Muscle Constitutive Model With a Tangent Modulus Approximation: Ansys Implementation and Verification.

Sophisticated muscle material models are required to perform detailed finite element simulations of soft tissue; however, state-of-the-art muscle models are not among the built-in materials in popular commercial finite element software packages. Implementing user-defined muscle material models is challenging for two reasons: deriving the tangent modulus tensor for a material with a complex strain energy function is tedious and programing the algorithm to compute it is error-prone. These challenges hinder widespread use of such models in software that employs implicit, nonlinear, Newton-type finite element methods. We implement a muscle material model in Ansys using an approximation of the tangent modulus, which simplifies its derivation and implementation. Three test models were constructed by revolving a rectangle (RR), a right trapezoid (RTR), and a generic obtuse trapezoid (RTO) around the muscle's centerline. A displacement was applied to one end of each muscle, holding the other end fixed. The results were validated against analogous simulations in FEBio, which uses the same muscle model but with the exact tangent modulus. Overall, good agreement was found between our Ansys and FEBio simulations, though some noticeable discrepancies were observed. For the elements along the muscle's centerline, the root-mean-square-percentage error in the Von Mises stress was 0.00%, 3.03%, and 6.75% for the RR, RTR, and RTO models, respectively; similar errors in longitudinal strain were observed. We provide our Ansys implementation so that others can reproduce and extend our results.

Mechanical characterization of dissected and dilated human ascending aorta using Fung-type hyperelastic models with pre-identified initial tangent moduli for low-stress distensibility.

Ascending aortic dissection (AD) is a potentially fatal vascular disease associated with degradation and fragmentation of the elastic fibers in the aortic media, increasing low-stress distensibility, and a dilated aorta may lead to dissection. In this study, a Fung-type hyperelastic model was formulated incorporating the initial tangent moduli (ITM) of stress-strain curves as an index of low-stress distensibility. ITM were correlated with the material constants by linearizing incompressible stress-strain relationships at zero strain. For uniaxial loading tests, the robustness of the material constants was examined in the stress ranges of 0-200, 0-180, and 0-160 kPa and to the ITM values of 100%, 95%, and 90%. Examination revealed stable changes in the material constants of 80% of the specimens. For equibiaxial stretch tests, the material constants were determined for each curve of the isotropic and anisotropic deformation groups by pre-identifying the ITM and minimizing fitting errors using isotropic or anisotropic models. The errors for all groups were <6% using a transversely isotropic model, and <10% for an orthotropic model. Comparisons with experimental curves showed that Fung-type models described both the ITM and significant stiffening at high stress levels. The mechanical characteristics of the aorta in the stage prior/posterior to dissection is such that while hardening occurs under both low- and high-stress levels with an increase in collagen content as an aging response, softening occurs under low-stress conditions due to histological abnormalities such as elastin deficiency and fragmentation. Numerical simulations using Fung-type models implied that elastic fiber degeneration and fragmentation in AD tissues reduced not only the low-stress stiffness but also the elastic stiffness with superimposed shear. The latter stiffness was modulated by the stiffening at high stress levels in tensile deformation behavior and normal-strain state under physiological loading conditions, and therefore provides further insight into wall rupture.

Strain Rate-Dependent Hyperbolic Constitutive Model for Tensile Behavior of PE100 Pipe Material.

It is not conservative to directly use the strength tested under the laboratory loading rates to evaluate the long-term creep strength of polymers. A suitable strain rate-dependent constitutive model is crucial for accurately predicting the long-term strength and mechanical behavior of polymer pressure pipes. In this study, the Kondner hyperbolic constitutive model is considered the base model in deriving the rate-dependent constitutive model for PE100 pipe material, and the yield stress and initial tangent modulus are the two rate-dependent parameters of the model. Uniaxial tension tests are carried out under five specified strain rates ranging from 10-5 s-1 to 5 × 10-2 s-1 to obtain these two parameters. It is demonstrated that the strain rate dependence of the yield stress and the initial tangent modulus can be described by either a power or a logarithm law. The predictions from the two models are in good agreement with the experiments. In contrast, the power-law rate-dependent Kondner model is more suitable for describing the rate-dependent tensile behavior of PE100 pipe material than the logarithm-law rate-dependent Kondner model, especially for the cases of very low strain rates which relate to the polymer pressure pipe applications.

