Viscoelastic Stress Relaxation Research Articles

Label-free multimodal electro-thermo-mechanical (ETM) phenotyping as a novel biomarker to differentiate between normal, benign, and cancerous breast biopsy tissues.

Technologies for quick and label-free diagnosis of malignancies from breast tissues have the potential to be a significant adjunct to routine diagnostics. The biophysical phenotypes of breast tissues, such as its electrical, thermal, and mechanical properties (ETM), have the potential to serve as novel markers to differentiate between normal, benign, and malignant tissue. We report a system-of-biochips (SoB) integrated into a semi-automated mechatronic system that can characterize breast biopsy tissues using electro-thermo-mechanical sensing. The SoB, fabricated on silicon using microfabrication techniques, can measure the electrical impedance (Z), thermal conductivity (K), mechanical stiffness (k), and viscoelastic stress relaxation (%R) of the samples. The key sensing elements of the biochips include interdigitated electrodes, resistance temperature detectors, microheaters, and a micromachined diaphragm with piezoresistive bridges. Multi-modal ETM measurements performed on formalin-fixed tumour and adjacent normal breast biopsy samples from N = 14 subjects were able to differentiate between invasive ductal carcinoma (malignant), fibroadenoma (benign), and adjacent normal (healthy) tissues with a root mean square error of 0.2419 using a Gaussian process classifier. Carcinoma tissues were observed to have the highest mean impedance (110018.8 ± 20293.8 Ω) and stiffness (0.076 ± 0.009 kNm-1) and the lowest thermal conductivity (0.189 ± 0.019 Wm-1K-1) amongst the three groups, while the fibroadenoma samples had the highest percentage relaxation in normalized load (47.8 ± 5.12%). The work presents a novel strategy to characterize the multi-modal biophysical phenotype of breast biopsy tissues to aid in cancer diagnosis from small-sized tumour samples. The methodology envisions to supplement the existing technology gap in the analysis of breast tissue samples in the pathology laboratories to aid the diagnostic workflow.

Triaxial Deformation of the Goldwyer Gas Shale at In Situ Stress Conditions—Part II: Viscoelastic Creep/Relaxation and Frictional Failure

To understand the geomechanical implications of long-term creep (time-dependent deformation) response of gas shale, short-duration creep was recorded from laboratory triaxial tests on ten Goldwyer gas shale samples in the onshore Canning Basin at in situ stress conditions under constant differential axial stress. A simple power-law function captures primary creep behaviour involving elastic compliance constant B and time-dependent factor n. Experimental creep data revealed larger axial creep strain in clay and organic-rich rocks, than those dominated by carbonates. Anisotropic nature of creep was observed depending upon the direction of constant axial stress application (perpendicular or parallel to the bedding plane). Upon the application of linear viscoelastic theory on laboratory creep fitting coefficients, differential horizontal stress accumulation over a geological time scale was estimated from the viscoelastic stress relaxation concept. Further, this model was used to derive lithology-dependent least principal stress (Shmin) magnitude at depth for two vertical wells intersecting the Goldwyer gas shale formations. This newly proposed Shmin model was found to have a profound influence on designing hydraulic fracture simulation. Further, pore size distribution and specific surface area value SN2 were derived from low-pressure gas adsorption experiments. These physical properties along with weak mineral components were linked with creep constitutive parameters to understand the physical mechanisms of creep. A strong correlation was noted between SN2 and creep parameters n and B. Finally, an attempt was made to investigate how gas shale composition and failure frictional properties can influence shear fracturing.

A Modular Platform for Cytocompatible Hydrogels with Tailored Mechanical Properties Based on Monolithic Matrices and Particulate Building Blocks.

