time-dependent behavior which agrees with prior studies on macroscale collagenous tissues, thus demonstrating consistent time-dependent behavior across length scales and tissue hierarchies. This new insight into the non-linear viscoelastic behavior of the building blocks of mammalian collagenous tissues may serve as the foundation for improved macroscale tissue models that capture the mechanical behavior across length scales.

Characterisation of the soft tissue viscous and elastic properties using ultrasound elastography and rheological models: validation and applications in plantar soft tissue assessment

Objective. The mechanical behaviour of soft tissue is influenced by its elastic and viscous characteristics. Therefore, the aim of this study was to develop a validated method to characterise the viscoelastic properties of soft tissues based on ultrasound elastography data. Approach. Plantar soft tissue was chosen as the tissue of interest, and gelatine-phantoms replicating its mechanical properties were manufactured for validation of the protocol. Both plantar soft tissue and the phantom were scanned using Reverberant shear wave ultrasound (US) elastography at 400–600 Hz. Shear wave speed was estimated using the US particle velocity data. The viscoelastic parameters were extracted by fitting the Young’s modulus as a function of frequency derived from the constitutive equations of the eight rheological models (four classic and their fractional-derivative versions) to the shear wave dispersion data. Furthermore, stress-time functions derived from the eight rheological models were fitted to the phantom stress-relaxation data. Main results. The viscoelastic parameters estimated using elastography data based on the fractional-derivative (FD) models, compared to the classic models, were closer to those quantified using the mechanical test. In addition, the FD-Maxwell and FD-Kelvin–Voigt models showed to more effectively replicate the viscoelastic behaviour of the plantar soft tissue with minimum number of model parameters ( = 0.72 for both models) . Hence the FD-KV and FD-Maxwell models can more effectively quantify the viscoelastic characteristics of the soft tissue compared to other models. Significance. In this study, a method for mechanical characterisation of the viscoelastic properties of soft tissue in ultrasound elastography was developed and fully validated. An investigation into the most valid rheological model and its applications in plantar soft tissue assessment were also presented. This proposed approach for the characterisation of viscous and elastic mechanical properties of soft tissue has implications in assessing the soft tissue function where those can be used as markers for diagnosis or prognosis of tissue status.

CHARACTERIZATION OF NATIVE AND DECELLULARIZED PORCINE TENDON UNDER TENSION AND COMPRESSION: A CLOSER LOOK AT GLYCOSAMINOGLYCAN CONTRIBUTION TO TENDON MECHANICS

Decellularised porcine superflexor tendon (pSFT) has been demonstrated to be a suitable scaffold for anterior cruciate ligament reconstruction[1]. While the role of collagen in tendons is well known, the mechanical role of glycosaminoglycans (GAGs) is less clear and may be altered by the decellularisation process.To determine the effects of decellularisation on pSFT GAG content and mechanical function and to investigate the consequences of GAG loss in tensile and compressive loading.pSFTs were decellularised following previous techniques [2]. For GAG removal, native pSFTs were treated with chondroitinase ABC (ChABC; 0.1U/mL, 72h). Cell and GAG removal was validated using histology and quantitative assays. Native, decellularised and ChABC treated groups (n=6) were biomechanically characterised. In tension, specimens underwent stress relaxation and strength testing using previous protocols [1]. Stress relaxation data was fitted to a modified Maxwell-Weichert model to determine time-dependent (E1 & E2) and time-independent moduli (E0). The toe and linear region moduli (Etoe, Elinear), in addition to tensile strength (UTS) and failure strain were determined from strength testing. In compression, specimens underwent confined loading conditions (ramp at 10 s-1 to 10% strain and hold). The aggregate modulus (HA) and zero-strain permeability (k0) were determined using previous techniques [3]. Data was analysed by one-way ANOVA with Tukey post-hoc test to determine significant differences between test groups (p<0.05).Quantitative assays showed no GAG reduction post-decellularisation, but a significant reduction after ChABC treatment. HA was only significantly reduced in the ChABC group. k0 was significantly higher for the ChABC group compared to decellularised. E0 was significantly reduced in the decellularised group compared to native and ChABC groups, while E1 and E2 were not different between groups. Etoe, Elinear, UTS and failure strain were not different between groups.Decellularisation does not affect GAG content or impair mechanical function in pSFT. GAG loss adversely affects pSFT compressive properties, revealing major mechanical contribution under compression, but no significant role under tension.

