Supporting Information: Spatiotemporally programmable metasurfaces via viscoelastic shell snapping

Supplementary Text 1: Material modeling and characterization We used the following incompressible neo-Hookean material model to define the instantaneous constitutive behavior of the shells, = tr − 3, (S1) where W is the strain energy density function, µ is the shear modulus, F is the deformation gradient tensor. To describe the viscoelastic behavior of the shells, Prony series were used and the shear modulus µ can be expressed as = 1 − ∑ 1 − ⁄ , (S2) where µ0 is the instantaneous shear modulus, n is the number of the series terms, is the dimensionless relaxation modulus, t is the time, and τi is the relaxation time constant. Here we characterize the viscoelastic properties of the silicone rubber (Dragon SkinTM30) and urethane rubber (VytaFlexTM 20). We modeled their viscou

Property Evolution and Reliability of Underfills Under Sustained High Temperature Storage

Automotive underhood electronics may be exposed to high temperature in the neighborhood of 100°C–200°C. Property evolution may impact reliability and accuracy of predictive models to assure desired use life. In this paper, evolution of properties of two underfill material properties are studied using DMA (Dynamic Mechanical Analyzer). The underfills are exposed to three different operational temperatures in the range of 100°C to 140°C for the measurements. The dynamic mechanical properties such as storage modulus (E′), loss modulus (E″), tangent delta (tan δ), and respective glass transition temperatures (Tg) are studied using DMA. Study of viscoelastic behavior of underfills is achieved by performing TTS (time-temperature superposition) experiments at 7 discrete frequencies 0.1, 0.21, 0.46, 1, 2.15, 4.64, and 10 Hz using DMA in three-point bend mode. From the selected reference temperatures, the master curves were constructed for storage moduli, loss moduli and tan delta as a function of frequency using TTS results. Using the WLF (Williams-Landel-Ferry) equation, the shift factors as a function of temperature were determined along the frequency axis. The relaxation modulus as a function of temperature and time can be obtained using the master curves of storage and loss moduli. A simple and detailed procedure has been established to find the Prony series constants.

Numerical and Experimental Investigations of Polymer Viscoelastic Materials Obtained by 3D Printing

The aim of this research is to determine the relaxation and creep modulus of 3D printed materials, and the numerical research is based on the finite volume method. The basic material for determining these characteristics is ABS (acrylonitrile butadiene styrene) plastic as one of the most widely used polymeric materials in 3D printing. The experimental method for determining the relaxation functions involved the use of a creep test, in which a constant increase of the stress of the material was performed over time to a certain predetermined value. In addition to this test, DMA (dynamic mechanical analysis) analysis was used. Determination of unknown parameters of relaxation functions in analytical form was performed on the basis of the expression for the storage modulus in the frequency domain. The influence of temperature on the values of the relaxation modulus is considered through the determination of the shift factor. Shift factor is determined on the basis of a series of tests of the relaxation function at different constant temperatures. The shift factor is presented in the form of the WLF (Williams-Landel-Ferry) equation. After obtaining such experimentally determined viscoelastic characteristics with analytical expressions for relaxation modulus and shift factors, numerical analysis can be performed. For this numerical analysis, a mathematical model with an incremental approach was used, as developed in earlier works although with a certain modification. In the experimental analysis, the analytical expression for relaxation modulus in the form of the Prony series is used, and since it is the sum of exponential functions, this enables the derivation of a recursive algorithm for stress calculation. Numerical analysis was performed on several test cases and the results were compared with the results of the experiment and available analytical solutions. A good agreement was obtained between the results of the numerical simulation and the results of the experiment and analytical solutions.

Effects of Lipid Deposition on Viscoelastic Response in Human Hepatic Cell Line HepG2

Hepatic steatosis is associated with various liver diseases. The main pathological feature of steatosis is the excessive lipid accumulation. Ultrasound has been extensively used for the diagnosis of hepatic steatosis. However, most ultrasound-based non-invasive methods are still not accurate enough for cases with light lipid infiltration. One important reason is that the extent to which lipid infiltration may affect mechanical properties of hepatocytes remains unknown. In this work, we used atomic force microscope and in vitro dose-dependent lipid deposition model to detect the quantitative changes of mechanical properties under different degrees of steatosis in a single-cell level. The results show that hepatic cells with lipid deposition can be treated as linear viscoelastic materials with the power law creep compliance and relaxation modulus. Further analysis showed that even slight accumulation of lipid can lead to measurable decrease of stiffness and increased fluidity in liver cells. The accurate detection of viscoelastic properties of hepatocytes and the analysis methods may provide novel insights into hepatic steatosis grading, especially in the very early stage with reversible liver lesion. The application of viscoelasticity index for grading fat deposition might be a new detection indicator in future clinical diagnosis.

