scholarly journals Energetic Formulation of Large-Deformation Poroelasticity

2022 ◽  
Author(s):  
Mina Karimi ◽  
Mehrdad Massoudi ◽  
Noel Walkington ◽  
Matteo Pozzi ◽  
Kaushik Dayal
Keyword(s):  
Free Energy ◽  
Large Deformation ◽  
Co2 Sequestration ◽  
Fluid Transport ◽  
Solid Phase ◽  
Free Energy Density ◽  
Numerical Approach ◽  
Nonlinear Constitutive Model ◽  
Energetic Formulation ◽  
Geomechanical Process

The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance, that include fracturing or damage of the solid phase, require a nonlinear description of the large deformations that can occur. This paper presents a variational energy-based continuum mechanics framework to model large-deformation poroelasticity. The approach begins from the total free energy density that is additively composed of the free energy of the components. A variational procedure then provides the balance of momentum, fluid transport balance, and pressure relations. A numerical approach based on finite elements is applied to analyze the behavior of saturated and unsaturated porous media using a nonlinear constitutive model for the solid skeleton. Examples studied include the Terzaghi and Mandel problems; a gas-liquid phase-changing fluid; multiple immiscible gases; and unsaturated systems where we model injection of fluid into soil. The proposed variational approach can potentially have advantages for numerical methods as well as for combining with data-driven models in a Bayesian framework.

scholarly journals A nonlinear strain-rate dependent constitutive model for uncured rubber materials under large deformation

2020 ◽  
Vol 37 ◽  
pp. 118-125
Author(s):  
Weihua Zhou ◽  
Changqing Fang ◽  
Huifeng Tan ◽  
Huiyu Sun
Keyword(s):  
Constitutive Model ◽  
Large Deformation ◽  
Mechanical Response ◽  
Uniaxial Tensile ◽  
Hysteresis Phenomenon ◽  
Mechanical Behaviors ◽  
Nonlinear Constitutive Model ◽  
Rate Dependent ◽  
Parallel Networks ◽  
Non Gaussian

Abstract Uncured rubber possesses remarkable hyperelastic and viscoelastic properties while it undergoes large deformation; therefore, it has wide application prospects and attracts great research interests from academia and industry. In this paper, a nonlinear constitutive model with two parallel networks is developed to describe the mechanical response of uncured rubber. The constitutive model is incorporated with the Eying model to describe the hysteresis phenomenon and viscous flow criterion, and the hyperelastic properties under large deformation are captured by a non-Gaussian chain molecular network model. Based on the model, the mechanical behaviors of hyperelasticity, viscoelasticity and hysteresis under different strain rates are investigated. Furthermore, the constitutive model is employed to estimate uniaxial tensile, cyclic loading–unloading and multistep tensile relaxation mechanical behaviors of uncured rubber, and the prediction results show good agreement with the test data. The nonlinear mechanical constitutive model provides an efficient method for predicting the mechanical response of uncured rubber materials.

Thermodynamical study of (CaGa2S4)x(BaGa2S4)1−x solid solutions

2021 ◽  
pp. 2150469
Author(s):  
T. G. Naghiyev ◽  
R. M. Rzayev
Keyword(s):  
Free Energy ◽  
Solid Solutions ◽  
Calculation Method ◽  
Solid Phase ◽  
Ternary Compounds ◽  
Free Energy Of Formation ◽  
Concentration Dependences ◽  
Solid Phase Reactions ◽  
Two Phases ◽  
Energy Of Formation

The solid solutions of [Formula: see text] were synthesized by solid-phase reactions from powder components of CaS, BaS, and Ga2S3. The temperature-concentration dependences of the Gibbs free energy of formation of [Formula: see text] solid solutions from ternary compounds and phase diagrams of the CaGa2S4–BaGa2S4 were determined by a calculation method. It was revealed that continuous solid solutions are formed in these systems. The spinodal decomposition of [Formula: see text] solid solutions into two phases is predicted at ordinary temperatures.

Alignment of carbon nanotubes under the influences of nematic liquid crystals and electric fields — an analytical study

2021 ◽  
Author(s):  
Setia Budi Sumandra ◽  
Bhisma Mahendra ◽  
Fahrudin Nugroho ◽  
Yusril Yusuf
Keyword(s):  
Carbon Nanotubes ◽  
Free Energy ◽  
Electric Field ◽  
Electric Fields ◽  
Analytical Study ◽  
Free Energy Density ◽  
Diameter Ratio ◽  
Order Parameters ◽  
Anchoring Strength ◽  
Length To Diameter Ratio

Carbon nanotubes (CNTs) have benefits in various fields, they are disadvantageous due to their tendency to form aggregates and poorly controlled alignment of the CNT molecules (characterized by order parameters). These deficiencies can be overcome by dispersing the CNTs in nematic liquid crystal (LC) and placing the mixture under the influence of an electric field. In this study, Doi and Landau–de Gennes free energy density equations are used to analytically confirm that an electric field increases the order parameters of CNTs and LCs in a dispersion mixture. The anchoring strength of the nematic LC is also found to affect the order parameters of the CNTs and LC. Further, increasing the length-to-diameter ratio of the CNTs increases their alignment without affecting the LC alignment. These findings indicate that CNT molecular alignment can be controlled by adjusting the CNT length-to-diameter ratio, anchoring the LCs, and adjusting the electric field strength.

On nematic surface energies

1997 ◽  
Vol 8 (3) ◽  
pp. 293-299 ◽  
Author(s):  
SANDRO FAETTI ◽  
EPIFANIO G. VIRGA
Keyword(s):  
Free Energy ◽  
Liquid Crystal ◽  
Energy Density ◽  
Continuum Theory ◽  
Free Energy Density ◽  
Optic Axis ◽  
Principal Curvatures ◽  
Equilibrium Equations ◽  
Line Integral ◽  
Surface Energies

We review the main outcomes of a continuum theory for the equilibrium of the interface between a nematic liquid crystal and an isotropic environment, in which the surface free energy density bears terms linear in the principal curvatures of the interface. Such geometric contributions to the energy occur together with more conventional elastic contribution, leading to an effective azimuthal anchoring of the optic axis, which breaks the isotropic symmetry of the interface. The theory assumes the interface to be fixed, as for a rigid cavity filled with liquid crystal, and so it does not apply to drops. It should be appropriate when the curvatures of the interface are small compared to that of the molecular interaction sphere. Also, interfaces bearing a sharp edge are encompassed within the theory; a line integral expresses the energy condensed along the edge: we see how it affects the equilibrium equations.

scholarly journals Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density

2019 ◽  
Vol 31 (17) ◽  
pp. 175101
Author(s):  
Stiven Villada-Gil ◽  
Viviana Palacio-Betancur ◽  
Julio C Armas-Pérez ◽  
Juan J de Pablo ◽  
Juan P Hernández-Ortiz
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Phase Transitions ◽  
Liquid Crystals ◽  
Energy Density ◽  
Free Energy Density ◽  
Landau Free Energy ◽  
Biaxial Liquid Crystals
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