A new viscoelastic model for human brain tissue using Lode invariants based rate-type thermodynamic framework

We develop new rate-type constitutive relations on a set of orthonormal tensor basis and the corresponding set of Lode invariants, which require only 9 material parameters to predict the mechanical response of the human brain tissue. The mode-dependent response of the tissue is captured by invoking the Hill-stable elastic potential of Prasad and Kannan (2020) and constructing a new form for the rate of dissipation, thus introducing the mode-of-deformation dependent modulus terms and the mode-of-deformation-rate dependent viscosities into the rate-type thermodynamic framework of Rajagopal and Srinivasa (2000). Through the analysis-driven construction of the rate of dissipation, we incorporate maximum change in the viscosities with respect to the mode-of-deformation rates and limit the number of material parameters. Our model satisfactorily predicts the complicated load-unload cycles (pre-conditioned and conditioned) and the stress relaxation data under multiple modes of deformation and multiple rates for the Corona Radiata (CR) region of the brain tissue. It also captures the tension–compression asymmetry in the response and the higher relaxation time in compression loading than in shear loading.

Remaining useful life evaluation for accelerated Wiener degradation process model with mixed random effects and measurement errors

AbstractThis paper evaluates the remaining useful life (RUL) for the accelerated Wiener process with mixed random effects and measurement errors. In the discussed model, the random effects are included in both the drift and diffusion parameters of the Wiener process to model the heterogeneity among different degradation paths of products. The measurement errors are introduced to describe the inaccuracy during the measurement process. The effect of the accelerated stress level is included in the drift parameter. The expectation‐maximization (EM) algorithm is applied to obtain the estimation of the model parameters. The expressions of the probability density functions (PDFs) and cumulative distribution functions (CDFs) of the lifetime and RUL distributions of products under the normal usage stress level are derived theoretically. Finally, an example of stress relaxation data is used to illustrate the effectiveness of the developed model and method.

The influence of blood composition and loading frequency on the behavior of embolus analogs

In cases of acute ischemic stroke (AIS), mechanical thrombectomy (MT) can be used to directly remove lodged thromboemboli. Despite improvements in patient outcomes, one of the key factors affecting MT success is the mechanical properties of the occlusive thrombus. Therefore, the goal of this study was to investigate the viscoelastic properties of embolus analogs (EAs) and determine the influence of EA hematocrit and loading frequency.Bovine blood EAs were created over a range of physiological hematocrits (0–60%) and cyclic uniaxial compression testing was performed at three loading frequencies to mimic in vivo loading conditions, followed by stress-relaxation testing. It was found that EAs exhibited behaviors typical of hyper-viscoelastic materials and that EA hematocrit played a large role in both EA stiffness and relaxation, with both parameters decreasing as hematocrit increased from 0 to 60%. The viscoelastic behavior of the EAs was also affected by the frequency at which they were loaded, with significant increases in peak stresses between the 0.5 and 2 Hz loaded EAs. Lower hematocrit EAs had very dense fibrin networks while the higher hematocrit EAs consisted of closely packed RBCs with little fibrin present. These results suggest that fibrin contributes to EA stiffness and relaxation behaviors while RBCs play a role in decreasing the overall viscous response and strain-rate dependency.An Ogden hyperelastic model was found to best reproduce the EA loading data while a 3-term Prony series was fit to the stress relaxation data. A hyper-viscoelastic modeling framework was then implemented combining the loading and stress-relaxation fits and the results could match the full cyclic loading data for EAs of varying hematocrit and loading frequency. The results of the experimental mechanical characterization and hyper-viscoelastic curve fitting can be incorporated in future modeling efforts to optimize mechanical thrombectomy for AIS patients.

Low temperature plasticity of microcrystalline Al–Li alloy

The plastic deformation of Al-3.8 at.% Li polycrystals processed by the equal-channel angular hydroextrusion (ECAH) were investigated during tension in the temperature range of 4.2–400 K. The evolution of the microstructure during loading was studied by the electron backscatter diffraction (EBSD) method, including the orientation and kernel average misorientation (KAM) mappings. In as-prepared state the microstructure characterized by grains with small misorientation angles and a high density of dislocations. The deformation of a sample at 120 K leads to increase in the density of deformation defects while at 290 K to their decrease. The strong temperature sensitivity of the yield strength indicates the thermally activated nature of the plastic deformation. An increase in the plasticity and strength of polycrystals with decreasing temperature is explained by a decrease in the dislocation annihilation due to a decrease in the mobility of atoms, resulting in increase in the strain hardening rate. A nonmonotonic dependence of the activation volume Va(T) with a maximum at 180 K was established from stress relaxation data. The analysis of stress-strain curves and microstructure evolution indicate a dominance of thermally activated mechanism of intersection of the forest dislocations below 180 K and an increase in the activity of recovery processes at moderate temperatures.