We establish a versatile hydrogel platform based on modular building blocks that allows the design of hydrogels with tailored physical architecture and mechanical properties. We demonstrate its versatility by assembling (i) a fully monolithic gelatin methacryloyl (Gel-MA) hydrogel, (ii) a hybrid hydrogel composed of 1:1 Gel-MA and gelatin nanoparticles, and (iii) a fully particulate hydrogel based on methacryloyl-modified gelatin nanoparticles. The hydrogels were formulated to exhibit the same solid content and comparable storage modulus but different stiffness and viscoelastic stress relaxation. The incorporation of particles resulted in softer hydrogels with enhanced stress relaxation. Murine osteoblastic cells cultured in two-dimensional (2D) on hydrogels showed proliferation and metabolic activity comparable to established collagen hydrogels. Furthermore, the osteoblastic cells showed a trend of increased cell numbers, cell expansion, and more defined protrusions on stiffer hydrogels. Hence, modular assembly allows the design of hydrogels with tailored mechanical properties and the potential to alter cell behavior.

Multiscale characterization of left ventricle active behavior in the mouse.

The myocardium possesses an intricately designed microarchitecture to produce an optimal cardiac contraction. The contractile behavior of the heart is generated at the sarcomere level and travels across several length scales to manifest as the systolic function at the organ level. While passive myocardial behavior has been studied extensively, the translation of active tension produced at the fiber level to the organ-level function is not well understood. Alterations in cardiac systolic function are often key sequelae in structural heart diseases, such as myocardial infarction and systolic heart failure; thus, characterization of the contractile behavior of the heart across multiple length scales is essential to improve our understanding of mechanisms collectively leading to depressed systolic function. In this study, we present a methodology to characterize the active behavior of left ventricle free wall (LVFW) myocardial tissues in mice. Combined with active tests in papillary muscle fibers and conventional in vivo contractility measurement at the organ level in an animal-specific manner, we establish a multiscale active characterization of the heart from fiber to organ. In addition, we quantified myocardial architecture from histology to shed light on the directionality of the contractility at the tissue level. The LVFW tissue activation-relaxation behavior under isometric conditions was qualitatively similar to that of the papillary muscle fiber bundle. However, the maximum stress developed in the LVFW tissue was an order of magnitude lower than that developed by a fiber bundle, and the time taken for active forces to plateau was 2-3 orders of magnitude longer. Although the LVFW tissue exhibited a slightly stiffer passive response in the circumferential direction, the tissues produced significantly larger active stresses in the longitudinal direction during active testing. Also, contrary to passive viscoelastic stress relaxation, active stresses relaxed faster in the direction with larger peak stresses. The multiscale experimental pipeline presented in this work is expected to provide crucial insight into the contractile adaptation mechanisms of the heart with impaired systolic function. STATEMENT OF SIGNIFICANCE: Heart failure cause significant alterations to the contractile-relaxation behavior of the yocardium. Multiscale characterization of the contractile behavior of the myocardium is essential to advance our understanding of how contractility translates from fiber to organ and to identify the multiscale mechanisms leading to impaired cardiac function. While passive myocardial behavior has been studied extensively, the investigation of tissue-level contractile behavior remains critically scarce in the literature. To the best of our knowledge, our study here is the first to investigate the contractile behavior of the left ventricle at multiple length scales in small animals. Our results indicate that the active myocardial wall is a function of transmural depth and relaxes faster in the direction with larger peak stresses.

Effects of tissue degradation by collagenase and elastase on the biaxial mechanics of porcine airways

