Mapping the Viscoelastic Behavior of Soft Solids From Time Harmonic Motion

2018 ◽  
Vol 85 (4) ◽  
Author(s):  
Yue Mei ◽  
Sevan Goenezen
Keyword(s):  
Inverse Method ◽  
Loss Modulus ◽  
Viscoelastic Behavior ◽  
Adjoint Equations ◽  
Optimization Strategy ◽  
Low Frequencies ◽  
Harmonic Motion ◽  
Soft Solids ◽  
Viscoelastic Moduli ◽  
Time Harmonic

We present a nondestructive approach to map the heterogeneous viscoelastic moduli from time harmonic motion via a constrained optimization strategy under the framework of finite element techniques. The adjoint equations are carefully derived to determine the gradient of the objective function with respect to the viscoelastic moduli. The feasibility of this inverse scheme is tested with simulated experiments under various driving frequencies. We observe that the overall strategy results in well-reconstructed moduli. For low frequencies, however, the mapped loss modulus is of inferior quality. To explain this observation, we analyze two simple one-dimensional (1D) models theoretically. The analysis reveals that the known displacement amplitude is less sensitive to the loss modulus value at low frequencies. Thus, we conclude that the inverse method is incapable of finding a well-reconstructed loss modulus distribution for low driving frequencies in the presence of noisy data. Overall, the inverse algorithms presented in this work are highly robust to map the storage and loss modulus with high accuracy given that a proper range of frequencies are utilized.

Influence of κ-Carrageenan, Modified Starch and Inulin Addition on Rheological and Sensory Properties of Non-fat and Non-added Sugar Dairy Dessert

2020 ◽  
Vol 16 (4) ◽  
pp. 462-469
Author(s):  
Zhaleh Sheidaei ◽  
Bahareh Sarmadi ◽  
Seyede M. Hosseini ◽  
Fardin Javanmardi ◽  
Kianoush Khosravi-Darani ◽  
...  
Keyword(s):  
Storage Modulus ◽  
Loss Modulus ◽  
Viscoelastic Behavior ◽  
Textural Properties ◽  
Complex Viscosity ◽  
Sensory Properties ◽  
Modified Starch ◽  
Consumer Health ◽  
Added Sugar ◽  
Textural Parameters

<P>Background: The high amounts of fat, sugar and calorie existing in dairy desserts can lead to increase the risk of health problems. Therefore, the development of functional and dietary forms of these products can help the consumer health. </P><P> Objective: This study aims to investigate the effects of &#954;-carrageenan, modified starch and inulin addition on rheological and sensory properties of non-fat and non-added sugar dairy dessert. </P><P> Methods: In order to determine the viscoelastic behavior of samples, oscillatory test was carried out and the values of storage modulus (G′), loss modulus (G″), loss angle tangent (tan &#948;) and complex viscosity (&#951;*) were measured. TPA test was used for analysis of the desserts’ texture and textural parameters of samples containing different concentrations of carrageenan, starch and inulin were calculated. </P><P> Results: All treatments showed a viscoelastic gel structure with the storage modulus higher than the loss modulus values. Increasing amounts of &#954;-carrageenan and modified starch caused an increase in G′ and G″ as well as &#951;* and a decrease in tan &#948;. Also, firmness and cohesiveness were enhanced. The trained panelists gave the highest score to the treatment with 0.1% &#954;-carrageenan, 2.5% starch and 5.5% inulin (sucralose as constant = 0.25%) and this sample was the best treatment with desirable attributes for the production of non-fat and non-added sugar dairy dessert. </P><P> Conclusion: It can be concluded that the concentration of &#954;-carrageenan and starch strongly influenced the rheological and textural properties of dairy desserts, whereas the inulin content had little effect on these attributes.</P>

A Molecular Structure-Informed Viscoelastic Constitutive Model for Natural Rubber Materials

2021 ◽  
Author(s):  
Jiwon Jung ◽  
Chanwook Park ◽  
myungshin RYU ◽  
Gunjin Yun
Keyword(s):  
Molecular Structure ◽  
Constitutive Equation ◽  
Molecular System ◽  
Loss Modulus ◽  
Low Frequency ◽  
Viscoelastic Behavior ◽  
Material Model ◽  
Coarse Grained ◽  
Diffusivity Coefficient ◽  
Element Analysis