Harmonic Distortion of Blood Pressure Waveform as a Measure of Arterial Stiffness.

Aging and disease alter the composition and elastic properties of the aortic wall resulting in shape changes in blood pressure waveform (BPW). Here, we propose a new index, harmonic distortion (HD), to characterize BPW and its relationship with other in vitro and in vivo measures. Using a Fourier transform of the BPW, HD is calculated as the ratio of energy above the fundamental frequency to that at the fundamental frequency. Male mice fed either a normal diet (ND) or a high fat, high sucrose (HFHS) diet for 2-10 months were used to study BPWs in diet-induced metabolic syndrome. BPWs were recorded for 20 s hourly for 24 h, using radiotelemetry. Pulse wave velocity (PWV), an in vivo measure of arterial stiffness, was measured in the abdominal aorta via ultrasound sonography. Common carotid arteries were excised from a subset of mice to determine the tangent modulus using biaxial tension-inflation test. Over a 24-h period, both HD and systolic blood pressure (SBP) show a large variability, however HD linearly decreases with increasing SBP. HD is also linearly related to tangent modulus and PWV with slopes significantly different between the two diet groups. Overall, our study suggests that HD is sensitive to changes in blood pressure and arterial stiffness and has a potential to be used as a noninvasive measure of arterial stiffness in aging and disease.

Gas Permeability and Mechanical Properties of Polyurethane-Based Membranes for Blood Oxygenators.

The production of medical devices follows strict guidelines where bio- and hemocompatibility, mechanical strength, and tear resistance are important features. Segmented polyurethanes (PUs) are an important class of polymers that fulfill many of these requirements, thus justifying the investigation of novel derivatives with enhanced properties, such as modulated carbon dioxide and oxygen permeability. In this work, three segmented polyurethane-based membranes, containing blocks of hard segments (HSs) dispersed in a matrix of soft segment (SS) blocks, were prepared by reacting a PU prepolymer (PUR) with tris(hydroxymethyl)aminomethane (TRIS), Congo red (CR) and methyl-ß-cyclodextrin (MBCD), rendering PU/TRIS, PU/CR and PU/MBCD membranes. The pure (control) PU membrane exhibited the highest degree of phase segregation between HSs and SSs followed by PU/TRIS and PU/MBCD membranes, and the PU/CR membrane displayed the highest degree of mixing. Pure PU and PU/CR membranes exhibited the highest and lowest values of Young's modulus, tangent moduli and ultimate tensile strength, respectively, suggesting that the introduction of CR increases molecular mobility, thus reducing stiffness. The CO2 permeability was highest for the PU/CR membrane, 347 Barrer, and lowest for the pure PU membrane, 278 Barrer, suggesting that a higher degree of mixing between HSs and SSs leads to higher CO2 permeation rates. The permeability of O2 was similar for all membranes, but ca. 10-fold lower than the CO2 permeability.

Regional biomechanical and failure properties of healthy human ascending aorta and root.

