Nonclassical Chiral Elasticity of the Gyroid Lattice.

The gyroid lattice is a metamaterial which allows chirality that is tunable by geometry. Gyroid lattices were made in chiral and nonchiral form by 3D printing. The chiral lattices exhibited nonclassical elastic effects including coupling between compressive stress and torsional deformation. Gyroid lattices can approach upper bounds on elastic modulus. Effective modulus is increased by distributed moments but is, for gyroid cylinders of sufficiently small radius, softened by a surface layer of incomplete cells. Such size dependence is similar to that in foams but is unlike most lattices.

Author Correction: Poisson's ratio and modern materials.

In the version of this Review Article originally published, parentheses were misplaced and the longitudinal and transverse speeds were inverted in two expressions for Poisson's ratio in Box 2; the expressions should have read, respectively, ν = (3B/G - 2)/(6B/G + 2) and ν = [½(Vl/Vt)2 - 1]/[(Vl/Vt)2 - 1].

Strong Cosserat Elasticity in a Transversely Isotropic Polymer Lattice.

Large size effects are experimentally measured in lattices of triangular unit cells: about a factor of 36 in torsion rigidity and 29 in bending rigidity. This nonclassical phenomenon is consistent with Cosserat elasticity, which allows for the rotation of points and distributed moments in addition to the translation of points and force stress of classical elasticity. The Cosserat characteristic length for torsion is ℓ_{t}=9.4 mm; for bending, it is ℓ_{b}=8.8 mm; these values are comparable to the cell size. Nonclassical effects are much stronger than in stretch-dominated lattices with uniform straight ribs. The lattice structure provides a path to the attainment of arbitrarily large effects.

Mechanical viscoelastic behavior of dental adhesives.

OBJECTIVES: The purpose of the study was to evaluate the mechanical properties of dental adhesive materials at different testing temperatures after dry and wet storage. METHODS: Specimens (d=1 mm, l=18 mm) from six materials were tested: Silorane Adhesive System (SL), Heliobond (HE), One-Step Plus (OS), Optibond Solo Plus (OP), cmf Adhesive System (CF) and Protobond (PR). Static and creep testing was performed by applying a constant torque below the proportional limit of the materials, while dynamic testing consisted of dynamic torsional loading. Experiments were performed after 24h of dry and wet storage under temperatures from 21°C to 50°C and various viscoelastic parameters were calculated. RESULTS: Shear modulus ranged from 0.19 to 1.99 GPa, while flexural modulus from 0.67 to 5.69 GPa. Most of the materials were affected by the presence of water and increase of temperature. OP showed the highest recovery after creep, while SL exhibited the highest permanent deformation. SIGNIFICANCE: Contact with water after polymerization and increase of temperature resulted in a decline of the mechanical properties, especially for the HEMA-containing adhesives.

Poisson's ratio and modern materials.

In comparing a material's resistance to distort under mechanical load rather than to alter in volume, Poisson's ratio offers the fundamental metric by which to compare the performance of any material when strained elastically. The numerical limits are set by ½ and -1, between which all stable isotropic materials are found. With new experiments, computational methods and routes to materials synthesis, we assess what Poisson's ratio means in the contemporary understanding of the mechanical characteristics of modern materials. Central to these recent advances, we emphasize the significance of relationships outside the elastic limit between Poisson's ratio and densification, connectivity, ductility and the toughness of solids; and their association with the dynamic properties of the liquids from which they were condensed and into which they melt.

Creep and dynamic viscoelastic behavior of endodontic fiber-reinforced composite posts.

PURPOSE: Fiber-reinforced composite (FRC) posts have gained much interest recently and understanding of their viscoelastic properties is important as they can be used in stress-bearing posterior restorations. The aim of this study was to evaluate the creep behavior and the viscoelastic properties of four commercial FRC posts under different temperatures and different storage conditions. METHODS: The FRC posts tested were Glassix, C-Post, Carbonite and Snowlight. For the creep measurements a constant load below the proportional limit of the posts was applied and the angular deformation of the specimens was recorded. The viscoelastic parameters were determined by using dynamic torsional loading under four different conditions. RESULTS: All materials were susceptible to creep and exhibited linear viscoelastic behavior. Residual strain was observed in all FRC posts. The viscoelastic properties were affected by the increase of temperature and water storage (p<0.001) resulting in their decline. Carbon fiber posts exhibited better performance than glass fiber posts. CONCLUSIONS: FRC posts exhibit permanent strains under regular masticatory stresses that can be generated in the oral cavity. Their properties are susceptible to changes in temperature, while direct contact with water also affects them deleteriously.

