Multiscale Constitutive Modeling of Polymer Materials

2007 ◽  
Author(s):  
Pavan K. Valavala ◽  
Gregory M. Odegard
Keyword(s):  
Elastic Modulus ◽  
Energy Level ◽  
Constitutive Modeling ◽  
Reasonable Agreement ◽  
Elastic Moduli ◽  
Glassy Polymer ◽  
Polymer Materials ◽  
Molecular Models ◽  
Modeling Framework ◽  
Average Modulus

A nonlinear multiscale constitutive modeling framework is used to predict the elastic modulus of a glassy polymer. A set of seven molecular models with different molecular configurations is utilized to study the effect of the minimized potential energy level on the predicted elastic moduli. It is found that the average modulus from the seven models considered in the current study is seen to be in reasonable agreement with the experimentally observed value, given the statistical uncertainly in the data.

scholarly journals The Effects of Creep on Elastic Modulus Measurement Using Nanoindentation

2000 ◽  
Vol 649 ◽  
Author(s):  
G. Feng ◽  
A.H.W. Ngan
Keyword(s):  
Elastic Modulus ◽  
Elastic Deformation ◽  
Elastic Moduli ◽  
Holding Time ◽  
Time Dependent ◽  
Nanoindentation Test ◽  
Modification Method ◽  
Unloading Rate ◽  
Modulus Measurement

ABSTRACTDuring the unloading segment of nanoindentation, time dependent displacement (TDD) accompanies elastic deformation. Consequently the modulus calculated by the Oliver-Pharr scheme can be overestimated. In this paper we present evidences for the influence of the measured modulus by TDD. A modification method is also presented to correct for the effects of TDD by extrapolating the TDD law in the holding process to the beginning of the unloading process. Using this method, the appropriate holding time and unloading rate can be estimated for nanoindentation test to minimise the effects of TDD. The elastic moduli of three materials computed by the modification method are compared with the results without considering the TDD effects.

Consistent red luminescence in π-conjugated polymers with tuneable elastic moduli over five orders of magnitude

2020 ◽  
Vol 7 (5) ◽  
pp. 1421-1426 ◽  
Author(s):  
Zhenfeng Guo ◽  
Akira Shinohara ◽  
Chengjun Pan ◽  
Florian J. Stadler ◽  
Zhonghua Liu ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Conjugated Polymers ◽  
Elastic Moduli ◽  
Luminescent Properties ◽  
Side Chains ◽  
Wide Range ◽  
Alkyl Side Chains ◽  
Red Luminescence

Bulky but flexible alkyl side chains enable π-conjugated polymers to possess wide-range elastic modulus tuneability, yet consistent red luminescent properties.

Coarse Aggregate Effects on Elastic Moduli of Concrete

1996 ◽  
Vol 1547 (1) ◽  
pp. 29-34 ◽  
Author(s):  
Bouzid Choubane ◽  
Chung-Lung Wu ◽  
Mang Tia
Keyword(s):  
Elastic Modulus ◽  
Dynamic Modulus ◽  
Laboratory Testing ◽  
Elastic Moduli ◽  
Coarse Aggregate ◽  
Textured Surface ◽  
Test Program ◽  
Static Modulus ◽  
Aggregate Effects ◽  
Strength And Stiffness

The results of a laboratory testing program carried out to investigate the effect of coarse aggregate types on the elastic modulus of typical pavement concretes are presented. The elastic modulus was determined in both flexure and compression using static and dynamic means. Three different mixes, made using three different aggregates, were compared. The water-cement ratio was kept at 0.53 throughout the test program. The results showed that within the tested range, the aggregate type significantly affected the studied properties of concrete. Calera aggregate (a dense limestone) with its rough-textured surface and angular shape produced a concrete with higher strength and stiffness than those of concretes made with Brooksville aggregate (a porous limestone) and river gravel. In addition, the measured dynamic modulus in compression was significantly different from that in flexure. Also, in flexure, the dynamic modulus was higher than the static modulus by an average of 23 percent, whereas in compression, the dynamic modulus appeared to be in the same range as the static modulus. The change in frequency from 1 to 7 Hz did not have a significant influence on the dynamic modulus.

scholarly journals A Novel Toolkit for Characterizing the Mechanical and Electrical Properties of Engineered Neural Tissues

