scholarly journals Numerical Modeling of Proppant Embedment in Viscoelastic Formations with the Fractional Maxwell Model

ACS Omega ◽  
2021 ◽  
Author(s):  
Xiang Ding ◽  
Fan Zhang ◽  
Na Chen ◽  
Yan Zhang
Keyword(s):  
Numerical Modeling ◽  
Maxwell Model ◽  
Fractional Maxwell Model ◽  
Proppant Embedment

scholarly journals A Modified Fractional Maxwell Numerical Model for Constitutive Equation of Mn-Cu Damping Alloy

Materials ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2020
Author(s):  
Baoquan Mao ◽  
Rui Zhu ◽  
Zhiqian Wang ◽  
Yuying Yang ◽  
Xiaoping Han ◽  
...  
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Constitutive Relation ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Maxwell Model ◽  
Nonlinear Viscoelastic ◽  
Fractional Maxwell Model ◽  
Hysteretic Characteristics ◽  
Nonlinear Elastic

To better describe its constitutive relation, we need a new constitutive equation for an important nonlinear elastic material, Mn-Cu damping alloy. In this work, we studied the nonlinear and hysteretic characteristics of the stress-strain curve of the M2052 alloy with the uniaxial cyclic tensile test with constant strain rate. The strain rate and amplitude correlations of M2052 resembled those of nonlinear viscoelastic material. Therefore, we created a new constitutive equation for the M2052 damping alloy by modifying the fractional Maxwell model, and we used the genetic algorithm to carry out numerical fitting with MATLAB. By comparing with the experimental data, we confirmed that the new constitutive equation could accurately depict the nonlinear constitutive relation and hysteretic property of the damping alloy. Taken together, this new constitutive equation for Mn-Cu damping alloy based on the fractional Maxwell model can serve as an effective tool for further studies of the constitutive relation of the Mn-Cu damping alloys.

A note on fractional Maxwell model for PMMA and PTFE

2011 ◽  
Vol 30 (7) ◽  
pp. 797-799 ◽  
Author(s):  
Kai-Xin Hu ◽  
Ke-Qin Zhu
Keyword(s):  
Maxwell Model ◽  
Fractional Maxwell Model

Unsteady flow of viscoelastic fluid between two cylinders using fractional Maxwell model

2012 ◽  
Vol 28 (2) ◽  
pp. 274-280 ◽  
Author(s):  
Muhammad Jamil ◽  
Constantin Fetecau ◽  
Corina Fetecau
Keyword(s):  
Unsteady Flow ◽  
Viscoelastic Fluid ◽  
Maxwell Model ◽  
Fractional Maxwell Model

Analytical Solution of 1-D Viscoelastic Consolidation of Soft Soils with Fractional Maxwell Model

2012 ◽  
Vol 157-158 ◽  
pp. 419-423
Author(s):  
Ya Peng Zhang ◽  
Feng Gao
Keyword(s):  
Analytical Solution ◽  
Soft Soil ◽  
Soil Layer ◽  
Viscoelastic Model ◽  
Integral Form ◽  
Maxwell Model ◽  
One Dimensional ◽  
The Laplace Transform ◽  
Fractional Maxwell Model ◽  
The One

Considering the rheological characteristics of soil, think the fractional maxwell with viscoelastic model can be described, the fractional maxwell model into integral form of saturated soft soil layer, the one dimensional compression, through the Laplace transform problems get instantaneous loading and single stage, the analytical solution of the loading conditions.

Viscoelastic Homogenization Approach for Damping Properties of Polymer Composites Using Fractional Calculus

2011 ◽  
Author(s):  
Yotsugi Shibuya
Keyword(s):  
Fractional Calculus ◽  
Polymer Composites ◽  
Polymer Matrix ◽  
Maxwell Model ◽  
Inverse Laplace Transform ◽  
Material System ◽  
Damping Properties ◽  
Stress Strain ◽  
Homogenization Approach ◽  
Fractional Maxwell Model

Polymer composites are attractive material system with damping ability to reduce vibration of mechanical structures and improve controllability of mechanical system. To understand effect of constituents and microstructure on damping properties of polymer composites, a detailed micromechanical study is needed to develop the method of analysis for microscopic viscoelastic deformation and macroscopic damping properties. Viscoelastic homogenization approach with fractional calculus is developed to evaluate effective damping properties of polymer composites. The microstructure of the composite is supposed to be periodic and polymer matrix is viscoelastic medium. Damping properties of the composite are evaluated from the stress strain diagram and associated energy dissipation during cyclic loading. Viscoelastic properties of the polymer matrix are identified using a generalized fractional Maxwell model with spring and fractional elements. Coefficients of elements in the generalized fractional Maxwell model are determined to be fitting into experimental data in frequency domain. The homogenized stress strain relation in time domain given by inverse Laplace transform is derived and numerical calculations are carried out.

Relaxation modulus in PMMA and PTFE fitting by fractional Maxwell model

2002 ◽  
Vol 21 (3) ◽  
pp. 325-331 ◽  
Author(s):  
A. Hernández-Jiménez ◽  
J. Hernández-Santiago ◽  
A. Macias-Garcı́a ◽  
J. Sánchez-González
Keyword(s):  
Relaxation Modulus ◽  
Maxwell Model ◽  
Fractional Maxwell Model
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