BackgroundCommon respiratory illnesses, such as emphysema and chronic obstructive pulmonary disease, are characterized by connective tissue damage and remodeling. Two major fibers govern the mechanics of airway tissue: elastin enables stretch and permits airway recoil, while collagen prevents overextension with stiffer properties. Collagenase and elastase degradation treatments are common avenues for contrasting the role of collagen and elastin in healthy and diseased states; while previous lung studies of collagen and elastin have analyzed parenchymal strips in animal and human specimens, none have focused on the airways to date.MethodsSpecimens were extracted from the proximal and distal airways, namely the trachea, large bronchi, and small bronchi to facilitate evaluations of material heterogeneity, and subjected to biaxial planar loading in the circumferential and axial directions to assess airway anisotropy. Next, samples were subjected to collagenase and elastase enzymatic treatment and tensile tests were repeated. Airway tissue mechanical properties pre- and post-treatment were comprehensively characterized via measures of initial and ultimate moduli, strain transitions, maximum stress, hysteresis, energy loss, and viscoelasticity to gain insights regarding the specialized role of individual connective tissue fibers and network interactions.ResultsEnzymatic treatment demonstrated an increase in airway tissue compliance throughout loading and resulted in at least a 50% decrease in maximum stress overall. Strain transition values led to significant anisotropic manifestation post-treatment, where circumferential tissues transitioned at higher strains compared to axial counterparts. Hysteresis values and energy loss decreased after enzymatic treatment, where hysteresis reduced by almost half of the untreated value. Anisotropic ratios exhibited axially led stiffness at low strains which transitioned to circumferentially led stiffness when subjected to higher strains. Viscoelastic stress relaxation was found to be greater in the circumferential direction for bronchial airway regions compared to axial counterparts.ConclusionTargeted fiber treatment resulted in mechanical alterations across the loading range and interactions between elastin and collagen connective tissue networks was observed. Providing novel mechanical characterization of elastase and collagenase treated airways aids our understanding of individual and interconnected fiber roles, ultimately helping to establish a foundation for constructing constitutive models to represent various states and progressions of pulmonary disease.

Discrete Measurements of the Least Horizontal Principal Stress from Core Data: An Application of Viscoelastic Stress Relaxation

Summary The emerging Paradox Oil Play in southeastern Utah is among the most significant unconventional plays in the western USA. The mean total undiscovered oil resources within just the Pennsylvanian Cane Creek interval of the Paradox Basin are believed to exceed 215 million barrels. However, to date, less than 5% (~9 million barrels) of the total Cane Creek resource has been produced from fewer than 40 wells, and only approximately one-half of those are horizontal wells. More than 95% of production is from the central Cane Creek Unit (CCU). Natural fractures are a key feature of many production wells, but stimulation by induced hydraulic fractures is not consistently successful. We hypothesize that more effective production in this play will rely on better fundamental characterization, especially on better quantification of the state of stress. Approximately 110 ft of core, well logs, and a diagnostic fracture injection test (DFIT) were acquired from the State 16-2 well within the CCU. With these data, we applied two methods to constrain and clarify the state of stress. The first technique, the Simpson’s coefficient method, provides lower bounds on the two horizontal principal stresses and relies on only limited data. Alternatively, the viscoelastic stress relaxation (VSR) method is used to estimate the least horizontal principal stress, building on observations that principal stresses become more isotropic as the viscous behavior of a rock is more pronounced. Results of these two methods support the hypothesis that the state of stress in the CCU of the Paradox Basin is nearly lithostatic and isotropic. Other factors consistent with this hypothesis include high formation pore pressure, which tends to reduce the possible stress states by changing the frictional failure equilibrium; lack of induced fractures in the core, which should be present in the case of stress anisotropy; and interbedded halite layers, which given their high degree of ductility, probably lead to greater VSR for the entire sedimentary package.

Rate-dependent evolution of wrinkling films due to growth on semi-infinite planar viscoelastic substrates