Biosensors ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 51 ◽  
Author(s):  
Meghan Robinson ◽  
Karolina Valente ◽  
Stephanie Willerth
Keyword(s):  
Elastic Modulus ◽  
Electrical Properties ◽  
Elastic Moduli ◽  
Direct Method ◽  
Hydrogel Scaffolds ◽  
Force Microscopy ◽  
Mechanical And Electrical Properties ◽  
Atomic Force ◽  
Neural Tissues ◽  
Electrical Signaling

We have designed and validated a set of robust and non-toxic protocols for directly evaluating the properties of engineered neural tissue. These protocols characterize the mechanical properties of engineered neural tissues and measure their electrophysical activity. The protocols obtain elastic moduli of very soft fibrin hydrogel scaffolds and voltage readings from motor neuron cultures. Neurons require soft substrates to differentiate and mature, however measuring the elastic moduli of soft substrates remains difficult to accurately measure using standard protocols such as atomic force microscopy or shear rheology. Here we validate a direct method for acquiring elastic modulus of fibrin using a modified Hertz model for thin films. In this method, spherical indenters are positioned on top of the fibrin samples, generating an indentation depth that is then correlated with elastic modulus. Neurons function by transmitting electrical signals to one another and being able to assess the development of electrical signaling serves is an important verification step when engineering neural tissues. We then validated a protocol wherein the electrical activity of motor neural cultures is measured directly by a voltage sensitive dye and a microplate reader without causing damage to the cells. These protocols provide a non-destructive method for characterizing the mechanical and electrical properties of living spinal cord tissues using novel biosensing methods.

Stimulating changes in the elastic modulus of polymer materials by molecular photochromism

RSC Advances ◽  
2014 ◽  
Vol 4 (108) ◽  
pp. 62920-62925 ◽  
Author(s):  
Yuhuan Jin ◽  
Daniel Harrington ◽  
Aaron A. Rachford ◽  
Jeffrey J. Rack
Keyword(s):  
Elastic Modulus ◽  
Amorphous Polymer ◽  
Polymer Materials

Photonastic effects are observed in an amorphous polymer via irradiation of a pendant photoreversible photochrome.

Determination of the elastic modulus of microscale ceramic particles via nanoindentation

2004 ◽  
Vol 19 (8) ◽  
pp. 2437-2447 ◽  
Author(s):  
J.W. Leggoe
Keyword(s):  
Elastic Modulus ◽  
Elastic Moduli ◽  
Aluminum Matrix ◽  
Scalar Particle ◽  
Accurate Estimate ◽  
Flat Punch ◽  
Silicon Carbide Particles ◽  
Material Mismatch ◽  
Particulate Reinforced

Nanoindentation of the reinforcement in a particulate reinforced metal matrix composite (PR MMC) enables direct investigation of reinforcement properties within the finished material. Mismatch between the elastic moduli of the reinforcement and matrix creates a “secondary indentation” effect, whereby the stiffer reinforcement particles themselves “indent” the more compliant matrix. A finite-element investigation was undertaken to quantify the additional penetration arising under secondary indentation for spherical and cylindrical particles. Modification of Sneddon’s equation for a flat punch by a scalar particle shape factor provided an accurate estimate of the additional penetration. The modified equation was combined with the analysis of Field and Swain to extract the particle elastic modulus from results obtained using a spherical indenter under a multiple partial-unloading indentation regime. The resulting methodology was used to determine the elastic moduli of silicon carbide particles and MicralTM microspheres in two aluminum-matrix PR MMCs.

Stress sensitivity of sandstones

Geophysics ◽  
1996 ◽  
Vol 61 (2) ◽  
pp. 444-455 ◽  
Author(s):  
Jack Dvorkin ◽  
Amos Nur ◽  
Caren Chaika
Keyword(s):  
Elastic Modulus ◽  
Effective Stress ◽  
Elastic Moduli ◽  
Hydrostatic Stress ◽  
Clay Content ◽  
Stress Sensitivity ◽  
High Porosity ◽  
Effective Pressure ◽  
Critical Porosity ◽  
Difference Formula