PURPOSE: Aortic dissection (AD) is a life-threatening event that occurs when the intimal entry tear propagates and separates inner from outer layers of the aorta. Diameter, the current criterion for aneurysm repair, is far from ideal and additional evidence to optimize clinical decision would be extremely beneficial. Biomechanical investigation of the regional failure properties of aortic tissue is essential to understand and proactively prevent AD. We previously studied biaxial mechanical properties of healthy human aorta. In this study, we investigated the regional failure properties of healthy human ascending aorta (AscAo) including sinuses of Valsalva (SOV), and sinotubular junction (STJ). RESULTS: A total of 430 intact tissue samples were harvested from 19 healthy donors whose hearts were excluded from heart transplantation. The donors had mean age of 51 ± 11.7 years and nearly equal gender distribution. Samples were excised from aortic regions and subregions at defined locations. Tissue strips were subjected to either biaxial or uniaxial failure testing. Wall thickness varied regionally being thickest at AscAo (2.08 ± 0.66 mm) and thinnest at SOV (1.46 ± 0.31 mm). Biaxial testing demonstrated hyperplastic behavior of aortic tissues. Posterior and lateral STJ subregions were found to be stiffer than anterior and medial subregions in both circumferential and longitudinal directions. Failure stresses were significantly higher in the circumferential than longitudinal directions in each subregion of AscAo, STJ, and SOV. Longitudinal failure stresses were significantly greater in AscAo than those in STJ or SOV. Longitudinal failure stresses in AscAo were much smaller anteriorly than posteriorly, and medially than laterally. CONCLUSIONS: The finding of weakest region at the sinotubular junction along the longitudinal direction corroborates clinical observations of that region being commonly involved as the initial site of intimal tear in aortic dissections. Failure stretch ratios correlated to elastic modulus at each region. Furthermore, strong correlation was seen between STJ failure stresses and elastic modulus at physiological pressure along both circumferential and longitudinal directions. Correlating in-vivo aortic elastic modulus based on in-vivo imaging with experimentally determined elastic modulus at physiological pressure and failure stresses may potentially provide valuable information regarding aortic wall strength. Better understanding of aortic biomechanics in normal physiologic and aneurysmal pathologic states may aid in determining risk factors for predicting dissection in patient-specific fashion.

Dry vs. wet: Properties and performance of collagen films. Part I. Mechanical behaviour and strain-rate effect.

Collagen forms one-third of the body proteome and has emerged as an important biomaterial for tissue engineering and wound healing. Collagen films are used in tissue regeneration, wound treatment, dural substitute etc. as well as in flexible electronics. Thus, the mechanical behaviour of collagen should be studied under different environmental conditions and strain rates relevant for potential applications. This study's aim is to assess the mechanical behaviour of collagen films under different environmental conditions (hydration, submersion and physiological temperature (37 °C)) and strain rates. The combination of all three environment factors (hydration, submersion and physiological temperature (37 °C)) resulted in a drop of tensile strength of the collagen film by some 90% compared to that of dry samples, while the strain at failure increased to about 145%. For the first time, collagen films were subjected to different strain rates ranging from quasi-static (0.0001 s-1) to intermediate (0.001 s-1, 0.01 s-1) to dynamic (0.1 s-1, 1 s-1) conditions, with the strain-rate-sensitivity exponent (m) reported. It was found that collagen exhibited a strain-rate-sensitive hardening behaviour with increasing strain rate. The exponent m ranged from 0.02-0.2, with a tendency to approach zero at intermediate strain rate (0.01 s-1), indicating that collagen may be strain-rate insensitive in this regime. From the identification of hyperelastic parameter of collagen film, it was found that the Ogden Model provides realistic results for future simulations.

Strain stiffening of peripheral nerves subjected to longitudinal extensions in vitro.

The mechanical response of peripheral nerves is crucial to understand their physiological and pathological conditions. However, their response to external mechanical solicitations is still partially unclear, since peripheral nerves could behave in a quite complex way. In particular, nerves react to longitudinal strains increasing their stiffness to keep axons integrity and to preserve endoneural structures from overstretch. In this work, the strain stiffening of peripheral nerves was investigated in vitro through a recently introduced computational framework, which is able to theoretically reproduce the experimental behaviour of excised tibial and sciatic nerves. The evolution and the variation of the tangent modulus of tibial and sciatic nerve specimens were quantitatively investigated and compared to explore how stretched peripheral nerves change their instantaneous stiffness.

Experimental Evaluation of Travoprost-Induced Changes in Biomechanical Behavior of Ex-Vivo Rabbit Corneas.

