scholarly journals APPLICATION OF THE MORI-TANAKA METHOD TO DESCRIBE THE RATE-DEPENDENT BEHAVIOR OF UNIDIRECTIONAL FIBROUS COMPOSITES

2021 ◽  
Vol 30 ◽  
pp. 114-120
Author(s):  
Soňa Valentová ◽  
Michal Šejnoha ◽  
Jan Vorel ◽  
Radek Sedláček ◽  
Pavel Padevět
Keyword(s):  
Cross Section ◽  
Micromechanical Model ◽  
Considerable Improvement ◽  
Fibrous Composites ◽  
Predictive Capability ◽  
First Order ◽  
Rate Dependent ◽  
Dependent Behavior ◽  
Leonov Model ◽  
Suitable Modification

This paper examines the possibility of using the Mori-Tanaka micromechanical model describe the rate dependent behavior of the polymer matrix based fibrous composites. The generalized Leonov model is adopted to capture the time and rate dependent character of the selected matrix, while fibers are assumed elastic. The performance of the Mori-Tanaka method is tested against the finite element simulations carried out in the framework of first-order homogenization. For simplicity, the periodichexagonal array model is chosen to represent the microstructural arrangement of fibers in the yarn cross-section. To match the predictions provided by the two approaches a suitable modification to the original Mori-Tanaka method is proposed. An extensive parametric study is presented to illustrate a considerable improvement of the predictive capability of the modified Mori-Tanaka method.

Fiber Cross-Section Shape Effect on Rate-Dependent Behavior of Polymer Matrix Composites with Fbgs Sensors

2013 ◽  
Vol 284-287 ◽  
pp. 132-137
Author(s):  
Zhi Zhai ◽  
Zheng Jia He ◽  
Xue Feng Chen ◽  
Jun Jie Ye ◽  
Xiao Jun Zhu
Keyword(s):  
Cross Section ◽  
Internal State ◽  
Micromechanical Model ◽  
Constitutive Relationship ◽  
Shape Effect ◽  
State Variables ◽  
Fiber Cross Section ◽  
Rate Dependent ◽  
Cross Section Shape ◽  
Section Shape

The micromechanical investigation of fiber cross-section shape effect on the rate sensitive nonlinear behavior of a glass/epoxy was performed at 10-5/s and 1/s, which considering four shapes, square, cross, circle and ellipse. With the strain of different rate loadings measured by Fibre Bragg gratings (FBGs) sensors, the rate-dependent inelastic constitutive relationship of epoxy is built by using an internal state variables viscoplasticity model. Then, through homogenizing the properties of unit cells, the responses of resin and its composites at 30° and 60° off-axis loadings are predicted by a micromechanical model compared with the experiments data. The effect of fiber cross-section fiber on the 30° and 90° off-axis responses are discussed with respect to the viscoplastic parameters of the resin determined. The results indicate that the micromechanical model accurately calculates the behavior of the PMCs employed. The square fiber causes the largest flow stress and plastic strain in the four cases. And the influences on overall responses for the four fiber shapes are enhanced with raising off-axis angles but weaken with the rate increase. However, the elliptical fiber yields the highest modulus in linear elastic stage. The square fiber is the most effective and the elliptical fiber is the least effective in the nonlinear deformation stage. Besides, the elastic properties are unaffected by loading rates when it is less than 1/s.

Dynamic evolution of shear rate-dependent behavior of rock discontinuity under shearing condition

2021 ◽  
Vol 28 (6) ◽  
pp. 1875-1887
Author(s):  
Lin-lin Gu ◽  
Zhen Wang ◽  
Feng Zhang ◽  
Fei Gao ◽  
Xiao Wang
Keyword(s):  
Shear Rate ◽  
Dynamic Evolution ◽  
Rock Discontinuity ◽  
Rate Dependent ◽  
Dependent Behavior

scholarly journals A graphical solution of a differential equation with application to hill’s treatment of nerve excitation

1937 ◽  
Vol 123 (832) ◽  
pp. 382-395 ◽  
Keyword(s):  
Viscous Medium ◽  
Graphical Solution ◽  
Initial Value ◽  
First Order ◽  
Rate Dependent ◽  
Monomolecular Reaction ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Physical And Chemical ◽  
Nerve Excitation

Linear differential equations with constant coefficients are very common in physical and chemical science, and of these, the simplest and most frequently met is the first-order equation a dy / dt + y = f(t) , (1) where a is a constant, and f(t) a single-valued function of t . The equation signifies that the quantity y is removed at a rate proportional to the amount present at each instant, and is simultaneously restored at a rate dependent only upon the instant in question. Familiar examples of this equation are the charging of a condenser, the course of a monomolecular reaction, the movement of a light body in a viscous medium, etc. The solution of this equation is easily shown to be y = e - t / a { y 0 = 1 / a ∫ t 0 e t /a f(t) dt , (2) where y 0 is the initial value of y . In the case where f(t) = 0, this reduces to the well-known exponential decay of y .

