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Abstract: Abstract Early work on modeling the mechanical response of fibrous tissues suggested a structural model based on integration of angular distributions of fiber bundles over the surface of a unit sphere. This paper considers a discrete fiber model, based on a regular icosahedron with six fiber bundles defined by the twelve uniformly distributed vertices on a unit sphere. Like the structural model, the icosahedron model introduces a weighted sum of the strain energies of the six fiber bundles with parameters that characterize the density and strength of each fiber bundle as well as the undulation of the fibers in the bundle. It is shown that even when all fiber directions are identical and weighted evenly, this discrete model exhibits anisotropic response for large deformations. The reason for this anisotropic response is that the uncoupled strain energies of the fiber bundles do not allow for coupling of the strains in the fiber directions that are needed to form the principal invariants of strain. Anisotropic strain invariants based on structural tensors defined by a regular icosahedron model are discussed that can characterize isotropy and material anisotropy. PubDate: 2022-02-23 DOI: 10.1007/s42558-022-00040-7
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Abstract: Abstract Indentation tests utilizing the load (P)-displacement (δ) data have been common for obtaining bulk moduli (E) of hydrated materials, including biological specimens and hydrogels. While experimentally simple to perform, the data analysis can sometimes be complicated, especially when adhesion between the indenter and sample occurs. The adhesion issue for nano/microindentation on hydrated materials has been addressed in several studies, but hardly any studies have reported the involvement of adhesion in analyzing mesoscale (0.1–1 mm) P-δ data. In this study, we evaluated three methods for analyzing experimental P-δ data acquired from mesoscale indentations on hydrated materials to obtain their E values. They were the classical Hertz model, a modified Hertz approach with P and δ values corrected using Hertz relations, and a modified Hertz approach with the correction of contact radius (a) by including the work of adhesion, W, between the indenter and the sample. The experimental P, a, and δ data were simultaneously collected using transparent gelatin gels, and these P-δ and P-a data were used to verify the adequacy of the three analysis methods. In particular, the E values from these methods were checked against the values obtained using the Johnson-Kendall-Roberts model and the P-a data. Accurate moduli resulted only when W was included in the analysis. The analysis with the inclusion of W was applied to obtain the E values of silicone and other model hydrogels, of which only the experimental P-δ data could be obtained, and their moduli were found to be close to the values reported. PubDate: 2021-12-24 DOI: 10.1007/s42558-021-00039-6
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Abstract: Abstract A new comprehensive simulation model at atomistic level is proposed to investigate the miscibility and predict the glass transition temperature (Tg) and mechanical properties of polyacrylamide/polyacrylic acid (PAAm/PAA) weakly interpenetrating polymer networks (IPN). Five simulation models with different composition ratios are created and simulated by means of molecular dynamics (MD) simulation. The influence of the monomer nature on the formation of the IPN is examined by the reproduction of swelling of polymer networks in monomer solution. The swelling results allow us to determine that even with low cross-linking ratios, the resulting IPN will be homogeneous if the PAAm is firstly synthesized. The values of the Tg of the different samples are also determined and strain/stress behavior curves are also predicted. All the systems present a single phase temperature and predicted Tg values are in good agreement with experimental values. The strain/stress curves indicate that incorporating PAAm in the systems improves their ductility, but reduces their hardening; while, integrating PAA gives this latter the required hardening. PubDate: 2021-09-24 DOI: 10.1007/s42558-021-00038-7
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Abstract: Abstract In previous studies by the authors, a kinematic framework using physical attributes arising from a Gram–Schmidt factorization of the deformation gradient has been developed. It describes a state of deformation in a locally convected coordinate system that is oblique Cartesian. Elastic constitutive equations have been established based upon two sets of scalar-valued, stress/strain, base pairs, both with physical interpretations in this convected coordinate system. In this paper, the authors derive a continuum model for soft, biologic, tubular structures. The presented model describes the behavior of isotropic and anisotropic materials in terms of physical attributes that are directly measurable in experiments. Data acquired from ring and axial tests of inflated, porcine, coronary sinus are investigated, and are used to illustrate the capabilities of our theoretical model. PubDate: 2021-06-19 DOI: 10.1007/s42558-021-00037-8