A mechanistic understanding of morphogenesis in biology, the fabrication of advanced meta surfaces with specific functionalities and structures with enhanced energy dissipation often have in common that the combined effects of energy dissipation due to viscoelasticity and a loss of stability govern both their mechanical response and their final forms. In this paper we show that the interplay between viscoelasticity and multistability crucially influences the evolution of deformations in viscoelastic structures undergoing large deformations. The influence is studied on a prototypical system of a uniaxially growing film on a semi-infinite planar viscoelastic substrate, where it is shown that during the evolution of deformation the choice of multiple developing modes is greatly affected by this interplay. For the analysis of the underlying mechanics of the mode competition in the post-buckling regime, when the system undergoes large deformations, a 3D general finite-strain visco-hyperelastic theory is built. It includes kinematic and material nonlinearities in the film and in the substrate. For the case of ramp-loading time functions the phase space of the solutions is characterized and the evolution of a deformation pattern is analyzed. We find that the interaction between multistability and viscoelasticity greatly increases the evolution time of the system and that the growth rate and viscoelastic stress-relaxation rate influence the choice of the final equilibrium deformation state of the structure. This shows that viscoelastic structures can evolve into (meta)stable equilibrium states that are unattainable using purely elastic structures. The nonlinear problem is solved numerically with the use of the finite-element method. In parallel, we develop analytical solutions for a simplified problem that is based on Föppl–von Karman plate kinematics to describe the mechanics of the film and substrate that is modeled as a 2D linear-viscoelastic continuum. A remarkably good match between the analytical and the numerical results was obtained.

Non-Maxwellian viscoelastic stress relaxations in soft matter.

Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, it is often not sufficient for capturing the complex relaxation dynamics of soft matter. In this Tutorial, we introduce and discuss the physics of non-Maxwellian linear stress relaxation as observed in soft materials, the ascribed origins of this effect in different systems, and appropriate models that can be used to capture this relaxation behavior. We provide a basic toolkit that can assist the understanding and modeling of the mechanical relaxation of soft materials for diverse applications.

Kinetic model for prediction of subcritical crack growth, crack tip relaxation, and static fatigue threshold in silicate glass

Prediction of brittle fracture of amorphous oxide glasses continues to be a challenge due to the existence of multiple fracture mechanisms that vary with loading conditions. To address this challenge, we present a model for all three regimes of crack growth in glasses. Regimes I and III are controlled by Arrhenius processes while regime II is transport controlled along with a simple Arrhenius model for viscoelastic stress relaxation. Through dimensional arguments and physical reasoning, we propose a single mechanism which underlies both regime III subcritical crack growth and near-crack-tip viscoelastic relaxation. By combining the subcritical crack growth and viscoelastic models we obtain a prediction for a threshold stress intensity, Kth, below which stresses around the crack relax faster than it propagates. For stress intensity KI<Kth, no subcritical crack growth is predicted to occur, allowing for the design of stable glass systems. The prediction is compared to measured subcritical fracture threshold data for soda-lime silica glasses.

New insights on carbon black suspension rheology—Anisotropic thixotropy and antithixotropy

We report a detailed experimental study of peculiar thixotropic dynamics of carbon black (CB, Vulcan XC-72) suspensions in mineral oil, specifically the observation of sequential stress increase then decrease at a fixed shear rate in a step-down test. We verify that such dynamics, though peculiar, come from a true material response rather than experimental artifacts. We also reveal how this long-time stress decay is associated with antithixotropic structural change rather than viscoelastic stress relaxation by using orthogonal superposition (OSP) rheometry to probe viscoelastic moduli during the step-down tests. The orthogonal storage and loss moduli are present, showing this two-timescale recovery then decay response, which demonstrates that this response is antithixotropic, and it involves shear-induced structuring. We further show a mechanical anisotropy in the CB suspension under shear using OSP. Based on the rheological results, a microstructural schematic is proposed, considering qualitatively thixotropic structure build-up, antithixotropic densification, and anisotropic structure evolution. Our observation for these CB suspensions is outside the standard paradigm of thixotropic structure-parameter models, and the elastic response provides us with new insight into the transient dynamics of CB suspensions.

Microscopic dynamics underlying the stress relaxation of arrested soft materials

Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.

