Constitutive Models for the Viscoelastic Behavior of Polyimide Membranes at Room and Deep Cryogenic Temperatures

Microstructural mechanisms such as domain switching in ferroelectric ceramics dissipate energy, the nature, and extent of which are of significant interest for two reasons. First, dissipative internal processes lead to hysteretic behavior at the macroscale (e.g., the hysteresis of polarization versus electric field in ferroelectrics). Second, mechanisms of internal friction determine the viscoelastic behavior of the material under small-amplitude vibrations. Although experimental techniques and constitutive models exist for both phenomena, there is a strong disconnect and, in particular, no advantageous strategy to link both for improved physics-based kinetic models for multifunctional rheological materials. Here, we present a theoretical approach that relates inelastic constitutive models to frequency-dependent viscoelastic parameters by linearizing the kinetic relations for the internal variables. This enables us to gain qualitative and quantitative experimental validation of the kinetics of internal processes for both quasistatic microstructure evolution and high-frequency damping. We first present the simple example of the generalized Maxwell model and then proceed to the case of ferroelectric ceramics for which we predict the viscoelastic response during domain switching and compare to experimental data. This strategy identifies the relations between microstructural kinetics and viscoelastic properties. The approach is general in that it can be applied to other rheological materials with microstructure evolution.

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Viscoelastic Properties of Human Tracheal Tissues

Journal of Biomechanical Engineering ◽

10.1115/1.4034651 ◽

2016 ◽

Vol 139 (1) ◽

Cited By ~ 9

Author(s):

Farzaneh Safshekan ◽

Mohammad Tafazzoli-Shadpour ◽

Majid Abdouss ◽

Mohammad B. Shadmehr

Keyword(s):

Tissue Engineering ◽

Smooth Muscle ◽

Stress Relaxation ◽

Connective Tissue ◽

Linear Viscoelasticity ◽

Viscoelastic Properties ◽

Constitutive Models ◽

Viscoelastic Behavior ◽

Tracheal Cartilage ◽

Human Trachea

The physiological performance of trachea is highly dependent on its mechanical behavior, and therefore, the mechanical properties of its components. Mechanical characterization of trachea is key to succeed in new treatments such as tissue engineering, which requires the utilization of scaffolds which are mechanically compatible with the native human trachea. In this study, after isolating human trachea samples from brain-dead cases and proper storage, we assessed the viscoelastic properties of tracheal cartilage, smooth muscle, and connective tissue based on stress relaxation tests (at 5% and 10% strains for cartilage and 20%, 30%, and 40% for smooth muscle and connective tissue). After investigation of viscoelastic linearity, constitutive models including Prony series for linear viscoelasticity and quasi-linear viscoelastic, modified superposition, and Schapery models for nonlinear viscoelasticity were fitted to the experimental data to find the best model for each tissue. We also investigated the effect of age on the viscoelastic behavior of tracheal tissues. Based on the results, all three tissues exhibited a (nonsignificant) decrease in relaxation rate with increasing the strain, indicating viscoelastic nonlinearity which was most evident for cartilage and with the least effect for connective tissue. The three-term Prony model was selected for describing the linear viscoelasticity. Among different models, the modified superposition model was best able to capture the relaxation behavior of the three tracheal components. We observed a general (but not significant) stiffening of tracheal cartilage and connective tissue with aging. No change in the stress relaxation percentage with aging was observed. The results of this study may be useful in the design and fabrication of tracheal tissue engineering scaffolds.

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Comparison Between a Quasilinear and a Nonlinear Viscoelastic Model for Brain Tissue

10.1115/imece2000-2567 ◽

2000 ◽

Author(s):

Kurosh K. Darvish ◽

Jeff R. Crandall

Keyword(s):

Brain Tissue ◽

Viscoelastic Model ◽

Constitutive Models ◽

Viscoelastic Behavior ◽

Bovine Brain ◽

Integral Model ◽

Nonlinear Viscoelastic ◽

Hereditary Integral ◽

Nonlinear Constitutive Models ◽

Nonlinear Viscoelastic Model

Abstract The nonlinearity of the viscoelastic behavior of brain tissue was studied. Two nonlinear constitutive models were developed using the experimental results of forced vibrations on bovine brain samples, namely a quasilinear viscoelastic model and a multiple hereditary integral model. The latter was found to be superior especially at higher frequencies (above 27 Hz).