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Abstract: Abstract This paper presents an investigation into the homogenization of the nonlinear behavior of graphene-based soft sandwich nanocomposites via the rule of mixtures (ROM). These composites consist of soft polymers embedded with large contiguous graphene films with unit atomic thickness. They have a representative volume element with a sandwich construction exhibiting in-plane isotropy. Their unique characteristic is that they consist of a matrix and reinforcement which both behave nonlinearly. In this work, the in-plane mechanical behavior of both constituents as well as the composite is modeled via the compressible Mooney-Rivlin (MR) constitutive model. Two approaches to homogenize this nonlinear behavior are considered. The first approach, referred to as the linear ROM, applies the ROM to the initial tangent moduli of the constituents, and derives the composite’s MR coefficients from the homogenized initial tangent modulus. The second approach, referred to as the nonlinear ROM, builds on Ogden’s bounds on the strain energy density, and applies the ROM directly to the MR coefficients of the constituents to derive the composite’s MR coefficients. The predictions from both approaches are compared to the embedded element (EE) technique in Abaqus which enforces a kinematic constraint between the explicitly modeled constituents resulting in a parallel model. It is demonstrated that the nonlinear ROM approach properly homogenizes the entire nonlinear stress-stretch curve (both normal and shear), including the nonlinear Poisson effects, and embodies the correct strain energy density (SED). The linear ROM predicts reasonably the normal stress-stretch curve and the SED, but it does not capture Poisson’s ratio and the shear response well and therefore is not recommended. The nonlinear ROM is found to work for a wide range of stretch values, various reinforcement volume fractions, and loading conditions, especially for high stiffness ratios. For lower stiffness ratios (i.e., for a stiffer matrix), the nonlinear stress-stretch curves (normal and shear) and the SED are captured well by the nonlinear ROM, but not the out of plane Poisson effects, due to the assumed isotropy in the Mooney-Rivlin model. Finally, an analogous approach to determine the variational Hashin-Shtrikman bounds on the homogenized Mooney-Rivlin constants is proposed. These variational bounds are found to be tighter compared to the Voigt and Reuss bounds as expected. PubDate: 2021-06-09 DOI: 10.1007/s42558-021-00036-9
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Abstract: Abstract This paper generalizes previous work on physically based nonlinear orthotropic invariants for thermomechanical response of soft materials to include the inelastic process of homeostasis, which causes a biological tissue to approach its homeostatic state. This process of homeostasis can cause a homogeneous material (one with the same constitutive equations and material constants as each material point) to develop a nonuniform state. Within the context of biological tissues, this means that the tissue cannot be unloaded elastically to a zero-stress state. A simplified version of the theory is used to describe elastic response of an artery from its nonuniform homeostatic state using a Fung-type exponential orthotropic strain energy function with material constants determined for a human carotid artery. As discussed in Safadi and Rubin (Int. J. Eng. Sci. 118(40), 2017), the approach of assuming a homeostatic state at systolic pressure and limiting extrapolation of the constitutive response to the physiological pressure range reduces uncertainty in the stress distributions in the artery. The specific results here show that the circumferential stress in the physiological pressure range exhibits a strong sensitivity to residual stresses known to exist in the cut unloaded state. This approach suggests that detailed experimental data on the response of the artery in its physiological pressure range and more complete understanding of mechanobiological processes during homeostasis are essential for determining an accurate constitutive equation of an artery. PubDate: 2021-04-13 DOI: 10.1007/s42558-021-00035-w