The viscoelasticity, anisotropy and location-dependence of mechanical properties of rabbit iris investigated using uniaxial tensile tests

Purpose Abnormal iris mechanical properties have been considered to be an important cause of pupillary-block and angle-closure glaucoma. In this research, viscoelasticity, anisotropy and location-dependence of mechanical properties of rabbit iris were investigated using uniaxial tensile test. Methods Iris strips were taken along three directions: inner-circumferential direction (ICD), outer-circumferential direction (OCD) and radial direction (RD), respectively. Quasi-static tensile tests and stress-relaxation tests were applied on the iris strips. Then the stress-stretch data was fitted with third order Ogden model; the stress-relaxation data was fitted with the third order Prony series model. Through comparing the tangent modulus and relaxation limit of the strips from different directions and locations, the viscoelasticity, anisotropy and location-dependence of mechanical properties of rabbit iris were explored. Results The tangent moduli of iris at the stretch of 1.05 along ICD, OCD, and RD were 3.2 ± 1.4 kPa, 4.2 ± 2.6 kPa and 1.5 ± 0.8 kPa, respectively. Iris strips in ICD and OCD were found to have almost the same stress-relaxation behavior, and both relaxed slower than iris strips in RD. Conclusions The mechanical properties of the iris were nonlinear, viscoelastic, anisotropic and location-dependent. The stress growth rate of the circumferential direction iris strip is significantly lower than that of RD, and the stress relaxation rate is significantly higher than that of RD. That is, the iris is more prone to deformation in RD. This study can provide more precise iris material parameters for exploring the mechanical causes of pupillary-block.

Validation of empirical changes to asphalt specifications based on phase angle and relaxation properties using data from a northern Ontario, Canada pavement trial

Polymer modified asphalt is generally accepted to provide positive benefit/cost outcomes in terms of extending pavement service life. It has recently been claimed that higher modification levels perform better. A 13-year-old pavement trial in Ontario, Canada is providing valuable insights on this issue. Dynamic shear rheometer (DSR) tests were conducted to monitor rheological changes upon oxidative aging. Gelled binders exhibit more solid-like response leading to less ability to relax thermal stress, and hence an accelerated decay in performance. This was further verified from relaxation spectra calculated from stress relaxation data. A test section constructed with a gel-type binder containing 7 % styrene-butadiene-styrene (SBS) modifier has a predicted service life of 23 years, nearly the same as the control which was tainted with recycled engine oil bottoms (REOB). In contrast, sol-type 3.5 % SBS modified binder and straight-run Cold Lake asphalt binder are expected to last around 60 % longer at 36 and 38 years, respectively. Conclusions from this study reiterate that current specifications fail to correlate with field performance. Improved binder grading is possible by limiting the slope of the phase angle master curve between 30° and 45°.

Minimum design requirements for a poroelastic mimic of articular cartilage

The exceptional functional performance of articular cartilage (load-bearing and lubrication) is attributed to its poroelastic structure and resulting interstitial fluid pressure. Despite this, there remains no engineered cartilage repair material capable of achieving physiologically relevant poroelasticity. In this work we develop in silico models to guide the design approach for poroelastic mimics of articular cartilage. We implement the constitutive models in FEBio, a PDE solver for multiphasic mechanics problems in biological and soft materials. We investigate the influence of strain rate, boundary conditions at the contact interface, and fiber modulus on the reaction force and load sharing between the solid and fluid phases. The results agree with the existing literature that when fibers are incorporated the fraction of load supported by fluid pressure is greatly amplified and increases with the fiber modulus. This result demonstrates that a stiff fibrous phase is a primary design requirement for poroelastic mimics of articular cartilage. The poroelastic model is fit to experimental stress-relaxation data from bovine and porcine cartilage to determine if sufficient design constraints have been identified. In addition, we fit experimental data from FiHy™, an engineered material which is claimed to be poroelastic. The fiber-reinforced poroelastic model was able to capture the primary physics of these materials and demonstrates that FiHy™ is beginning to approach a cartilage-like poroelastic response. We also develop a fiber-reinforced poroelastic model with a bonded interface (rigid contact) to fit stress relaxation data from an osteochondral explant and FiHy™ + bone substitute. The model fit quality is similar for both the chondral and osteochondral configurations and clearly captures the first order physics. Based on this, we propose that physiological poroelastic mimics of articular cartilage should be developed under a fiber-reinforced poroelastic framework.