Abstract This paper presents a molecular structure-informed viscoelastic constitutive equation that adopts the Doi-Edward’s tube model with coarse-grained molecular dynamics (MD) simulation and primitive path analysis. Since this model contains polymer physics-related parameters directly obtained from molecular simulations, it can reflect molecular information in predictions of the viscoelastic behavior of elastomers, unlike other empirical models. The proposed incremental formulations and constitutive stiffness matrix were implemented into implicit finite element analysis (FEA) codes as a user-supplied material model and viscoelastic properties (storage, loss modulus, and tan⁡δ) were calculated from the constitutive equation. While obtaining polymer dynamics parameter of the molecular system, a relationship between self-diffusivity coefficient (D_c) and the polymerization degree of the polymer was confirmed. Furthermore, a series of parametric studies showed that increase of the primitive path length (L) and decrease of D_c have led to the strengthening of moduli and decrease of tan⁡δ peak. Moreover, under the same condition, the shift of tan⁡δ peak to low-frequency domain was observed, which implies a decline in free volume in the molecular system and an increase in the glass transition temperature.

Characterization of Cracks From Ultrasonic Scattering Data

1987 ◽  
Vol 54 (4) ◽  
pp. 754-760 ◽  
Author(s):  
J. D. Achenbach ◽  
D. A. Sotiropoulos ◽  
H. Zhu
Keyword(s):  
Scattered Field ◽  
Inverse Method ◽  
Crack Opening ◽  
Elastic Solid ◽  
Scattering Data ◽  
Crack Plane ◽  
Ultrasonic Scattering ◽  
Low Frequencies ◽  
Planar Crack

An inverse method for ultrasonic scattering data is proposed, to characterize a planar crack of general shape contained in an elastic solid. The method is based on an integral representation for the scattered field in the frequency domain. For a given scattered field the inverse problem has been formulated as a nonlinear optimization problem. At low frequencies its solution gives the location of the crack, the orientation of the crack-plane, and the crack-opening volumes. In addition the Mode I stress-intensity factor is obtained for a related static stress state corresponding to service loads.

Nonseparable Behavior in Rubber Viscoelasticity

1989 ◽  
Vol 62 (1) ◽  
pp. 68-81 ◽  
Author(s):  
J. L. Sullivan ◽  
K. A. Mazich
Keyword(s):  
Stress Relaxation ◽  
Relaxation Spectrum ◽  
Loss Modulus ◽  
Large Strain ◽  
Viscoelastic Behavior ◽  
Strain Effects ◽  
Mixed Response ◽  
Strain Stress ◽  
Necessary And Sufficient ◽  
Solid Liquid

Abstract New large-strain rubber viscoelasticity results for a filled and an unfilled IIR vulcanizate and previously published results for two NR gum vulcanizates have been discussed. The data show that the “mixed” response functions of large-strain stress relaxation, and the incremental storage and relaxation moduli do not demonstrate factorizability of time and strain effects. This is a consequence of the elastic and relaxation contributions in each of the mixed functions being different. The incremental dynamic data also show that the loss modulus for the filled IIR and unfilled NR vulcanizates (unavailable for the unfilled IIR) are separable functions of time and strain. This directly shows that the relaxation spectra for the filled IIR and unfilled NR vulcanizates are independent of strain for the deformations studied. In fact, it is argued that a necessary and sufficient condition for the relaxation spectrum to be independent of strain is that the loss modulus is a factorizable function of time and strain effects. The quantitative success of the Generalized Solid-Liquid (GSL) model in representing the viscoelastic behavior of the gum NR vulcanizate has been reviewed. Although the GSL model applies only to unfilled vulcanizates, it has also been successfully used to qualitatively interpret the results for the filled IIR compounds. Both successes are attributed to the physical assumptions intrinsic to the GSL model; more specifically, 1) the relaxation spectrum is independent of the state of strain, and 2) the deformational dependences of elastic and relaxation contributions to the overall response of the system need not be the same. Physical arguments justifying these assumptions have been covered. It has also been shown with the aid of the GSL model, that a material might exist which demonstrates factorizability in stress relaxation and incremental loss modulus behaviors but nonfactorizability in the incremental storage and relaxation moduli.

scholarly journals A Study of the Synergistic Interaction of Konjac Glucomannan/Curdlan Blend Systems under Alkaline Conditions