Our observations made on dry‐sandstone ultrasonic velocity data relate to the variation in velocity (or modulus) with effective stress, and the ability to predict a velocity for a rock under one effective pressure when it is known only under a different effective pressure. We find that the sensitivity of elastic moduli, and velocities, to effective hydrostatic stress increases with decreasing porosity. Specifically, we calculate the difference between an elastic modulus, [Formula: see text], of a sample of porosity ϕ at effective pressure [Formula: see text] and the same modulus, [Formula: see text], at effective pressure [Formula: see text]. If this difference, [Formula: see text], is plotted versus porosity for a suite of samples, then the scatter of ΔM is close to zero as porosity approaches the critical porosity value, and reaches its maximum as porosity approaches zero. The dependence of this scatter on porosity is close to linear. Critical porosity here is the porosity above which rock can exist only as a suspension—between 36% and 40% for sandstones. This stress‐sensitivity pattern of grain‐supported sandstones (clay content below 0.35) practically does not depend on clay content. In practical terms, the uncertainty of determining elastic moduli at a higher effective stress from the measurements at a lower effective stress is small at high porosity and increases with decreasing porosity. We explain this effect by using a combination of two heuristic models—the critical porosity model and the modified solid model. The former is based on the observation that the elastic‐modulus‐versus‐porosity relation can be approximated by a straight line that connects two points in the modulus‐porosity plane: the modulus of the solid phase at zero porosity and zero at critical porosity. The second one reflects the fact that at constant effective stress, low‐porosity sandstones (even with small amounts of clay) exhibit large variability in elastic moduli. We attribute this variability to compliant cracks that hardly affect porosity but strongly affect the stiffness. The above qualitative observation helps to quantitatively constrain P‐ and S‐wave velocities at varying stresses from a single measurement at a fixed stress. We also show that there are distinctive linear relations between Poisson’s ratios (ν) of sandstone measured at two different stresses. For example, in consolidated medium‐porosity sandstones [Formula: see text], where the subscripts indicate hydrostatic stress in MPa. Linear functions can also be used to relate the changes (with hydrostatic stress) in shear moduli to those in compressional moduli. For example, [Formula: see text], where [Formula: see text] is shear modulus and [Formula: see text] is compressional modulus, both in GPa, and the subscripts indicate stress in MPa.

Microstructures and Elastic Moduli of Binary Titanium Alloys Containing Biocompatible Alloying Elements

2005 ◽  
Vol 475-479 ◽  
pp. 2291-2294 ◽  
Author(s):  
Hi Won Jeong ◽  
Seung Eon Kim ◽  
Yong Taek Hyun ◽  
Yont Tai Lee ◽  
Joong Kuen Park
Keyword(s):  
Elastic Modulus ◽  
Titanium Alloys ◽  
Elastic Moduli ◽  
Stress Shielding ◽  
Lattice Parameter ◽  
Alloying Elements ◽  
Shielding Effect ◽  
Dominant Factor ◽  
Transition Elements ◽  
Pulse Echo

New titanium alloys with a low elastic modulus have been developed for biomedical applications to avoid the stress shielding effect of an artificial prosthesis. The newly developed alloys contained the transition elements like Zr, Hf, Nb, Ta which were non-cytotoxicity elements and β stabilizers. In the present paper the elastic moduli of Ti-xM containing Zr, Hf, Nb, Ta were evaluated by measuring the velocity of supersonic wave (Pulse Echo Overlap). The effectiveness of the alloying elements for lowering the elastic modulus was investigated. In addition, the dominant factors for the low modulus were discussed. Ta was the most effective in lowering the elastic modulus of the alloys. The effectiveness of Hf was not acceptable for decreasing the elastic modulus. The dominant factor was the lattice parameter for Zr, and the poisson's ratio for Nb, Ta, respectively, in lowering the elastic modulus of Ti.

A Methodology for Optimal Design of Composite Laminates Using Polar Formalism

2016 ◽  
Vol 32 (3) ◽  
pp. 255-266
Author(s):  
M. Kazemi ◽  
G. Verchery
Keyword(s):  
Elastic Modulus ◽  
Composite Laminates ◽  
Elastic Moduli ◽  
Optimization Technique ◽  
Laminated Plates ◽  
Flexural Stiffness ◽  
Numerical Examples ◽  
Composite Laminated Plates ◽  
Plane Anisotropy ◽  
Laminated Structures

AbstractAn innovative optimization technique is presented for the design of composite laminated plates subjected to in-plane loads. A list of quasi-homogeneous laminates that can be used as angle-ply materials is proposed as a comprehensive solution for optimum lay-up. Two optimization procedures are performed: Dimensioning of the flexural stiffness and the elastic modulus, which provides the optimal orientations for the layers and offer highest in-plane resistance to composite laminated structures. The polar formalism for plane anisotropy is used to represent the flexural stiffness and elastic modulus tensors. Numerical examples are resolved for two materials with different elastic moduli.

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