VTN-phase stability testing using the Branch and Bound strategy and the convex-concave splitting of the Helmholtz free energy density

2020 ◽  
Vol 504 ◽  
pp. 112323
Author(s):  
Tomáš Smejkal ◽  
Jiří Mikyška
Keyword(s):  
Free Energy ◽  
Energy Density ◽  
Branch And Bound ◽  
Phase Stability ◽  
Helmholtz Free Energy ◽  
Free Energy Density ◽  
Stability Testing

Constitutive Relations for Pressure-Driven Stiffening in Poroelastic Tissues

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Adam M. Reeve ◽  
Martyn P. Nash ◽  
Andrew J. Taberner ◽  
Poul M. F. Nielsen
Keyword(s):  
Free Energy ◽  
Energy Density ◽  
Constitutive Relation ◽  
Helmholtz Free Energy ◽  
Perfusion Pressure ◽  
Constitutive Relations ◽  
Swelling Pressure ◽  
Free Energy Density ◽  
Simple Shear Deformation ◽  
Pressure Driven

Vascularized biological tissue has been shown to increase in stiffness with increased perfusion pressure. The interaction between blood in the vasculature and other tissue components can be modeled with a poroelastic, biphasic approach. The ability of this model to reproduce the pressure-driven stiffening behavior exhibited by some tissues depends on the choice of the mechanical constitutive relation, defined by the Helmholtz free energy density of the skeleton. We analyzed the behavior of a number of isotropic poroelastic constitutive relations by applying a swelling pressure, followed by homogeneous uniaxial or simple-shear deformation. Our results demonstrate that a strain-stiffening constitutive relation is required for a material to show pressure-driven stiffening, and that the strain-stiffening terms must be volume-dependent.

A Thermodynamic-Consistent Model for the Thermo-Chemo-Mechanical Couplings in Amorphous Shape-Memory Polymers

2021 ◽  
pp. 2150022
Author(s):  
Lu Dai ◽  
Rui Xiao
Keyword(s):  
Free Energy ◽  
Energy Density ◽  
Shape Memory ◽  
Helmholtz Free Energy ◽  
Chemical Potential ◽  
Shape Memory Polymers ◽  
Free Energy Density ◽  
Entropy Inequality ◽  
Limited Attention ◽  
Solvent Molecules

Chemically-responsive amorphous shape-memory polymers (SMPs) can transit from the temporary shape to the permanent shape in responsive to solvents. This effect has been reported in various polymer-solvent systems. However, limited attention has been paid to the constitutive modeling of this behavior. In this work, we develop a fully thermo-chemo-mechanical coupled thermodynamic framework for the chemically-responsive amorphous SMPs. The framework shows that the entropy, the chemical potential and the stress can be directly obtained if the Helmholtz free energy density is defined. Based on the entropy inequality, the evolution equation for the viscous strain, the temperature and the number of solvent molecules are also derived. We also provide an explicit form of Helmholtz free energy density as an example. In addition, based on the free volume concept, the dependence of viscosity and diffusivity on the temperature and solvent concentration is defined. The theoretical framework can potentially advance the fundamental understanding of chemically-responsive shape-memory effect. Meanwhile, it can also be used to describe other important physical processes such as the diffusion of solvents in glassy polymers.

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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