Materials ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 3543
Author(s):  
Weijian Ye ◽  
Bowen Yan ◽  
Jie Pang ◽  
Daming Fan ◽  
Jianlian Huang ◽  
...  
Keyword(s):  
Thermal Stability ◽  
Loss Modulus ◽  
Physical Property ◽  
Konjac Glucomannan ◽  
Gel Strength ◽  
Water Holding Capacity ◽  
Low Frequencies ◽  
Ideal Mixing ◽  
Alkaline Conditions ◽  
Water Holding

To improve the gelation performance of konjac glucomannan (KGM) thermo-irreversible gel in the condition of alkaline, this study investigated the interactions between KGM and curdlan (CUD) in terms of the sol state and gelation process. The apparent viscosity, rheological properties during heating and cooling, thermodynamic properties, gelation properties and water holding capacity of KGM/CUD blend systems in an alkaline environment were studied using physical property testing instruments and methods. The results showed that the viscosity of the KGM/CUD blended solution was greater than the value calculated from the ideal mixing rules in the condition of alkaline (pH = 10.58). As the proportion of CUD in the system increased, the intersection of storage modulus (G’) and loss modulus (G”) shifted to low frequencies, the relaxation time gradually increased, and the degree of entanglement of molecular chains between these two components gradually increased. The addition of CUD helped decrease the gelation temperature of KGM, increased the gelation rate and inhibited the thinning phenomenon of KGM gels at low temperatures (2–20 °C). The addition of CUD increased the hardness and gel strength of KGM but did not significantly improve the water holding capacity of the KGM/CUD blend gel. The process of mixing KGM and CUD improved the thermal stability of the gel. In summary, KGM/CUD exhibited excellent compatibility under alkaline conditions, and the blend systems produced a “viscosifying effect”. KC8 and KC5 show better thermal stability, low temperature resistance and gel strength compared to KGM. This blended gel can be used as a structural support material to provide reference for the development of konjac bionic vegetarian products.

Viscoelasticity of Rubber

1952 ◽  
Vol 25 (3) ◽  
pp. 490-499
Author(s):  
Robert B. Blizard
Keyword(s):  
Shear Modulus ◽  
General Expression ◽  
Viscoelastic Behavior ◽  
Viscous Medium ◽  
Modulus Function ◽  
Cross Linking ◽  
Frequency Range ◽  
Frequency Curve ◽  
Low Frequencies ◽  
Single Section

Abstract A theory has been obtained for the viscoelastic behavior of rubber in the frequency range above that at which creep is important and below that at which it behaves like a hard solid. The rubber chains are treated as springs in a viscous medium, and a general expression is obtained for the contribution to modulus of a single section of chain as a function of its length and terminations. A statistical estimate is made of the number of chain segments having given length and terminations. A modulus function is found for the group of chains with each kind of termination, and these are added in the proper amounts to give the form of the modulus vs. frequency curve for any amount of cross-linking. Measurements of shear modulus were made on one apparatus at frequencies between 0.0125 and 750 cps. Agreement is good if a pure viscosity is added to the theory. However, at low frequencies the imaginary part of modulus does not decrease as much as predicted.

The Dynamic Viscoelastic Behavior of Wood-Plastic Composites

2013 ◽  
Vol 815 ◽  
pp. 639-644 ◽  
Author(s):  
Pei Ying Liu ◽  
Zhi Hong Jiang
Keyword(s):  
Glass Transition ◽  
Transition Temperature ◽  
Glass Transition Temperature ◽  
Storage Modulus ◽  
Loss Modulus ◽  
Viscoelastic Behavior ◽  
Peak Frequency ◽  
Wood Plastic Composite ◽  
Plastic Composite ◽  
Positive Effect

Wood-plastic composite is a kind of viscoelastic materials. This paper presents the dynamic viscoelastic behavior of WPCs at different temperature, frequency and bamboo flours levels. The storage modulus decreased with the rise of temperature, the loss modulus and tanδ increased as temperature increased but decreased after reaching the peak. Frequency had a little influence on storage modulus and loss modulus, but the glass transition temperature increased with the increase of frequency, while the tanδ decreased. The glass transition temperature of this kind WPCs is about 85°C. The addition of bamboo flours had a positive effect on the dynamic viscoelastic behavior. From the results above, the activation energy of the WPCs was measured using an Arrhenius relationship to investigate the interphase between the wood and plastic.