Purpose: To assess the effects of prostaglandin F2α analogues travoprost on the biomechanical behavior of ex-vivo rabbit cornea. Materials and Methods: 18 Japanese white rabbits were included in the study. The left eye (treated group, Tr) of each rabbit was preserved for 10 days in storage medium Eusol-C solution with 1:10 travoprost diluent, while the contralateral eye (control group, Co) was preserved in a similar but travoprost-free medium. Strips of corneal tissue were dissected and tested under cyclic load conditions with up to 0.1 N uniaxial tension force. The resulting load-elongation data were used to derive the stress-strain behavior and the tangent modulus (Et) of the tissue. Differences in Et between the treated (Et-Tr) and control group (Et-Co) were assessed statistically to determine the biomechanical effects of travoprost on the cornea. Results: Central corneal thickness (CCT) in the two groups was similar before (P = 0.073) and remained similar after storage (P = 0.303) although it became significantly thicker in both groups after preservation (P < 0.01). Compared with the control group, the travoprost treated corneas exhibited lower Et values but the differences reduced and became insignificant with rises in stress to which the tissue was subjected (1 - Et-Tr/Et-Co = -11.7 ± 41.8%, P < 0.05 at 10 kPa stress; -9.2 ± 36.1%, P > 0.05 at 20 kPa; -7.3 ± 35.4%, P > 0.05 at 30 kPa). Conclusions: Significant reductions in corneal stiffness, that are associated with the use of travoprost, were observed experimentally under low applied stresses. This stiffness-reduction effect should be considered in clinical management, especially in primary open angle glaucoma treatment.

Cement-Stabilized Waste Sand as Sustainable Construction Materials for Foundations and Highway Roads.

In this study, cement-treated waste sand as a by-product material produced from Al-Ahsa quarries (Saudi Arabia) was experimentally tested and investigated as a base course material for the foundation of structures and roads. The study aimed to use the waste sand as a construction material by improving its strength, bearing capacity, and stiffness. The waste sand was mixed with different percentages of Portland cement content (0, 2, 4, 6, and 8%) at the maximum dry density and optimum water content of the standard Proctor compaction conditions of a non-treated sample. Unconfined compressive strength and California Bearing Ratio (CBR) tests for different curing times were conducted. X-ray diffraction (XRD), laser-scanning microscopy (LSM), and X-ray spectroscopy (XPS) were used to explore the microstructure and composition of the treated sand. The results showed that the compressive strength, initial tangent modulus, and CBR of the treated sand increase with the increase in cement content and curing time. Furthermore, good correlations were established among the strength, initial tangent modulus, and CBR. Based on the obtained results, cement-stabilized waste sand is a potential material for use in construction. This is expected to save the environment and reduce the cost of road construction.

New Evaluation Procedure for Multi-Dimensional Mechanical Strains and Tangent Moduli of Breast Implants: IDEAL IMPLANT® Structured Breast Implant Compared to Silicone Gel Implants.

The IDEAL IMPLANT® Structured Breast Implant is a dual lumen saline-filled implant with capsular contracture and deflation/rupture rates much lower than single-lumen silicone gel-filled implants. To better understand the implant's mechanical properties and to provide a potential explanation for these eight-year clinical results, a novel approach to compressive load testing was employed. Multi-dimensional strains and tangent moduli, metrics describing the shape stability of the total implant, were derived from the experimental load and platen spacing data. The IDEAL IMPLANT was found to have projection, diametric, and areal strains that were generally less than silicone gel implants, and tangent moduli that were generally greater than silicone gel implants. Despite having a relatively inviscid saline fill, the IDEAL IMPLANT was found to be more shape stable compared to gel implants, which implies potentially less interaction with the capsule wall when the implant is subjected to compressive loads. Under compressive loads, the shape stability of a higher cross-link density, cohesive gel implant was unexpectedly found to be similar to or the same as a gel implant. In localized diametric compression testing, the IDEAL IMPLANT was found to have a palpability similar to a gel implant, but softer than a cohesive gel implant.

New microscale constitutive model of human trabecular bone based on depth sensing indentation technique.