The effect of temperature on the viscoelastic properties of nano-hybrid composites.

OBJECTIVES: The purpose of this study was to examine the viscoelastic properties of nanofilled dental composites under both static and dynamic testing and to determine the influence of temperature, medium of storage and storage time. METHODS: Three nanofilled composites, one packable and one ormocer were tested. The specimens were examined dry at 21 degrees C and wet at 21, 37 and 50 degrees C after being stored for 24h and 1 month under both static and dynamic testing. Shear modulus, elastic modulus, loss tangent, Poisson's ratio and other viscoelastic parameters were calculated. Data were analyzed with one-way and two-way analysis of variance (ANOVA) (p=0.05). RESULTS: All materials tested showed a significant decrease in their moduli with the increase of temperature, while the effect of water storage was different among the composites. Grandio was the composite with the highest Young's modulus followed by Filtek P60. SIGNIFICANCE: Most of the materials tested did not have elastic moduli near to that of dentin, making them less satisfactory in posterior restorations. The materials possessing nanosized filler particles had different elastic properties among them and this implies that filler size is not the only factor that affects the elastic behavior of dental composites.

Composite materials with viscoelastic stiffness greater than diamond.

We show that composite materials can exhibit a viscoelastic modulus (Young's modulus) that is far greater than that of either constituent. The modulus, but not the strength, of the composite was observed to be substantially greater than that of diamond. These composites contain bariumtitanate inclusions, which undergo a volume-change phase transformation if they are not constrained. In the composite, the inclusions are partially constrained by the surrounding metal matrix. The constraint stabilizes the negative bulk modulus (inverse compressibility) of the inclusions. This negative modulus arises from stored elastic energy in the inclusions, in contrast to periodic composite metamaterials that exhibit negative refraction by inertial resonant effects. Conventional composites with positive-stiffness constituents have aggregate properties bounded by a weighted average of constituent properties; their modulus cannot exceed that of the stiffest constituent.

The effect of temperature on viscoelastic properties of glass ionomer cements and compomers.

The objective of this study was to determine the viscoelastic properties of different types of glass ionomer cements (GICs) and compomers under varying temperature conditions found in the mouth. The materials tested were a conventional GIC (Aqua Ionofil U), a resin modified GIC (Fuji II LC), a highly viscous GIC (Voco Ionofil Molar), and two polyacid modified composite resins/compomers (Glasiosite and Dyract Flow). Six groups of four specimens were prepared from each material. One group was stored dry for 24 h and was subsequently tested dry at 21 degrees C. Each of the remaining five groups was stored for 24 h in distilled water at the temperatures 21, 30.5, 37, 43.5, and 50 degrees C, respectively, and was subsequently tested at that temperature. Shear storage modulus and loss tangent were determined by conducting dynamic torsional loading. Static shear moduli were determined by applying a constant torque (below the proportional limit of the materials) for 10 s and recording the angular deformation of the specimens. Data were analyzed by ANOVA and Duncan's test (alpha= 0.05). It was found that the viscoelastic properties varied significantly (p < 0.05) across the different materials. The compomer Glasiosite, with the highest filler content, and the highly viscous GIC Voco Ionofil Molar exhibited the highest elastic moduli and lowest loss tangents. Viscoelastic properties varied also significantly (p < 0.05) with temperature levels, but changes in the tested region were not indicative of a glass transition. Dynamic shear storage moduli were highly correlated to the static ones. Storage in water lowered the values of elastic moduli.

Fatigue of packable dental composites.