Effect of Surface Dissolution on Dislocation Activation in Stressed FeSi6.5 Steel.

The effects of surface dissolution on dislocation activation in FeSi6.5 steel are quantitatively studied by analyzing the stress relaxation data using the thermal activation theory of dislocation. The stressed FeSi6.5 steel sample in acid solutions (H2SO4 or HCl) exhibits a much higher rate of stress reduction with time compared with that in air or deionized water. As the stress relaxation time is prolonged to 20 min, the relaxation rates are 0.055 MPa·min-1 in water and 0.074, 0.1, 0.11 MPa·min-1 in H2SO4 solutions with pH 4, 3, and 2, respectively. In a NaCl solution, a slight increase in the relaxation rate compared with air was found. Higher acidity (lower pH) of the solution inducing higher stress relaxation rate implies the softening is associated with the anodic dissolution of the surface layer and the accelerated (additional) flow of dislocations. The analyses using the thermal activation theory of dislocation during relaxation reveal the mechanism for the accelerated plastic flow induced by the corrosive medium. The variations of these parameters are related to the relaxation of the stress field of dislocations and the weakening of interaction between slip dislocations and short-range obstacles. The chemomechanical effect, including a reduction in apparent activation energy and a decrease in waiting time for dislocation to obtain sufficient thermal activation energy to cross obstacles, causes an increase in the stress relaxation rate (plastic strain rate). The study confirms that surface dissolution accelerates the plastic flow of metals and supports the view that surface dissolution facilitates dislocation slip. It is helpful to improve the formability of brittle metals.

Strain-dependent stress relaxation behavior of healthy right ventricular free wall

The increasing evidence of stress-strain hysteresis in large animal or human myocardium calls for extensive characterizations of the passive viscoelastic behavior of the myocardium. Several recent studies have investigated and modeled the viscoelasticity of the left ventricle while the right ventricle (RV) viscoelasticity remains poorly understood. Our goal was to characterize the biaxial viscoelastic behavior of RV free wall (RVFW) using two modeling approaches. We applied both quasi-linear viscoelastic (QLV) and nonlinear viscoelastic (NLV) theories to experimental stress relaxation data from healthy adult ovine. A three-term Prony series relaxation function combined with an Ogden strain energy density function was used in the QLV modeling, while a power-law formulation was adopted in the NLV approach. The ovine RVFW exhibited an anisotropic and strain-dependent viscoelastic behavior relative to anatomical coordinates, and the NLV model showed a higher capacity in predicting strain-dependent stress relaxation than the QLV model. From the QLV fitting, the relaxation term associated with the largest time constant played the dominant role in the overall relaxation behavior at most strains from early to late diastole, whereas the term associated with the smallest time constant was pronounced only at low strains at early diastole. From the NLV fitting, the parameters showed a nonlinear dependence on the strain. Overall, our study characterized the anisotropic, nonlinear viscoelasticity to capture the elastic and viscous resistances of the RVFW during diastole. These findings deepen our understanding of RV myocardium dynamic mechanical properties. Statement of significanceAlthough significant progress has been made to understand the passive elastic behavior of the right ventricle free wall (RVFW), its viscoelastic behavior remains poorly understood. In this study, we originally applied both quasi-linear viscoelastic (QLV) and nonlinear viscoelastic (NLV) models to published experimental data from healthy ovine RVFW. Our results revealed an anisotropic and strain-dependent viscoelastic behavior of the RVFW. The parameters from the NLV fitting showed nonlinear relationships with the strain, and the NLV model showed a higher capacity in predicting strain-dependent stress relaxation than the QLV model. These findings characterize the anisotropic, nonlinear viscoelasticity of RVFW to fully capture the total (elastic and viscous) resistance that is critical to diastolic function.