A new constitutive model for human trabecular bone is presented in the present study. As the model is based on indentation tests performed on single trabeculae it is formulated in a microscale. The constitutive law takes into account non-linear viscoelasticity of the tissue. The elastic response is described by the hyperelastic Mooney-Rivlin model while the viscoelastic effects are considered by means of the hereditary integral in which stress depends on both time and strain. The material constants in the constitutive equation are identified on the basis of the stress relaxation tests and the indentation tests using curve-fitting procedure. The constitutive model is implemented into finite element package Abaqus® by means of UMAT subroutine. The curve-fitting error is low and the viscoelastic behaviour of the tissue predicted by the proposed constitutive model corresponds well to the realistic response of the trabecular bone.

Influence of Short-Term Orthokeratology to Corneal Tangent Modulus: A Randomized Study.

PURPOSE: Influence of orthokeratology on corneal biomechanics is equivocal using Ocular Response Analyzer, ORA. Implementing indentation method, corneal tangent modulus was measured and monitored in short-term orthokeratology. MATERIALS AND METHODS: Sixteen young subjects with refractive errors between -4D to -5D sphere and astigmatism within -1.50D were recruited. One randomly selected eye wore orthokeratology lens (treatment), and the fellow eye wore conventional rigid gas permeable lens (control). Lenses were worn for 30 and 60 minutes and one night separately with a week of washout period in between. The first two visits were randomly scheduled and before the overnight visit. Eyes were kept closed during all the lens wearing periods. Corneal radius, thickness, and biomechanics (using both ORA and an indentation device) were compared between eyes prior to each visit, and then before and after lens wear. Associations between baseline corneal biomechanics and central cornea from overnight visit were investigated. RESULTS: Corneal parameters were similar in each visit before lens wear. Significant corneal flattening was observed in treatment eyes, and flattening increased with wearing time. Control eyes showed no significant corneal curvature changes. Corneal resistance factor (CRF) reduced by 0.42mmHg (± 0.68mmHg) after 30 minutes of orthokeratology treatment. Corneal hysteresis (CH) reduced by 0.42mmHg (+/- 0.63mmHg) in control eyes from overnight wear. Both eyes showed stable tangent modulus, E, throughout the study. A lower CH (r = 0.51, p = 0.046) and a higher E (r = 0.53, p = 0.037) at baseline was significantly associated with greater corneal flattening along the flattest meridian in treatment eyes. CONCLUSIONS: Short-term orthokeratology had no significant effect on corneal tangent modulus. Changes in CH and CRF could be related to their intrinsic measurement variability. Corneal tangent modulus provided another measure of corneal biomechanics. Long-term study is required to investigate predictive role of corneal biomechanics in orthokeratology.

In vivo passive mechanical properties estimation of Achilles tendon using ultrasound.

A methodology is proposed for estimating Achilles tendon tangent modulus in vivo, to account for its large deformations and non-linear behavior. True stress is found dividing the axial force by the tendon true cross-sectional area (CSA), whose shrinking caused by axial tension is estimated with Poisson׳s coefficient. The true strain is calculated as the integral of incremental deformations along the tendon length change. Triceps surae tendon CSA and ankle moment arm, with the foot at relaxed equilibrium position, are estimated from subject-personalized data. Healthy males (N=19) volunteered for the study. The test consisted of passive ankle mobilization at the dynamometer with 5°/s velocity, from 30° of plantar flexion to the limit of dorsiflexion. Ultrasound was used to track myotendinous junction (MTJ) and tendon elongation, with the probe oriented over the medial gastrocnemius. Non-linear tendon stiffness pattern was observed during the joint range of motion, reaching 200N/mm peaks for the subjects with greater amplitudes of maximum dorsiflexion. The maximum values of modulus of elasticity, calculated from usual engineering stress and strain, (188.56±99.19MPa) were smaller than those reported in the literature for active maximum voluntary contractions tests. Maximum values for tangent modulus from true stress and strain were 312.38±171.95MPa. Such differences are likely to increase in large deformations.