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 in vitro model of fibrosis using crosslinked native extracellular matrix-derived hydrogels to modulate biomechanics without changing composition

Extracellular matrix (ECM) is a dynamic network of proteins, proteoglycans and glycosaminoglycans, providing structure to the tissue and biochemical and biomechanical instructions to the resident cells. In fibrosis, the composition and the organization of the ECM are altered, and these changes influence cellular behaviour. Biochemical (i. e. protein composition) and biomechanical changes in ECM take place simultaneously in vivo. Investigating these changes individually in vitro to examine their (patho)physiological effects has been difficult. In this study, we generated an in vitro model to reflect the altered mechanics of a fibrotic microenvironment through applying fibre crosslinking via ruthenium/sodium persulfate crosslinking on native lung ECM-derived hydrogels. Crosslinking of the hydrogels without changing the biochemical composition of the ECM resulted in increased stiffness and decreased viscoelastic stress relaxation. The altered stress relaxation behaviour was explained using a generalized Maxwell model. Fibre analysis of the hydrogels showed that crosslinked hydrogels had a higher percentage of matrix with a high density and a shorter average fibre length. Fibroblasts seeded on ruthenium-crosslinked lung ECM-derived hydrogels showed myofibroblastic differentiation with a loss of spindle-like morphology together with greater α-smooth muscle actin (α-SMA) expression, increased nuclear area and circularity without any decrease in the viability, compared with the fibroblasts seeded on the native lung-derived ECM hydrogels. In summary, ruthenium crosslinking of native ECM-derived hydrogels provides an exciting opportunity to alter the biomechanical properties of the ECM-derived hydrogels while maintaining the protein composition of the ECM to study the influence of mechanics during fibrotic lung diseases. Statement of significanceFibrotic lung disease is characterized by changes in composition and excessive deposition of extracellular matrix (ECM). ECM fibre structure also changes due to crosslinking, which results in mechanical changes. Separating the changes in composition and mechanical properties has been difficult to date. In this study, we developed an in vitro model that allows alteration of the mechanical changes alone by applying fibre crosslinking in native lung ECM-derived hydrogels. Characterisations of the crosslinked hydrogels indicated the model mimicked mechanical properties of fibrotic lung tissue and reflected altered fibre organisation. This ECM-based fibrosis model provides a method to preserve the native protein composition while altering the mechanical properties providing an important tool, not only for lung but also other organ fibrosis.

3D printable hybrid acrylate-epoxy dynamic networks

Polymer networks with dynamic bonds, also known as covalent adaptable networks (CANs) combine the superior mechanical properties and chemical resistance of thermosets with the ability to be reprocessed, a feat formerly attributed only to thermoplastics. Inspired by an evergrowing body of research on dynamic poly(β-hydroxy ester) networks, a polyacrylate/epoxy-acid thermoset was designed, which contains a high concentration of β-hydroxy ester bonds that partake in transesterification reactions that facilitate the repair and recycle of the cured material at feasible temperatures. Firstly, liquid formulations are subjected to UV light to initiate acrylate homopolymerization to obtain the intermediate, partially-cured material. A subsequent thermal treatment triggers the epoxy-acid reaction, which improves the mechanical properties and helps increase the likelihood of transesterifications as new β-hydroxy ester groups are formed. The effect of thermal post-treatment and the choice of catalyst on viscoelastic properties and stress relaxation behavior of these materials is studied. Results show that, transesterification reactions reach equilibrium in less than 4 h at 180 °C during which time the overall cross-linking density increases further. As to the choice of catalyst, a commonly used zinc acetylacetonate outperforms an imidazole-type base. Thanks to the dynamic bonds, damaged samples can be repaired fully using simple procedures. Recyclability is tested by grinding pristine samples and re-molding them under pressure and temperature. Practically complete recovery of viscoelastic properties is confirmed.