OBJECTIVE: The purpose of the study was to measure the fatigue properties of four dental resin composites using a dynamic mechanical analysis and to relate the results with viscoelastic properties. METHODS: Dynamic torsional loading was conducted at resonance at 30-50Hz. Specimens were thoroughly cured and tested dry at 21 degrees C. RESULTS: All of the specimens showed a loss of strength following repeated stress, due to material fatigue. The material with the highest shear modulus had the lowest damping and the highest fatigue strength. SIGNIFICANCE: Dental composites exhibit a modest loss of strength due to fatigue. Since mastication involves many cycles of stress during the life of a restoration, fatigue properties should be taken into account in restoration design.

Dynamic and static elastic moduli of packable and flowable composite resins and their development after initial photo curing.

OBJECTIVE: The purpose of this study was to evaluate the dynamic (storage) shear modulus and the static shear modulus of elasticity of packable and flowable composite resins and to investigate their development after initial photo-curing. METHODS: Three pairs of a packable versus a flowable composite and a microfill composite resin were tested (Alert/Flow It, Filtek P60/Filtek Flow, Admira/Admira Flow, A 110). Cylindrical specimens (0.85 mm x 18 mm) were made for each material. All specimens were conditioned and tested dry at 21 degrees C. The specimens were tested at 30 min, 24h and 1 week after the end of photo curing. Storage shear modulus and loss tangent were determined by conducting dynamic torsional loading in the frequency range from 1 to 150 Hz. Static shear modulus measurements were made by applying a constant load (below the proportional limit of the materials) for 10s and recording the angular deformation of the specimens. Data were analyzed by ANOVA and Duncan's Post hoc test (alpha=0.05). RESULTS: Storage shear moduli (at 1 week measurement) ranged from 3.39 to 9.67 GPa, and loss tangents from 0.0735 to 0.0235; static shear moduli ranged between 2.66 and 9.80 GPa. High values of elastic moduli and low tandelta values were obtained with packable composites, while low moduli values were obtained with flowable composites. Statistically significant (alpha=0.05) differences were recorded between materials of the same category. Storage time, 24h and 1 week after initial polymerization, resulted in significant increases in both moduli of elasticity. Dynamic shear storage moduli were highly correlated to the static ones (r(2)=0.92; P<0.05). SIGNIFICANCE: The results of the aging studies showed that the rigidity of these materials increases significantly even 1 week after the clinician turns off the curing unit.

Modeling deformation-induced fluid flow in cortical bone's canalicular-lacunar system.

To explore the potential role that load-induced fluid flow plays as a mechano-transduction mechanism in bone adaptation, a lacunar-canalicular scale bone poroelasticity model is developed and implemented. The model uses micromechanics to homogenize the pericanalicular bone matrix, a system of straight circular cylinders in the bone matrix through which bone fluids can flow, as a locally anisotropic poroelastic medium. In this work, a simplified two-dimensional model of a periodic array of lacunae and their surrounding systems of canaliculi is used to quantify local fluid flow characteristics in the vicinity of a single lacuna. When the cortical bone model is loaded, microscale stress, and strain concentrations occur in the vicinity of individual lacunae and give rise to microscale spatial variations in the pore fluid pressure field. Furthermore, loading of the bone matrix containing canaliculi generates fluid pressures in the contained fluids. Consequently, loading of cortical bone induces fluid flow in the canaliculi and exchange of fluid between canaliculi and lacunae. For realistic bone morphology parameters, and a range of loading frequencies, fluid pressures and fluid-solid drag forces in the canalicular bone are computed and the associated energy dissipation in the models compared to that measured in physical in vitro experiments on human cortical bone. The proposed model indicates that deformation-induced fluid pressures in the lacunar-canalicular system have relaxation times on the order of milliseconds as opposed to the much shorter times (hundredths of milliseconds) associated with deformation-induced pressures in the Haversian system.

Dynamic mechanical analysis of viscoelastic functions in packable composite resins measured by torsional resonance.