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Abstract: Abstract Dielectric elastomer actuators (DEA) have been demonstrated to exhibit a quasi-immediate electro-mechanical actuation response with relatively large deformation capability. The properties of DEA make them suitable to be used in the form of major active components within soft robotics and biomimetic artificial muscles. However, some of the electro-active material properties impose limitations on its applications. Therefore, researchers attempt to modify the structure of the homogeneous DEA material by the incorporation of fillers that possess distinct electro-mechanical properties. This modification of the material’s structure leads to a fabricated inhomogeneous composite. From the point of mathematical material modelling and numerical simulation, we propose a material model and a computational framework using the finite element method, which is capable of emulating nonlinear electro-elastic interactions. We consider a coupled electro-mechanical description with the electric and the electro-mechanical properties of the material assumed to be nonlinearly dependent on the deformation. Furthermore, we demonstrate a coupled ansatz that expresses the electric response as dielectrically quasi-linear with only density-dependent electric permittivity. We couple the electro-mechanical models to the extended tube model, which is a suitable approach for the realistic emulation of the hyperelastic response of rubber-like materials. Thereafter, we demonstrate analytical and numerical solutions of a homogeneous electro-elastic body with the Neo-Hookean material model and the extended tube model to express the hyperelastic response. Finally, we use the finite element method to investigate several heterogeneous configurations consisting of soft DEA matrix filled with spherical stiff inclusions with changing volume fraction and ellipsoidal inclusions with varying aspect ratio. PubDate: 2021-03-27 DOI: 10.1007/s42558-020-00031-6
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Abstract: Abstract We provide an extension to previous analysis of the localised beading instability of soft slender tubes under surface tension and axial stretching. The primary questions pondered here are as follows: under what loading conditions, if any, can bifurcation into circumferential buckling modes occur, and do such solutions dominate localisation and periodic axial modes' Three distinct boundary conditions are considered: in case 1 the tube’s curved surfaces are traction-free and under surface tension, whilst in cases 2 and 3 the inner and outer surfaces (respectively) are fixed to prevent radial displacement and surface tension. A linear bifurcation analysis is conducted to determine numerically the existence of circumferential mode solutions. In case 1 we focus on the tensile stress regime given the preference of slender compressed tubes towards Euler buckling over axisymmetric periodic wrinkling. We show that tubes under several loading paths are highly sensitive to circumferential modes; in contrast, localised and periodic axial modes are absent, suggesting that the circumferential buckling is dominant by default. In case 2, circumferential mode solutions are associated with negative surface tension values and thus are physically implausible. Circumferential buckling solutions are shown to exist in case 3 for tensile and compressive axial loads, and we demonstrate for multiple loading scenarios their dominance over localisation and periodic axial modes within specific parameter regimes. PubDate: 2021-03-24 DOI: 10.1007/s42558-021-00034-x
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Abstract: Abstract Contraction in myocardial tissue is the result of a complex process through which chemical energy on the cellular level is converted into the mechanical energy needed to circulate blood throughout the body. Due to its vital role for the organism, myocardial contractility is one of the most intensively investigated subjects in medical research. In this contribution, we suggest a novel phenomenological approach for myocardial contraction that is capable of producing realistic intracellular calcium concentration (ICC) and myocyte shortening graphs, can be easily calibrated to capture different ICC and contraction characteristics and, at the same time, is straightforward to implement and ensures efficient computer simulations. This study is inspired by the fact that existing models for myocardial contractility either contain a number of complex equations and material parameters, which reduce their feasibility, or are very simple and cannot accurately mimic reality, which eventually influences the realm of computer simulations. The proposed model in this manuscript considers first the evolution of the ICC through a logarithmic-type ordinary differential equation (ODE) having the normalized transmembrane potential as the argument. The ICC is further put into an exponential-type ODE which determines the shortening of the myocyte (active stretch). The developed approach can be incorporated with phenomenological or biophysically based models of cardiac electrophysiology. Through examples on the material level, we demonstrate that the shape of the ICC and myocardial shortening curves can be easily modified and accurately fitted to experimental data obtained from rat and mouse hearts. Moreover, the performance of the model in organ level simulations is illustrated through several multi-field initial-boundary value problems in which we show variations in volume-time relations, heterogeneous characteristics of myocardial contraction and application of a drug in a virtual left ventricle model. PubDate: 2021-02-27 DOI: 10.1007/s42558-021-00033-y