EXPERIMENTAL RESEARCH ON VISCOELASTICITY PROPERTY OF DIFFERENT LAYERS PERIODONTAL LIGAMENT UNDER COMPRESSION

The periodontal ligament (PDL) exhibits different material mechanical properties along the long axis of the teeth. To explore the creep and the relaxation effects of dissimilar layers of PDL, this paper took the central incisors of porcine mandibular as experimental subjects and divided them perpendicular to the teeth axis into five layers. Creep experiments and relaxation experiments on five layers were conducted to obtain the creep compliance and relaxation modulus at different layers. Linear elastic model, generalized Kelvin model, and generalized Maxwell model were used to describe the major characteristics of the PDL: Instantaneous elasticity, creep and relaxation. Fitting accuracy of three-parameter, five-parameter, and seven-parameter of the model was compared, and the constitutive equations of different layers were established by the least square method. The results presented that the creep strain and the relaxation stress of PDL were exponentially correlated with time under different loading conditions. Different layers showed a significant effect on the creep strain and relaxation stress of PDL. Along the long axis of the teeth, the changing rule of the creep compliance and relaxation modulus of each layer showed quite the contrary, and the instantaneous elastic modulus first decreased to the minimum, then increased to the maximum. Higher instantaneous elastic modulus led to lower creep compliance and higher relaxation modulus. The generalized Kelvin model and the generalized Maxwell model well characterized the creep and relaxation properties of PDL. Fitting accuracy increased with the number of model parameters. The relaxation time of PDL was about one order of magnitude shorter than the creep retardation time, which indicated that the relaxation effect lasted shorter than the creep effect.

New Mechanistic Procedure to Predict the Critical Cracking Temperature of Asphalt Concrete from Bending Beam Rheometer and Indirect Tension Test Data

This study presents a new mechanistic procedure for determining the critical cracking temperature of asphalt concrete (AC) using data from bending beam rheometer (BBR) test of asphalt binder and indirect tension (IDT) test of AC. This new procedure uses BBR creep data to generate the mixture relaxation modulus mastercurve by utilizing the Hirsch model, time-temperature superposition principle, and Prony series-based interconversion method. The Hirsch model parameters are calibrated by comparing creep data from BBR and IDT creep tests performed at the same temperature. Boltzmann hereditary integral and second-order heat equation are then used to calculate thermal stress from the developed relaxation modulus mastercurve. IDT strength data is transferred from test strain rate to thermal strain rate using the viscoelastic continuum damage model. Since a strain gauge is not attached for traditional laboratory IDT strength testing, this study derived an analytical equation based on the Hondros solution to compute the horizontal strain rate from the applied vertical displacement rate. Finally, the critical cracking temperature is determined by coupling the thermal stress and strength profiles. Using the procedure presented in this paper, the critical cracking temperatures of four AC mixtures were predicted from BBR and IDT data. Their actual critical cracking temperatures were measured using thermal stress restrained specimen test performed in the laboratory to validate the method. The predicted critical cracking temperatures are found to be very close to the laboratory measured values. The developed procedure has substantial practical and technical importance in predicting the critical cracking temperature of AC because it utilizes widely available BBR and IDT tests.

Viscoelastic Behaviour of Flexible Thermoplastic Polyurethane Additively Manufactured Parts: Influence of Inner-Structure Design Factors

Material extrusion based additive manufacturing is used to make three dimensional parts by means of layer-upon-layer deposition. There is a growing variety of polymers that can be processed with material extrusion. Thermoplastic polyurethanes allow manufacturing flexible parts that can be used in soft robotics, wearables and flexible electronics applications. Moreover, these flexible materials also present a certain degree of viscoelasticity. One of the main drawbacks of material extrusion is that decisions related to specific manufacturing configurations, such as the inner-structure design, shall affect the final mechanical behaviour of the flexible part. In this study, the influence of inner-structure design factors upon the viscoelastic relaxation modulus, E(t), of polyurethane parts is firstly analysed. The obtained results indicate that wall thickness has a higher influence upon E(t) than other inner-design factors. Moreover, an inadequate combination of those factors could reduce E(t) to a small fraction of that expected for an equivalent moulded part. Next, a viscoelastic material model is proposed and implemented using finite element modelling. This model is based on a generalized Maxwell model and contemplates the inner-structure design. The results show the viability of this approach to model the mechanical behaviour of parts manufactured with material extrusion additive manufacturing.