The objective of this study was to evaluate the viscoelastic functions of packable composite resins with the use of a resonant dynamic mechanical analysis technique in torsion. The materials tested were: Alert (Jeneric Pentron), Prodigy Condensable (Kerr Corporation), Surefil (Dentsply DeTrey), and Filtek P60 (3M Dental Products). Dynamic torsional loading was conducted in the frequency range from 1 to 150 Hz. Composite specimens were tested after storage in water at 37 degrees C for 24 h. One group was thermal cycled for 3000 cycles with temperatures of 5-37-50 degrees C. Measurements were taken at 21 degrees C dry, and at 37 and 50 degrees C wet. Storage modulus, loss tangent, and other viscoelastic parameters were determined from the amplitude/frequency curves. Data for storage modulus and loss tangent of the materials were analyzed by means of ANOVA and Student-Newman-Keuls test (alpha = 0.05). It was found that there were significant differences (P < 0.001) in storage modulus and loss tangent among the packable composites tested. The highest value of storage modulus, in measurements at 21 degrees C, was for Alert (10.3 GPa), followed by Filtek P60 (9.31 GPa), Surefil (7.29 GPa), and Prodigy Condensable (6.74 GPa). There were significant differences (P < 0.001) in storage modulus and loss tangent among the four different conditions tested. Storage modulus decreased at higher temperatures, whereas the loss tangent increased. Thermal cycling increased storage modulus and decreased loss tangent. The results showed that both monomer and filler composition and filler loading of the materials significantly affect their viscoelastic functions, and the mechanical properties of the products cannot be characterized from the packability alone.

Size effects in the elasticity and viscoelasticity of bone.

Size effects of large magnitude are observed in the torsional shear modulus and damping of bovine plexiform bone. Damping increases and stiffness decreases with specimen size over all sizes studied. Measurements were conducted in torsion using a laser-based micromechanics apparatus capable of viscoelastic studies over a range of frequencies up to 100 kHz, upon samples of various size, with no parasitic friction or other errors that could mimic any size effect. Torsional tan delta at 1 Hz varies by about a factor of five over the size range 2.8-6.2 mm thick, and is more dependent on specimen thickness at 1 Hz than it is at higher frequency. The size effects are attributed to compliance and viscoelasticity of the interfaces between laminae. These laminae must be substantially stiffer than whole bone. Observed size effects are likely to play a role in understanding scaling laws of bones in living organisms.

Dynamic viscoelastic behavior of resin cements measured by torsional resonance.

OBJECTIVE: The purpose of the study was to measure the viscoelastic properties of four dental resin composite cements using a dynamic mechanical analysis technique. METHODS: Dynamic torsional loading was conducted in the frequency range from 1 to 80 Hz. Cement specimens were tested after storage in 37 degrees C water for 24 h. One group was thermal cycled prior to testing. Measurements were taken at 21, 37, and 50 degrees C. Storage modulus, loss tangent and other viscoelastic parameters were determined from the amplitude/frequency curves. RESULTS: Storage moduli of the cements ranged from 2.9 to 4.1 GPa at 37 degrees C. Loss tangents ranged from 0.054 to 0.084. Storage moduli decreased in a regular way with increasing temperature, whereas, loss tangents increased. Thermal cycling caused small decreases in storage moduli. SIGNIFICANCE: Resin cements with higher filler loading were found to have higher storage moduli and lower loss tangents. Since these properties have been associated with better clinical performance in the areas of retention and prevention of fracture of porcelain and resin restorations, the more highly filled cements may be recommended. Temperature variations influenced viscoelastic behavior of the cements. However, within the temperature range studied no sharp drop in modulus was seen, so the materials should function satisfactorily in the oral cavity.

Micromechanically based poroelastic modeling of fluid flow in Haversian bone.