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Abstract: Abstract Superabsorbent gels (lightly cross-linked copolymer gels with water absorption capacity up to several thousands g/g) have recently attracted substantial attention due to their novel applications in agriculture, environmental management, and civil engineering. As superabsorbent hydrogels (SAHs) are conventionally prepared by copolymerization of polyelectrolyte and temperature-sensitive neutral monomers, their response is strongly affected by temperature, pH, and ionic strength of solutions. A characteristic feature of SAHs is an anomalous increase in their elastic modulus with degree of swelling. Constitutive equations are derived for the mechanical response and equilibrium swelling of SAHs. An advantage of the model is that it involves only six material constants. These quantities are found by fitting experimental data in equilibrium swelling tests and uniaxial compressive tests on a series of N-isopropylacrylamide-co-2-acrylamido-2-methylpropane sulfonic acid gels with various molar fractions of ionic comonomers. An acceptable agreement is demonstrated between the observations and results of simulation. The model is applied to examine the effects of temperature, pH, and molar fraction of monovalent salt in aqueous solutions on equilibrium swelling of SAHs with various molar fractions of comonomers in the feed. PubDate: 2021-02-05 DOI: 10.1007/s42558-020-00032-5
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Abstract: Abstract Experimental inflation tests, conducted on 90 pig corneas before and after corneal collagen crosslinking (CXL) treatment, are simulated with the finite element method. The experimental sample consists of five groups of corneas treated with different UV-A irradiation times (2.5, 5, 10, 15, and 20 min) at constant irradiance 9 mW/cm2. The linear elastic shell theory is used to estimate the equivalent material stiffness of the corneas, revealing that it increases with the exposure time in CXL corneas. In the view of numerical simulations, a simple mechanical model assuming piecewise constant elastic modulus across the corneal thickness is introduced, to estimate the effective increment of the material stiffness in the anterior stroma and the effective depth of the stiffness increment. The two effective quantities are used in the finite element models to simulate the post-CXL tests. Numerical models are able to describe the mechanical effects of CXL in the cornea. The increment of equivalent material stiffness has to be ascribed to a localized increment of the material stiffness in the anterior layers of the cornea, while the posterior layers preserve the original material stiffness. According to the simplified model, the increment of the material stiffness of the anterior cornea increases with the irradiation dose, while the effective reinforcement depth decreases with the irradiation dose. This trend, predicted by a simple mechanical model by imposing equilibrium and compatibility, has been verified by the numerical calculations that captured the global mechanical response of the corneas in untreated and post-CXL conditions. PubDate: 2020-11-25 DOI: 10.1007/s42558-020-00030-7
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Abstract: Abstract Hydrogels are highly hydrated polymer networks. The synergistic association of a fluid and an elastic phase is the key of numerous applications of hydrogels as food or cosmetic products, drug delivery vectors, wound dressings, scaffolds for tissue regeneration... Since the natural environment for many of these applications is a wet or liquid one, exchange of fluid or solute may occur via the liquid continuum which exists between the environment and the constitutive solvent. In addition to purely osmotic forces, stresses acting on the network are able to drive solvent flow. This is the basis of poroelasticity, initially studied within the framework of consolidated, fluid saturated rocks. The specificity of hydrogels lies on their high stretchability, which makes extended non-linear elasticity the rule rather than the exception when dealing with fracture mechanics. The association of poro- and non-linear elasticity brings the study of rupture of hydrogels at the forefront of research in mechanics. Along this review, we intend to explore the various ways the environment may affect the nucleation, growth and path stability of a crack in a hydrogel. This goal is pursued from a physicist and experimentalist point of view, with special emphasis on dimensionless relevant parameters and order-of-magnitude estimates. A substantial part of the paper is devoted to an introduction to the specific features of soft gel fracture mechanics. We then try and put forward the wide variety of theoretical and experimental issues relevant to environmental crack control with some tentative insight into tissue engineering and living tissue biomechanics. PubDate: 2020-11-19 DOI: 10.1007/s42558-020-00027-2