Thickness dependence of viscoelastic stress relaxation of laminated microbeams due to mismatch strain

Thickness dependence of viscoelastic stress relaxation of laminated microbeams due to mismatch strain

Water in polyurethane networks: physical and chemical ageing effects and mechanical parameters

The chemical structure, polymer mobility and mechanical properties are studied for a cross-linked amorphous poly(ether urethane) (PU) from glass transition to rubber elasticity for juvenile dry samples and for water-saturated states after exposure to humid air (r.h. = 29, 67, 95, 100%) at 60∘C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$60~^\\circ \\hbox {C}$$\\end{document} during 1 y of ageing. For saturated samples, network chain cleavage is the chemical ageing mechanism, but it is too weak and slow to affect on the physical properties significantly within 1 y. Water acts primarily in a physical manner. Within 1 d, H2O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {H}_{{2}}\\hbox {O}$$\\end{document} molecules replace part of the weak urethane H-bonds by H2O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {H}_{{2}}\\hbox {O}$$\\end{document}–urethane H-bonds and reduce all other physical interactions between network chains by solvating hydrophilic segments. Thus, the cooperative polymer mobility strongly amplifies: The gain of specific conformational entropy doubles across the caloric glass transition, which shifts by −17 K. A H2O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {H}_{{2}}\\hbox {O}$$\\end{document} concentration of only cH2O≈(0.4…0.5)cH2O,max\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {c}_{{\\mathrm{H}_2\\mathrm{O}}}~\\approx ~(0.4~\\ldots ~0.5)~\\hbox {c}_{\\mathrm{\\mathrm{H}_2\\mathrm{O},max}}$$\\end{document} suffices for the major part of these fast rearrangements. Some part of the water slowly forms (during 3–4 months) a finely dispersed water-rich mixed phase with the PU chains. Except the new phase, these molecular processes of physical ageing strongly affect the mechanical properties at damage-free deformation. For dry PU in the glass transition, the shear modulus, μrelaxed\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _{\\mathrm{relaxed}}$$\\end{document}(T), after viscoelastic stress relaxation only depends on the deformation-induced entropy change—like in the rubber elastic state. Within one month, water drastically decreases the viscoelastic response, as expected for plasticisation. However, μrelaxed\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _{\\mathrm{relaxed}}$$\\end{document}(T) slightly grows in wet PU. H2O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {H}_{{2}}\\hbox {O}$$\\end{document} molecules cause these opposite trends by boosting the cooperative mobility (i.e. extension of the accessible conformational space and entropy by reduction in energy barriers) and by occupation of free volume compartments. Water quickly reduces the fracture parameters by about 50%. We explain that embrittlement by the H2O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {H}_{{2}}\\hbox {O}$$\\end{document}-induced facilitation of cooperative network chain motions, which let fracture proceed with less energy. In summary, our findings provide a detailed conception of the molecular effects the H2O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {H}_{2}\\hbox {O}$$\\end{document} molecules have on the PU network, and they explain the consequences for the mechanical properties.

Predicting variations of the least principal stress with depth: Application to unconventional oil and gas reservoirs using a log-based viscoelastic stress relaxation model

Knowledge of layer-to-layer variations of the least principal stress, S hmin, with depth is essential for optimization of multi-stage hydraulic fracturing in unconventional reservoirs. Utilizing a geomechanical model based on viscoelastic stress relaxation in relatively clay rich rocks, we present a new method for predicting continuous S hmin variations with depth. The method utilizes geophysical log data and S hmin measurements from routine diagnostic fracture injection tests (DFITs) at several depths for calibration. We consider a case study in the Wolfcamp formation in the Midland Basin, where both geophysical logs and values of S hmin from DFITs are available. We compute a continuous stress profile as a function of the well logs that fits all of the DFITs well. We utilized several machine learning technologies, such as bootstrap aggregation (or bagging), to improve the generalization of the model and demonstrate that the excellent fit between predicted and observed stress values is not the result of over-fitting the calibration points. The model is then validated by accurately predicting hold-out stress measurements from four wells within the study area and, without recalibration, accurately predicting stress as a function of depth in an offset pad about 6 miles away.