Measurement of corneal tangent modulus using ultrasound indentation.

Biomechanical properties are potential information for the diagnosis of corneal pathologies. An ultrasound indentation probe consisting of a load cell and a miniature ultrasound transducer as indenter was developed to detect the force-indentation relationship of the cornea. The key idea was to utilize the ultrasound transducer to compress the cornea and to ultrasonically measure the corneal deformation with the eyeball overall displacement compensated. Twelve corneal silicone phantoms were fabricated with different stiffness for the validation of measurement with reference to an extension test. In addition, fifteen fresh porcine eyes were measured by the developed system in vitro. The tangent moduli of the corneal phantoms calculated using the ultrasound indentation data agreed well with the results from the tensile test of the corresponding phantom strips (R(2)=0.96). The mean tangent moduli of the porcine corneas measured by the proposed method were 0.089±0.026MPa at intraocular pressure (IOP) of 15mmHg and 0.220±0.053MPa at IOP of 30mmHg, respectively. The coefficient of variation (CV) and intraclass correlation coefficient (ICC) of tangent modulus were 14.4% and 0.765 at 15mmHg, and 8.6% and 0.870 at 30mmHg, respectively. The preliminary study showed that ultrasound indentation could be applied to the measurement of corneal tangent modulus with good repeatability and improved measurement accuracy compared to conventional surface displacement-based measurement method. The ultrasound indentation can be a potential tool for the corneal biomechanical properties measurement in vivo.

Noninvasive measurement of scleral stiffness and tangent modulus in porcine eyes.

PURPOSE: We investigated an indentation technique to measure the scleral stiffness and tangent modulus of porcine eyes. METHODS: The scleral load-displacement responses were measured with a universal testing machine as a function of IOP in 15 porcine eyes ex vivo using a 5-mm diameter cylindrical flat-punch indenter. The scleral radius of curvature and scleral thickness were measured using a DSLR camera (Alpha 900) and a camera-mounted stereomicroscope (M205C), respectively. The relationships between scleral stiffness, tangent modulus, and IOP were examined. RESULTS: The mean local scleral radius of curvature and scleral thickness were 7.86 ± 0.49 and 1.03 ± 0.14 mm, respectively. The average scleral stiffness and scleral tangent modulus of porcine eyes were 0.13 ± 0.02 N/mm and 0.20 ± 0.04 MPa at 15 mm Hg, respectively. The scleral stiffness and scleral tangent modulus were correlated positively with IOP (scleral stiffness, 0.989 < r < 0.999, P < 0.001; scleral tangent modulus, 0.989 < r < 0.999, P < 0.001). CONCLUSIONS: The scleral indentation technique can provide a noninvasive approach to measure scleral stiffness and tangent modulus.

Intrinsic stiffness of extracellular matrix increases with age in skeletal muscles of mice.

Advanced age is associated with increases in muscle passive stiffness, but the contributors to the changes remain unclear. Our purpose was to determine the relative contributions of muscle fibers and extracellular matrix (ECM) to muscle passive stiffness in both adult and old animals. Passive mechanical properties were determined for isolated individual muscle fibers and bundles of muscle fibers that included their associated ECM, obtained from tibialis anterior muscles of adult (8-12 mo old) and old (28-30 mo old) mice. Maximum tangent moduli of individual muscle fibers from adult and old muscles were not different at any sarcomere length tested. In contrast, the moduli of bundles of fibers from old mice was more than twofold greater than that of fiber bundles from adult muscles at sarcomere lengths >2.5 µm. Because ECM mechanical behavior is determined by the composition and arrangement of its molecular constituents, we also examined the effect of aging on ECM collagen characteristics. With aging, muscle ECM hydroxyproline content increased twofold and advanced glycation end-product protein adducts increased threefold, whereas collagen fibril orientation and total ECM area were not different between muscles from adult and old mice. Taken together, these findings indicate that the ECM of tibialis anterior muscles from old mice has a higher modulus than the ECM of adult muscles, likely driven by an accumulation of densely packed extensively crosslinked collagen.