To explore the hypothesis that load-induced fluid flow in bone is a mechano-transduction mechanism in bone adaptation, unit cell micro-mechanical techniques are used to relate the microstructure of Haversian cortical bone to its effective poroelastic properties. Computational poroelastic models are then applied to compute in vitro Haversian fluid flows in a prismatic specimen of cortical bone during harmonic bending excitations over the frequency range of 10(0) to 10(6) Hz. At each frequency considered, the steady state harmonic response of the poroelastic bone specimen is computed using complex frequency-domain finite element analysis. At the higher frequencies considered, the breakdown of Poisueille flow in Haversian canals is modeled by introduction of a complex fluid viscosity. Peak bone fluid pressures are found to increase linearly with loading frequency in proportion to peak bone stress up to frequencies of approximately 10 kHz. Haversian fluid shear stresses are found to increase linearly with excitation frequency and loading magnitude up until the breakdown of Poisueille flow. Tan delta values associated with the energy dissipated by load-induced fluid flow are also compared with values measured experimentally in a concurrent broadband spectral analysis of bone. The computational models indicate that fluid shear stresses and fluid pressures in the Haversian system could, under physiologically realistic loading, easily reach the level of a few Pascals, which have been shown in other works to elicit cell responses in vitro.

Application of nonlinear viscoelastic models to describe ligament behavior.

Recent experiments in rat medial collateral ligament revealed that the rate of stress relaxation is strain dependent and the rate of creep is stress dependent. This nonlinear behavior requires a more general description than the separable quasilinear viscoelasticity theory commonly used in tissue biomechanics. The purpose of this study was to determine whether the nonlinear theory of Schapery or the modified superposition method could adequately model the strain-dependent stress-relaxation behavior of ligaments. It is shown herein that both theories describe available nonlinear experimental ligament data well and hence can account for both elastic and viscous nonlinearities. However, modified superposition allows for a more direct interpretation of the relationship between model parameters and physical behavior, such as elastic and viscous nonlinearities, than does Schapery's theory. Hence, the modified superposition model is suggested to describe ligament data demonstrating both elastic nonlinearity and strain-dependent relaxation rate behavior. The behavior of the modified superposition model under a sinusoidal strain history is also examined. The model predicts that both elastic and viscous behaviors are dependent on strain amplitude and frequency.

Investigation of bovine bone by resonant ultrasound spectroscopy and transmission ultrasound.

The method of resonant ultrasonic spectroscopy (RUS) was evaluated for bovine bone and compared with the traditional wave transmission ultrasound method. In RUS, the resonance structure of a cubic or rectangular specimen is scanned. For some low-damping materials, a single measurement yields sufficient resonant frequencies to determine all of the anisotropic elastic constants. Bone has a high viscoelastic damping at ultrasonic frequency. Consequently, resonance peaks of a cubic specimen tend to overlap. Therefore, the usual RUS method must be modified for application to bone; even so, one cannot obtain all the elastic constants. Concurrent studies with transmission ultrasound were conducted. Results were used to generate a map of the elastic moduli vs position along the bone axis. Stiffness was greatest in the mid part of the bovine femur.

A broadband viscoelastic spectroscopic study of bovine bone: implications for fluid flow.

To explore the hypothesis that mechanical excitation-induced fluid flow and/or fluid pressure are potential mechanical transduction mechanisms in bone adaptation, a complementary experimental and analytical modeling effort has been undertaken. Experimentally, viscoelastic tan delta properties of saturated cortical bovine bone were measured in both torsion and bending, and significant tan delta values in the 10(0)-10(5) Hz range were observed, although the nature of the damping is not consistent with a fluid pressure hypothesis. Analytically, micromechanically based poroelasticity models were exercised to quantify energy dissipation associated with load-induced fluid flow in large scale channels. The modeling results indicate that significant damping due to fluid flow occurs only above 1 MHz frequencies. Together, the experimental and analytical results indicate that at excitation frequencies presumed to be physiological (1-100 Hz), mechanical loading of bone generates extremely small pore fluid pressures, making the hypothesized fluid-pressure transduction mechanism upon osteocytes untenable.

Damping properties of lead metaniobate.

Mechanical damping, tan delta, of lead metaniobate was determined experimentally over a wide range of frequency. Damping at audio and sub-audio frequency was lower than at ultrasonic frequency. The experiments were conducted in torsion and bending using an instrument capable of determining viscoelastic properties over more than 10 decades of time and frequency. Mechanical damping was higher in bending than torsion at all frequencies. Damping observed in this study at the highest frequencies approach the high value 0.09 previously observed at ultrasonic frequency.