Multicoating Inhomogeneities Problem for Effective Viscoelastic Properties of Particulate Composite Materials

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Yao Koutsawa ◽  
Mohammed Cherkaoui ◽  
El Mostafa Daya
Keyword(s):  
Loss Modulus ◽  
Micromechanical Model ◽  
Polymer System ◽  
High Capacity ◽  
Viscoelastic Behavior ◽  
Particulate Composite ◽  
Micromechanical Modeling ◽  
High Loss ◽  
Wide Range ◽  
The Matrix

The present work extends the multicoated micromechanical model of Lipinski et al. (2006, “Micromechanical Modeling of an Arbitrary Ellipsoidal Multi-Coated Inclusion,” Philos. Mag., 86(10), pp. 1305–1326) in the quasistatic domain to compute the effective material moduli of a viscoelastic material containing multicoated spherical inclusions displaying elastic or viscoelastic behavior. Losses are taken into account by introducing the frequency-dependent complex stiffness tensors of the viscoelastic matrix and the multicoated inclusions. The advantage of the micromechanical model is that it is applicable to the case of nonspherical multicoated inclusions embedded in anisotropic materials. The numerical simulations indicate that with proper choice of material properties, it is possible to engineer multiphase polymer system to have a high-loss modulus (good energy dissipation characteristics) for a wide range of frequencies without substantially degrading the stiffness of the composite (storage modulus). The numerical analyses show also that with respect to the relative magnitudes of the loss factors and the storage moduli of the matrix, inclusion and coating, the overall properties of the viscoelastic particulate composite are dominated by the properties of the matrices in some frequency ranges. The model can thus be a suitable tool to explore a wide range of microstructures for the design of materials with high capacity to absorb acoustic and vibrational energies.

scholarly journals Prony series calculation for viscoelastic behavior modeling of structural adhesives from DMA data.

2020 ◽  
Vol 21 (2) ◽  
pp. 1-10
Author(s):  
Manuel Alejandro Tapia Romero ◽  
Mariamne Dehonor Gomez ◽  
Luis Edmundo Lugo Uribe
Keyword(s):  
Product Design ◽  
Complex Modulus ◽  
Loss Modulus ◽  
Viscoelastic Behavior ◽  
Relaxation Modulus ◽  
Mechanical Analysis ◽  
Behavior Modeling ◽  
Prony Series ◽  
Product Design Process ◽  
Material Sample

In product design is important to choose the correct material for a specific application. Viscoelastic behavior let us know how much energy the material can dissipate on its internal structure or either return it to the surroundings, and the property that describe this is the Complex Modulus G*, it is a complex quantity that can be separated in a real and an imaginary part called G' storage modulus and iG'' loss modulus respectively. These properties can be measured experimentally from a small material sample easily by performing Dynamical Mechanical Analysis (DMA). In Product Design process there are both, computational and physical validations and there is the need of improving computational studies by understanding the physics of each component. Viscoelastic characteristics of materials can be represented by Prony series, also known as relaxation modulus in function of time. Relaxation modulus can be defined in most of Computer Aided Engineering (CAE) Software. In this article the procedure for calculating Prony Series from DMA data will be explained.

Viscoelastic Properties of Thixotropic Semisolid Alloy Relating the Microstructure

2019 ◽  
Vol 285 ◽  
pp. 380-384
Author(s):  
Gerardo Sanjuan-Sanjuan ◽  
Ángel Enrique Chavez-Castellanos
Keyword(s):  
Storage Modulus ◽  
Viscoelastic Properties ◽  
Loss Modulus ◽  
Viscoelastic Behavior ◽  
Complex Viscosity ◽  
Plateau Modulus ◽  
Complex Shear ◽  
Different Temperatures ◽  
Semisolid Alloy ◽  
The Subject

The subject of this work is to investigate viscoelastic properties such as loss modulus (G ́ ́), storage modulus (G ́), complex shear modulus (G*), complex viscosity (η*) and loss angle () at different temperatures by means of a small-amplitude oscillatory test. These properties allow to provide information about materials structure. For this purpose, we employed a tin-lead alloy (Sn-15%Pb) which exhibits a similar microstructure to aluminum alloys and is the classic alloy for semisolid thixotropic studies. It is interesting to note that the Sn-15%Pb alloy exhibits a slightly decrease in storage modulus (G ́) over the entire frequency (0.01-10Hz) at high temperatures, showing its viscoelastic behavior. In addition, a detailed analysis of master curves (oscillatory tests) was made to relate the semisolid microstructure (solid fraction) with the plateau modulus (GN0) which is directly related with both molecular weight or percolation threshold in polymer and gels science respectively.

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