Modeling the Viscoelastic Behavior of Quartz and Clay Minerals in Shale by Nanoindentation Creep Tests

The viscoelastic behavior of minerals in shales is important in predicting the macroscale creep behavior of heterogeneous bulk shale. In this study, in situ indentation measurements of two major constitutive minerals (i.e., quartz and clay) in Longmaxi Formation shale from the Sichuan Basin, South China, were conducted using a nanoindentation technique and high-resolution optical microscope. Firstly, quartz and clay minerals were identified under an optical microscope based on their morphology, surface features, reflection characteristics, particle shapes, and indentation responses. Three viscoelastic models (i.e., three-element Voigt, Burger’s, and two-dashpot Kelvin models) were then used to fit the creep data for both minerals. Finally, the effects of peak load on the viscoelastic behavior of quartz and clay minerals were investigated. Our results show that the sizes of the residual imprints on clay minerals were larger than that of quartz for a specific peak load. Moreover, the initial creep rates and depths in clay minerals were higher than those in quartz. However, the creep rates of quartz and clay minerals displayed similar trends, which were independent of peak load. In addition, all three viscoelastic models produced good fits to the experimental data. However, due to the poor fit in the initial holding stage of the three-element Voigt model and instability of the two-dashpot Kelvin model, Burger’s model is best in obtaining the regression parameters. The regression results indicate that the viscoelastic parameters obtained by these models are associated with peak load, and that a relatively small peak load is more reliable for the determination of viscoelastic parameters. Furthermore, the regression values for the viscoelastic parameters of clay minerals were lower than those of quartz and the bulk shale, suggesting the former facilitates the viscoelastic deformation of shale. Our study provides a better understanding of the nanoscale viscoelastic properties of shale, which can be used to predict the time-dependent deformation of shale.

Role of smooth muscle activation in the static and dynamic mechanical characterization of human aortas

Experimental data and a suitable material model for human aortas with smooth muscle activation are not available in the literature despite the need for developing advanced grafts; the present study closes this gap. Mechanical characterization of human descending thoracic aortas was performed with and without vascular smooth muscle (VSM) activation. Specimens were taken from 13 heart-beating donors. The aortic segments were cooled in Belzer UW solution during transport and tested within a few hours after explantation. VSM activation was achieved through the use of potassium depolarization and noradrenaline as vasoactive agents. In addition to isometric activation experiments, the quasistatic passive and active stress–strain curves were obtained for circumferential and longitudinal strips of the aortic material. This characterization made it possible to create an original mechanical model of the active aortic material that accurately fits the experimental data. The dynamic mechanical characterization was executed using cyclic strain at different frequencies of physiological interest. An initial prestretch, which corresponded to the physiological conditions, was applied before cyclic loading. Dynamic tests made it possible to identify the differences in the viscoelastic behavior of the passive and active tissue. This work illustrates the importance of VSM activation for the static and dynamic mechanical response of human aortas. Most importantly, this study provides material data and a material model for the development of a future generation of active aortic grafts that mimic natural behavior and help regulate blood pressure.

Viscoelastic parameterization of human skin cells characterize material behavior at multiple timescales

Countless biophysical studies have sought distinct markers in the cellular mechanical response that could be linked to morphogenesis, homeostasis, and disease. Here, an iterative-fitting methodology visualizes the time-dependent viscoelastic behavior of human skin cells under physiologically relevant conditions. Past investigations often involved parameterizing elastic relationships and assuming purely Hertzian contact mechanics, which fails to properly account for the rich temporal information available. We demonstrate the performance superiority of the proposed iterative viscoelastic characterization method over standard open-search approaches. Our viscoelastic measurements revealed that 2D adherent metastatic melanoma cells exhibit reduced elasticity compared to their normal counterparts—melanocytes and fibroblasts, and are significantly less viscous than fibroblasts over timescales spanning three orders of magnitude. The measured loss angle indicates clear differential viscoelastic responses across multiple timescales between the measured cells. This method provides insight into the complex viscoelastic behavior of metastatic melanoma cells relevant to better understanding cancer metastasis and aggression.

Finite deformation and fractional order viscoelasticity of an auxetic foam

Auxetic foams exhibit novel mechanical properties due to their unique microstructure for improved energy-absorption and cavity expansion applications that have fascinated the scientific community since their inception. Given the advancements in material processing and performance of polymer open cell auxetic foams, there is a strong desire to fully understand the nonlinear rate-dependent deformation of these materials. The influence of nonlinear compressibility is introduced here along with relaxation effects to improve model predictions for different stretch rates and finite deformation regimes. The viscoelastic behavior of the material is analyzed by comparing fractional order and integer order calculus models. All results are statistically validated using maximum entropy methods to obtain Bayesian posterior densities for the hyperelastic, auxetic, and viscoelastic parameters. It is shown that fractional order viscoelasticity provides [Formula: see text]–[Formula: see text] improvement in prediction over integer order viscoelastic models when the model is calibrated at higher stretch rates where viscoelasticity is more significant.

Soft-Tissue-Mimicking Using Hydrogels for the Development of Phantoms

With the currently available materials and technologies it is difficult to mimic the mechanical properties of soft living tissues. Additionally, another significant problem is the lack of information about the mechanical properties of these tissues. Alternatively, the use of phantoms offers a promising solution to simulate biological bodies. For this reason, to advance in the state-of-the-art a wide range of organs (e.g., liver, heart, kidney as well as brain) and hydrogels (e.g., agarose, polyvinyl alcohol –PVA–, Phytagel –PHY– and methacrylate gelatine –GelMA–) were tested regarding their mechanical properties. For that, viscoelastic behavior, hardness, as well as a non-linear elastic mechanical response were measured. It was seen that there was a significant difference among the results for the different mentioned soft tissues. Some of them appear to be more elastic than viscous as well as being softer or harder. With all this information in mind, a correlation between the mechanical properties of the organs and the different materials was performed. The next conclusions were drawn: (1) to mimic the liver, the best material is 1% wt agarose; (2) to mimic the heart, the best material is 2% wt agarose; (3) to mimic the kidney, the best material is 4% wt GelMA; and (4) to mimic the brain, the best materials are 4% wt GelMA and 1% wt agarose. Neither PVA nor PHY was selected to mimic any of the studied tissues.

Fatigue fracture characterization by cyclic material forces in viscoelastic solids at small strain

The study at hand introduces a new approach to characterize fatigue crack growth in small strain linear viscoelastic solids by configurational mechanics. In this study, Prony series with n-Maxwell elements are used to describe the viscoelastic behavior. As a starting point in this work, the local balance of energy momentum is derived using the free energy density. Moreover, at cyclic loading, the cyclic free energy substitutes the free energy. Using the cyclic free energy, the balance of cyclic energy momentum is obtained. The newly derived balance law at cyclic loading is appropriate for each cycle. In the finite element framework, nodal material forces and cyclic nodal material forces are obtained using the weak and discretized forms of the balance of energy momentum and cyclic energy momentum, respectively. The crack driving force and the cyclic crack driving force are determined by the nodal material forces and the cyclic nodal material forces, respectively. Finally, numerical examples are shown to illustrate path-independence of the domain integrals using material forces and cyclic material forces. The existence of the balance of energy momentum and cyclic energy momentum are also illustrated by numerical examples.