Colloidal hydrogels made of gelatin nanoparticles exhibit fast stress relaxation at strains relevant for cell activity

Viscoelastic properties of hydrogels such as stress relaxation or plasticity have been recognized as important mechanical cues that dictate the migration, proliferation, and differentiation of embedded cells. Stress relaxation rates in conventional hydrogels are usually much slower than cellular processes, which impedes rapid cellularization of these elastic networks. Colloidal hydrogels assembled from nanoscale building blocks may provide increased degrees of freedom in the design of viscoelastic hydrogels with accelerated stress relaxation rates due to their strain-sensitive rheology which can be tuned via interparticle interactions. Here, we investigate the stress relaxation of colloidal hydrogels from gelatin nanoparticles in comparison to physical gelatin hydrogels and explore the particle interactions that govern stress relaxation. Colloidal and physical gelatin hydrogels exhibit comparable rheology at small deformations, but colloidal hydrogels fluidize beyond a critical strain while physical gels remain primarily elastic independent of strain. This fluidization facilitates fast exponential stress relaxation in colloidal gels at strain levels that correspond to strains exerted by cells embedded in physiological extracellular matrices (10-50%). Increased attractive particle interactions result in a higher critical strain and slower stress relaxation in colloidal gels. In physical gels, stress relaxation is slower and mostly independent of strain. Hence, colloidal hydrogels offer the possibility to modulate viscoelasticity via interparticle interactions and obtain fast stress relaxation rates at strains relevant for cell activity. These beneficial features render colloidal hydrogels promising alternatives to conventional monolithic hydrogels for tissue engineering and regenerative medicine. Statement of significanceIn the endeavor to design biomaterials that favor cell activity, research has long focused on biochemical cues. Recently, the time-, stress-, and strain-dependent mechanical properties, i.e. viscoelasticity, of biomaterials has been recognized as important factor that dictates cell fate. We herein present the viscoelastic stress relaxation of colloidal hydrogels assembled from gelatin nanoparticles, which show a strain-dependent fluidization at strains relevant for cell activity, in contrast to many commonly used monolithic hydrogels with primarily elastic behavior.

A 3D finite strain viscoelastic model with uncoupled structural and stress relaxations for shape memory polymers

In this paper, a 3D finite strain viscoelastic model with uncoupled structural and stress relaxations is proposed to characterize the thermomechanical behaviors of amorphous shape memory polymers (SMPs). The temperature- and rate-dependent viscoelastic behaviors and stress relaxation are described by the modified Eyring model and nonlinear Adam-Gibbs model based on molecular mechanism. A modified weight function analogous to frozen fraction in phase transition theory is proposed to further improve accuracy of the model. The developed model is implemented with MATLAB to simulate shape recovery experiments of amorphous SMPs under constraints or free in the literature. Good consistency between simulation results and experimental data is obtained.

In-vitro stress relaxation response of neonatal peripheral nerves

Characterizing the viscoelastic behavior of neonatal peripheral nerves is critical in understanding stretch-related peripheral nerve injuries (PNIs) in neonates. This study investigated the in-vitro viscoelastic stress relaxation response of neonatal piglet brachial plexus (BP) and tibial nerves at two different strain levels (10% and 20%) and stress relaxation testing durations (90- and 300-seconds). BP and tibial nerves from 20 neonatal piglets were harvested and pre-stretched to either 10% or 20% strain at a dynamic rate of 100 mm/min to simulate conditions, such as shoulder dystocia, that may lead to stretch-related PNIs in neonates. At constant strain, the reduction in stress was recorded for 90- or 300-seconds. The biomechanical data were then fit to a viscoelastic model to acquire the short- and long-term stress relaxation time-constants. Though no significant differences in the degree of stress relaxation were found between the two tested strain levels after 90 seconds in both nerve types, reduction in stress was moderately greater (p = 0.056) at 10% strain than at 20% for BP after 300 seconds. The reduction in stress was significantly higher in nerves subjected to a 300 second testing duration than 90 second for both strain levels and nerve types. When comparing BP and tibial nerve stress relaxation response, BP nerve relaxed significantly more than tibial at both strain levels after 90 seconds, but no significant differences were observed after 300 seconds. Our results confirm that neonatal peripheral nerve tissue is highly viscoelastic. These novel biomechanical data can be incorporated into finite element and computational models studying neonatal PNIs.