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Abstract: Abstract Dynamics of solvent release from polymer gels with small solvent-filled cavities is investigated starting from a thermodynamically consistent and enriched multiphysics stress-diffusion model. Indeed, the modeling also accounts for a new global volumetric constraint which makes the volume of the solvent in the cavity and the cavity volume equal at all times. This induces a characteristic suction effect into the model through a negative pressure acting on the cavity walls. The problem is solved for gel-based spherical microcapsules and microtubules. The implementation of the mathematical model into a finite element code allows to quantitatively describe and compare the dynamics of solvent release from full spheres, hollow spheres, and tubules in terms of a few key quantities such as stress states and amount of released solvent under the same external conditions. PubDate: 2020-10-06 DOI: 10.1007/s42558-020-00029-0
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Abstract: Abstract A micromechanical analysis is proposed for the establishment of the macroscopic constitutive relations for viscoelastic composite materials undergoing large deformations. The composites are assumed to possess a triply periodic microstructure and their viscoelastic constituents are modeled by the incorporation of the viscoelastic effects with an arbitrary chosen hyperelastic strain energy function. Furthermore, an energy limiter is introduced which enforces the saturation of the viscoelastic strain energy function. The value of the strain energy at the saturation corresponds to the failure energy of the viscoelastic constituent. In conjunction with the derived micromechanical analysis, the occurrence of the energy saturation of the viscoelastic constituent predicts the composite failure. Applications are given for the determination of the macroscopic (overall) response and creep of a viscoelastic unidirectional composite, and the behavior of viscoelastic porous materials. In all cases, failure occurrences of the unidirectional composite and porous materials are predicted. PubDate: 2020-09-06 DOI: 10.1007/s42558-020-00028-1
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Abstract: Abstract A critical event during the process of cell infection by a viral particle is attachment, which is driven by adhesive interactions and resisted by bending and tension. The biophysics of this process has been studied extensively, but the additional role of externally applied force or displacement has generally been neglected. In this work, we study the adhesive force-displacement response of viral particles against a cell membrane. We have built two models: one in which the viral particle is cylindrical (say, representative of a filamentous virus such as Ebola) and another in which it is spherical (such as SARS-CoV-2 and Zika). Our interest is in initial adhesion, in which case deformations are small, and the mathematical model for the system can be simplified considerably. The parameters that characterize the process combine into two dimensionless groups that represent normalized membrane bending stiffness and tension. In the limit where bending dominates, for sufficiently large values of normalized bending stiffness, there is no adhesion between viral particles and the cell membrane without applied force. (The zero external force contact width and pull-off force are both zero.) For large values of normalized membrane tension, the adhesion between virus and cell membrane is weak but stable. (The contact width at zero external force has a small value.) Our results for pull-off force and zero force contact width help to quantify conditions that could aid the development of therapies based on denying the virus entry into the cell by blocking its initial adhesion. PubDate: 2020-08-28 DOI: 10.1007/s42558-020-00026-3
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Abstract: Abstract The biomechanical behavior of sclera is conferred by the composition and structure of its extracellular matrix, which is mainly composed of collagen fibers and sulfated glycosaminoglycans (GAGs). Pathological conditions and visual disorders such as glaucoma and myopia could cause significant changes to the mechanical properties and GAG content of sclera. There exists sufficient evidence for the contribution of collagen fibers to the scleral biomechanics; however, possible mechanical roles of GAGs are not fully known. The primary objective of this work was to examine the mechanical function of GAGs through characterizing their effects on the scleral tensile response. For this purpose, chondroitinase ABC was used to deplete GAGs from posterior porcine scleral samples. Comprehensive biochemical and histological analyses were then performed to confirm and quantify GAG removal. Stress-controlled tensile tests with preconditioning were conducted in order to characterize the viscoelastic tensile behavior of treated and untreated specimens. It was found that the enzyme treatment caused a significant thickness reduction but it did not cause any significant change in the tensile properties of sclera. Overall, the findings of this study suggested that alternations in the GAG content of posterior scleral tissue are not important to tensile properties of sclera that are measured by stress-controlled experiments. PubDate: 2020-07-26 DOI: 10.1007/s42558-020-00025-4