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A Comparison Between Fractional-Order and Integer-Order Differential Finite Deformation Viscoelastic Models: Effects of Filler Content and Loading Rate on Material Parameters

International Journal of Applied Mechanics ◽

10.1142/s1758825118500990 ◽

2018 ◽

Vol 10 (09) ◽

pp. 1850099 ◽

Cited By ~ 9

Author(s):

Hesam Khajehsaeid

Keyword(s):

Fractional Order ◽

Differential Operators ◽

Filler Content ◽

Viscoelastic Model ◽

Constitutive Models ◽

Viscoelastic Behavior ◽

Fractional Model ◽

Material Parameters ◽

Integer Order ◽

Viscoelastic Models

Elastomers or rubber-like materials exhibit nonlinear viscoelastic behavior such as creep and relaxation upon mechanical loading. Differential constitutive models and hereditary integrals are the main frameworks followed in the literature for modeling the viscoelastic behavior at finite deformations. Regular differential operators can be replaced by fractional-order derivatives in the standard models in order to make fractional viscoelastic models. In the present paper, the relaxation behavior of elastomers is formulated both in terms of ordinary (integer-order) and fractional differential viscoelastic models. The derived constitutive equations are fitted to several experimental data to compare their efficiency in modeling the stress relaxation phenomenon. Specifically, a fractional viscoelastic model with one fractional dashpot (FD) is compared with two ordinary models including respectively one and two ordinary dashpots (OD). The models are compared in fitting accuracy, number of required material parameters and also variation of parameters from one compound to another to clarify the effects of filler content and deformation rate. It is shown that, the results of the ordinary model with one OD is not good at all. The fractional model with one FD and the ordinary model with two ODs provide good fittings for all compounds whereas the former uses only three parameters and the latter uses five material parameters. For the fractional model, the order of the Maxwell element and the associated relaxation time approximately remain the same for different compounds of each material at certain loading rates, but it is not the case for the ordinary differential models.

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Constitutive models for predicting field-dependent viscoelastic behavior of magnetorheological elastomer using machine learning

Smart Materials and Structures ◽

10.1088/1361-665x/ab972d ◽

2020 ◽

Vol 29 (8) ◽

pp. 087001

Author(s):

Kasma Diana Saharuddin ◽

Mohd Hatta Mohammed Ariff ◽

Irfan Bahiuddin ◽

Saiful Amri Mazlan ◽

Siti Aishah Abdul Aziz ◽

...

Keyword(s):

Machine Learning ◽

Constitutive Models ◽

Viscoelastic Behavior ◽

Magnetorheological Elastomer ◽

Field Dependent

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Cryogenic atomic force microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100084570 ◽

1991 ◽

Vol 49 ◽

pp. 54-55

Author(s):

K. A. Fisher ◽

M. G. L. Gustafsson ◽

M. B. Shattuck ◽

J. Clarke

Keyword(s):

Room Temperature ◽

Rapid Freezing ◽

Cryogenic Temperatures ◽

Soft Or ◽

Electrically Conductive ◽

Force Microscopy ◽

Flexible Molecules ◽

Advantages And Disadvantages ◽

Atomic Force ◽

Chemical Perturbation

The atomic force microscope (AFM) is capable of imaging electrically conductive and non-conductive surfaces at atomic resolution. When used to image biological samples, however, lateral resolution is often limited to nanometer levels, due primarily to AFM tip/sample interactions. Several approaches to immobilize and stabilize soft or flexible molecules for AFM have been examined, notably, tethering coating, and freezing. Although each approach has its advantages and disadvantages, rapid freezing techniques have the special advantage of avoiding chemical perturbation, and minimizing physical disruption of the sample. Scanning with an AFM at cryogenic temperatures has the potential to image frozen biomolecules at high resolution. We have constructed a force microscope capable of operating immersed in liquid n-pentane and have tested its performance at room temperature with carbon and metal-coated samples, and at 143° K with uncoated ferritin and purple membrane (PM).

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Nonlinear Viscoelastic Finite Element Analysis of Adhesive Joints

Tire Science and Technology ◽

10.2346/1.2148803 ◽

1988 ◽

Vol 16 (3) ◽

pp. 146-170 ◽

Cited By ~ 4

Author(s):

S. Roy ◽

J. N. Reddy

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Viscoelastic Behavior ◽

Bonded Joints ◽

Adhesively Bonded ◽

Element Analysis ◽

Adhesively Bonded Joints ◽

Nonlinear Viscoelastic ◽

Structural Failures ◽

Updated Lagrangian

Abstract A good understanding of the process of adhesion from the mechanics viewpoint and the predictive capability for structural failures associated with adhesively bonded joints require a realistic modeling (both constitutive and kinematic) of the constituent materials. The present investigation deals with the development of an Updated Lagrangian formulation and the associated finite element analysis of adhesively bonded joints. The formulation accounts for the geometric nonlinearity of the adherends and the nonlinear viscoelastic behavior of the adhesive. Sample numerical problems are presented to show the stress and strain distributions in bonded joints.

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