In-situ monitoring of reinforcement compaction response via MXene-coated glass fabric sensors

In this study, MXene-coated glass fabric sensors were used to obtain reinforcement compaction and stress relaxation data within a closed mold. A layer of MXene-coated sensor was embedded within a multilayer glass fiber preform to monitor compaction forces under both dry and wet conditions i.e., when the stack was fully impregnated with resin or a test fluid. The effect of the test fluid type on compressibility and sensor piezo-resistivity was also determined. The sensors showed excellent sensitivity in both dry and impregnated states and were able to successfully monitor different loading conditions such as peak stresses carried by the reinforcement, long-term stress relaxation and cyclic loads. Polynomial data fitting and machine learning models were used to calibrate the sensors to predict the compaction response. An electro-mechanical based model, on the lines of traditional viscoelastic stress relaxation model, was used to represent piezo-resistivity for long term relaxation. The proposed technique has great potential of in-situ monitoring of mold clamping forces and part thickness by measuring piezo-resistive changes taking place throughout a molding cycle using MXene based embedded smart sensors.

An Engineering Prediction Model for Stress Relaxation of Polymer Composites at Multiple Temperatures.

This study develops an engineering prediction model for stress relaxation of polymer composites, allowing the prediction of stress relaxation behaviour under a constant strain, over a range of temperatures. The model is based on the basic assumption that in the stress relaxation process the reversible strain is transformed to irreversible strain continuously. A strain-hardening model is proposed to incorporate nonlinear elastic behaviour, and a creep rate model is used to describe the irreversible deformation in the process. By using stress relaxation data at different temperatures, under different strains, the dependence on temperature and initial strain of the model parameters can be established. The effectiveness of the proposed model is verified and validated using three polymer composite materials. The performance of the model is compared with three commonly used stress relaxation models such as the parallel Maxwell and Prony series models. To ease the use of the proposed model in realistic structural problems, a user subroutine is developed, and the stress relaxation of a plate structure example is demonstrated.

Quasi-linear viscoelastic behavior of fresh porcine ureter.

To evaluate the viscoelastic properties of the fresh porcine ureter. Prove the QLV theory can sufficiently model the stress relaxation function of porcine ureters, and determine the QLV model constants which may provide insight into the synthesis of ureteral scaffolds with biomimetic viscoelastic properties in tissue engineering. Hysteresis tests were applied to study the differences in dissipated energy ratio for each different strain group. In stress relaxation tests, samples were sub-grouped and quickly ramping up to 5%, 20%, and 30% strain in each group and gradually relaxed to a corresponding level. Bringingtogether the quasi-linear viscoelasticity (QLV) theory and stress relaxation function to determine the eight constants of the ureteral tissue, and fitting the raw data with the model via MATLAB. The hysteresis response measurement results revealed that the porcine ureter was a highly dissipative material and there were differences between toe and linear region in stress-stain curve. The stress relaxation results revealed ureters responded with time-dependent decay of stress. The eight constants of the ureteral QLV model were determined for three different strain groups, and we proved that the QLV model can sufficiently adapt the experimental data of the ureter stress relaxation. This study investigated the time-dependent properties of the porcine ureter, and demonstrated the QLV theory could be used to evaluate the viscoelastic properties of the porcine ureteral tissue.

Architecture and Composition Dictate Viscoelastic Properties of Organ-Derived Extracellular Matrix Hydrogels.

The proteins and polysaccharides of the extracellular matrix (ECM) provide architectural support as well as biochemical and biophysical instruction to cells. Decellularized, ECM hydrogels replicate in vivo functions. The ECM’s elasticity and water retention renders it viscoelastic. In this study, we compared the viscoelastic properties of ECM hydrogels derived from the skin, lung and (cardiac) left ventricle and mathematically modelled these data with a generalized Maxwell model. ECM hydrogels from the skin, lung and cardiac left ventricle (LV) were subjected to a stress relaxation test under uniaxial low-load compression at a 20%/s strain rate and the viscoelasticity determined. Stress relaxation data were modelled according to Maxwell. Physical data were compared with protein and sulfated GAGs composition and ultrastructure SEM. We show that the skin-ECM relaxed faster and had a lower elastic modulus than the lung-ECM and the LV-ECM. The skin-ECM had two Maxwell elements, the lung-ECM and the LV-ECM had three. The skin-ECM had a higher number of sulfated GAGs, and a highly porous surface, while both the LV-ECM and the lung-ECM had homogenous surfaces with localized porous regions. Our results show that the elasticity of ECM hydrogels, but also their viscoelastic relaxation and gelling behavior, was organ dependent. Part of these physical features correlated with their biochemical composition and ultrastructure.