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Abstract: Abstract It is shown that a widely used class of constitutive models for the mechanical response of elastic arteries, which includes the so-called HGO model, responds as if it were inextensible in simple tension in the zero limit of a non-dimensional ratio of material parameters. A significant auxetic response is predicted for an incompressible hyperelastic elastic sheet reinforced with inextensible cords. Thus, a significant lateral deformation of arterial specimens modelled by this class of materials should be observed in simple tension for small values of the non-dimensional parameter. However, such a response has not been observed experimentally. The analysis therefore suggests that predictions for this class of strongly anisotropic constitutive models for arteries should be treated with caution. PubDate: 2020-06-02 DOI: 10.1007/s42558-020-00024-5
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Abstract: Abstract Like other organs such as artery, bladder and left ventricle, human intact gallbladders (GBs) possess viscoelasticity/hysteresis in pressure-volume curves during in vitro or in vivo dynamic experiments made by using saline infusion and withdrawal cycle to simulate GB physiological emptying-filling cycle in normal and diseased conditions. However, such a viscoelastic property of GBs has not been modelled and analysed so far. A non-linear discrete viscous model and a passive elastic model were proposed to identify the elastic, active and viscous pressure responses in the experimental pressure-volume data of an intact GB under passive and active conditions found in the literature in the paper. It turns out that the elastic, viscous and active pressure responses can be separated in less than 2% error from the pressure-volume curves. The peak active state in the GB occurs at 30% dimensionless volume. The GB stimulated with cholecystokinin (CCK) or treated with indomethacin is subject to almost constant stiffness at low dimensionless volume (≤ 70%) but quick increasing stiffness at high dimensionless volume (>70%) and a larger work-to-energy ratio (0.57–0.61) compared with the normal GB in the passive state. The models are sensitive to the change in the biomechanical property of the GBs stimulated or treated with hormonal or pharmacological agents, showing a potential in clinical application. These results may contribute fresh content to the biomechanics of GBs and be helpful to GB disease diagnosis. PubDate: 2020-05-25 DOI: 10.1007/s42558-020-00023-6
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Abstract: Abstract In this note, we develop simple analytical formulas to estimate the effect of residual stresses on the pulse wave velocity in blood vessels. We combine these formulas with three constitutive models of the arterial wall. Particularly, we consider the Fung model and two models accounting for the dispersion of collagen fibers via 8 and 16 structure tensors accordingly. The residual stresses come into play with a description of the initial kinematics—the opening angle. Our numerical examples reveal that residual stresses reduce the pulse wave velocity. The latter effect becomes especially pronounced at high values of blood pressure. PubDate: 2020-05-22 DOI: 10.1007/s42558-020-00022-7
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Abstract: Abstract Traction force microscopy (TFM) aims at determining the forces exerted by cells on their substrate. Traction quantification relies on the knowledge of the mechanical properties of the substrate, i.e., typically its Young’s modulus. Because of the challenges associated with the mechanical analysis of very soft elastomers, a large range of modulus values are reported in literature for the same materials. In order to provide a reliable characterization, a systematic study was performed, including a large number of micro-scale indentation experiments. The mechanical behavior of four elastomer configurations (Sylgard 184 40:1 and 60:1, and CY9:10 and 10:9), frequently used for TFM studies, was investigated. The good repeatability of the experimental procedure allowed characterizing the modulus variability within each material sample and between batches. The corresponding uncertainty is in the range of 10%, consequently directly affecting the reliability of cell traction force values. Material aging, immersion in a liquid, and illumination were considered as specific factors potentially influencing the stiffness of TFM substrates. The results show that stiffness changes significantly over the first 3 weeks following elastomer production, while immersion in a isoosmolar solution and illumination have generally modest influence on micro-scale stiffness. PubDate: 2020-05-20 DOI: 10.1007/s42558-020-00021-8
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