The flow properties of honey–malt spread

2017 ◽  
Vol 23 (5) ◽  
pp. 415-425 ◽  
Author(s):  
M Dianat ◽  
M Taghizadeh ◽  
F Shahidi ◽  
SMA Razavi
Keyword(s):  
Flow Behavior ◽  
Time Dependent ◽  
Malt Extract ◽  
Barley Malt ◽  
First Order ◽  
Dependent Behavior ◽  
Thixotropic Behaviour ◽  
Order Stress ◽  
Temperature Levels ◽  
Independent Behavior

In this study, the effect of barley malt extract at two brix levels (74 and 79 °Bx) and three ratios of malt extract/honey (65:35, 70:30 and 75:25) on the flow behavior properties of honey–malt spread at three temperature levels (35 ℃, 45 ℃ and 55 ℃) was investigated. Time-dependent behavior data of the spread samples were appropriately fitted to the Weltman, first-order stress decay with a zero stress value and first-order stress decay with a non-zero stress value models. Also, the Power-law, Herschel–Bulkley, Casson and Bingham models were used for curve fitting the time-independent behavior data. Regarding the R2 and root mean square error coefficients, the first-order stress decay with a non-zero stress value and Herschel–Bulkley models were selected as the suitable models to describe the flow behavior of samples. The results for time-dependent properties showed that spread samples exhibit a thixotropic behaviour, as the viscosity for all samples decreased with increase in shearing time at a constant shear rate of 50 s−1.

Micromechanical Modeling of Viscoplastic Behavior of Laminated Polymer Composites With Thermal Residual Stress Effect

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Qiang Chen ◽  
Xuefeng Chen ◽  
Zhi Zhai ◽  
Xiaojun Zhu ◽  
Zhibo Yang
Keyword(s):  
Residual Stress ◽  
Polymer Matrix Composites ◽  
Micromechanical Model ◽  
Thermal Residual Stress ◽  
Micromechanical Modeling ◽  
Multiscale Approach ◽  
Stress Effect ◽  
Accurate Analysis ◽  
Rate Dependent ◽  
Residual Stress Effect

In this paper, a multiscale approach has been developed for investigating the rate-dependent viscoplastic behavior of polymer matrix composites (PMCs) with thermal residual stress effect. The finite-volume direct averaging micromechanics (FVDAM), which effectively predicts nonlinear response of unidirectional fiber reinforced composites, is incorporated with improved Bodner–Partom model to describe the viscoplastic behavior of PMCs. The new micromechanical model is then implemented into the classical laminate theory, enabling efficient and accurate analysis of multidirectional PMCs. The proposed multiscale theory not only predicts effective thermomechanical viscoplastic response of PMCs but also provides local fluctuations of fields within composite microstructures. The deformation behaviors of several unidirectional and multidirectional PMCs with various fiber configurations are extensively simulated at different strain rates, which show a good agreement with the experimental data found from the literature. Influence of thermal residual stress on the viscoplastic behavior of PMCs is closely related to fiber orientation. In addition, the thermal residual stress effect cannot be neglected in order to accurately describe the rate-dependent viscoplastic behavior of PMCs.

Model Development for PZT Bimorph Actuation Employed for Micro-Air Vehicles

2016 ◽  
Author(s):  
John Crews ◽  
Nikolas Bravo ◽  
Ralph Smith
Keyword(s):  
Model Development ◽  
Micro Air Vehicles ◽  
Energy Model ◽  
Comprehensive Model ◽  
Actuator Dynamics ◽  
Rate Dependent ◽  
Dependent Behavior ◽  
Bimorph Actuators ◽  
Homogenized Energy Model ◽  
Air Vehicles

In the paper, we discuss the development of a model for PZT bimorph actuators used to power micro-air vehicles including Robobee. Due to highly dynamic drive regimes required for the actuators, models must quantify the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in these regimes. We employ the homogenized energy model (HEM) framework to model the actuator dynamics and numerically we illustrate the capability of the model to characterize the inherent hysteresis. This provides a comprehensive model, which can be inverted and implemented for certain control regimes.

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