A physically motivated constitutive model for 3D numerical simulation of skeletal muscles.

A detailed numerical implementation within the FEM is presented for a physically motivated three-dimensional constitutive model describing the passive and active mechanical behaviors of the skeletal muscle. The derivations for the Cauchy stress tensor and the consistent material tangent are provided. For nearly incompressible skeletal muscle tissue, the strain energy function may be represented either by a coupling or a decoupling of the distortional and volumetric material response. In the present paper, both functionally different formulations are introduced allowing for a direct comparison between the coupled and decoupled isochoric-volumetric approach. The numerical validation of both implementations revealed significant limitations for the decoupled approach. For an extensive characterization of the model response to different muscle contraction modes, a benchmark model is introduced. Finally, the proposed implementation is shown to provide a reliable tool for the analysis of complex and highly nonlinear problems through the example of the human mastication system by studying bite force and three-dimensional muscle shape changes during mastication.

Influence of glucocorticosteroids on the biomechanical properties of in-vivo rabbit cornea.

Understanding corneal biomechanical responses during long-term glucocorticosteroids administration is important in clinical practice. The purpose of this study is to investigate the biomechanical influence of fluorometholone 0.1% eye drops on rabbit cornea. Thirty-eight Japanese white rabbits were randomly divided into three groups; a fluorometholone group, a supernatant group and a blank control group. For each rabbit in fluorometholone group, one cornea was treated with fluorometholone 0.1% eye drops four times a day for 8 weeks, while corneas of rabbits in supernatant group were treated in the same frequency with supernatant fraction centrifuged from fluorometholone 0.1% eye drops. The rabbits in the blank control group were not given any treatment. At the end of the 8 week observation period, the rabbits were euthanized and the eyes immediately enucleated and prepared for inflation testing. The experimental pressure-deformation data was used to derive the stress-strain behavior of each eye using an inverse modeling procedure. Comparisons of mechanical stiffness of corneas were conducted among the three groups to determine the influence of fluorometholone. The results showed that corneal stiffness decreased as the fluorometholone administration time prolonged. Comparisons of tangent modulus indicated average stiffness reductions of 34.2% and 33.5% in the fluorometholone group compared to the supernatant and control groups, respectively, at the end of the observation period. The stiffness-reduction effect of fluorometholone on the cornea should be considered in clinical management, especially when administrating it to biomechanically weakened corneas, such as after refractive surgeries and in cases of keratoconus.

Interpretation of the stiffness and permeability of Sand-Kaolin mixtures in the framework of homogenization

This study deals with the behaviour of mixtures of sand and saturated kaolin paste considered as composite materials made of permeable and deformable (with non-linear behaviour) matrix (the kaolin paste) with rigid and impervious inclusions (the sand grains). Oedometric and permeability tests conducted on such mixtures highlight the key role of the state of the clay paste, and show the existence of a threshold of sand grain concentration above which a structuring effect influences both modulus and permeability. At the light of these experiments, the usual and tangent homogenization process (with simplifying assumptions to make the problem manageable) has been applied to estimate the mixture permeability and tangent compressibility. Qualitative and quantitative comparisons with experimental data point out the domain of interest and the limitations of such approaches.

O estudo lida com o comportamento de misturas compostas por areia e uma pasta de caulinita considerada um material composto feito de uma matriz (caulinita) permeável e deformável (com comportamento não-linear) com inclusões rígidas e impermeáveis (grãos de areia). Testes de permeabilidade e odométricos conduzidos nestas misturas enfatizam o papel chave de estado da pasta argilosa e mostram a existência de uma concentração crítica de grãos de areia com efeito estruturante que influencia o módulo e a permeabilidade. Sob a luz destes experimentos o processo de homogeneização usual e tangente (com hipóteses simplificadoras para tornar o problema tratável) foi aplicado para estimar a permeabilidade da mistura e a compressibilidade tangente. Comparações qualitativas e quantitativas com dados experimentais apontam o domínio de interesse bem como a limitação destas abordagens.