Journal ArticleDOI
Diffusion of chemically reacting fluids through nonlinear elastic solids: Mixture model and stabilized methods
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In this article, a stabilized mixed finite element method for advection-diffusion-reaction phenomena that involve an anisotropic viscous fluid diffusing and chemically reacting with an elastic solid is presented.Abstract:
This paper presents a stabilized mixed finite element method for advection-diffusion-reaction phenomena that involve an anisotropic viscous fluid diffusing and chemically reacting with an anisotropic elastic solid. The reactive fluid–solid mixture theory of Hall and Rajagopal (Diffusion of a fluid through an anisotropically chemically reacting thermoelastic body within the context of mixture theory. Math Mech Solid 2012; 17: 131–164) is employed wherein energy and entropy production relations are captured via an equation describing the Lagrange multiplier that results from imposing the constraint of maximum rate of entropy production. The primary partial differential equations are thus reduced to the balance of mass and balance of linear momentum equations for the fluid and the solid, together with an equation for the Lagrange multiplier. Present implementation considers a simplification of the full system of governing equations in the context of isothermal problems, although anisothermal studies are bein...read more
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ナノパーティクルテクノロジーハンドブック = Nanoparticle technology handbook
ナノパーティクルテクノロジーハンドブック編集委員会,益男 細川 +1 more
TL;DR: In this paper, the authors discuss the effect of gender stereotypes on the performance of women in the field of computer games, and propose a method to improve gender equality in video games.
Journal ArticleDOI
A unified mixture formulation for density and volumetric growth of multi-constituent solids in tissue engineering
Timothy J. Truster,Arif Masud +1 more
TL;DR: A unified computational method is developed for the modeling of growth in hard and soft biological tissues using a mixture theory approach, whereby a polymeric scaffold is infused by cells and cross-linking proteins to modeling concurrent and coexisting constituents.
Journal ArticleDOI
Chemo-mechanical coupling and material evolution in finitely deforming solids with advancing fronts of reactive fluids
TL;DR: In this paper, a mixture theory model is employed for coupled chemo-mechanical problems involving chemically reacting fluids flowing through deformable elastic solids, where the constitutive relations for the constituents in the mixture model are based on maximization of the rate of entropy production.
Journal ArticleDOI
Chemo-mechanical coupling in curing and material-interphase evolution in multi-constituent materials
TL;DR: In this article, a mixture model for curing and interphase evolution is presented that is based on a consistent thermodynamic theory for multi-constituent materials, cast in a stabilized finite element method that is developed employing variational multi-scale ideas for edge-based stabilization and consistent tying of the constituents at domain boundaries.
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Modeling Approaches and Some Physical Considerations Concerning Thermodynamics and the Theory of Mixtures Applied to Time-Dependent Behaviors in Heterogeneous Materials
TL;DR: Following a brief review of the theory of continuum mixtures, recent developments and applications emphasizing time-dependent behaviors of heterogeneous materials are described, and remarks are made concerning related homogenization and thermodynamic developments.
References
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Journal ArticleDOI
Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
TL;DR: In this paper, an approach is developed for deriving variational methods capable of representing multiscale phenomena, which leads to the well-known Dirichlet-to-Neumann formulation.
Journal ArticleDOI
Lagrangian-Eulerian finite element formulation for incompressible viscous flows☆
TL;DR: In this paper, a finite element formulation for incompressible viscous flows in an arbitrarily mixed Lagrangian-Eulerian description is given for modeling the fluid subdomain of many fluid-solid interaction, and free surface problems.
Journal ArticleDOI
Continuum theories of mixtures: basic theory and historical development
R. J. Atkin,R. E. Craine +1 more
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A constrained mixture model for growth and remodeling of soft tissues
TL;DR: It was thought that the most important characteristics of soft tissues were their complex mechanical properties: they often exhibit nonlinear, anisotropic, nearly incoherent, and often incoherent properties as discussed by the authors.
Book
Mechanics of Mixtures
TL;DR: In this article, a discussion of a mixture of immiscible fluids is given, and the status of Darcy's law within the context of mixture theory is discussed. And the entropy inequality constitutive theory steady state problems diffusing singular surface wave propagation in solids infused with fluids are discussed.