Showing papers on "Mixture theory published in 2021"

A combined viscoelasticity-viscoplasticity-anisotropic damage model with evolving internal state variables applied to fiber reinforced polymer composites

Abstract: A thermodynamically-consistent large strain viscoelasticity-viscoplasticity-damage Internal State Variable (ISV) constitutive material model integrated with a mixture theory combining each individu...

A macro-microscopic coupled constitutive model for fluid-saturated porous media with compressible constituents.

Abstract: The paper provides a macro-microscopic coupled constitutive model for fluid-saturated porous media with respect to the compressibility of the solid skeleton, the real solid material and the fluid phase. The derivation of the model is carried out based on the theory of porous media and is consistent with the second law of thermodynamics. Unlike some traditional concepts, in the present paper, two different sets of independent variables are introduced to implement the coupled behavior between the compressibility of the solid skeleton and the real solid material. Altogether the proposed model exploits five independent variables, i.e. the deviatoric part of the right Cauchy-Green deformation tensor, the partial density of solid phase, the density of the real solid material, the density of the real fluid material and the relative velocity of the fluid phase. Subsequently, the linearized version of the proposed constitutive model is also presented and compared with some models by other authors. It is found that Biot's model can also be derived based on the proposed model, which indicates the present work bridges the gap between the theory of porous media and the theory used in the model by Biot.

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

Abstract: This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook (2007), Subramaniam et al., (2018), and Adler and Lele (2019), in which artificial diffusion terms are added to the conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al., (2010) and Tiwari et al., (2013), in which the diffusion and sharpening terms (together called regularization terms) are added to the conservation equations. The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al., (2020), in which the regularization terms are added to the conservation equations. The primary objective of this work is to compare these three methods in terms of their ability to maintain: constant interface thickness; the conservation property; and accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer-Meshkov instability of a copper-aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. This is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.

On the Evolution of a Plane Harmonic Wave in a Nonlinear Elastic Composite Material Modeled by a Two-Phase Mixture*

Abstract: A nonlinear plane longitudinal elastic displacement wave is studied theoretically within the framework of the Murnaghan model for a harmonic initial profile. The main novelty is that the evolution of waves is analyzed by the developed approximate method of constraints on the displacement gradient within the framework of two-phase mixture theory. It is shown that the initially excited wave is divided into four modes, all modes are dispersed and distorted, and each mode wave is represented as a superposition of the first and second harmonics. The amplitude of the second harmonic depends on many parameters, including the direct dependence on time. This dependence means that the second harmonic will dominate over time.

Unified analysis of Navier-Stokes Cahn-Hilliard models with non-matching densities.

Abstract: Over the last decades, many diffuse-interface Navier-Stokes Cahn-Hilliard models with non-matching densities have appeared in the literature. These models claim to describe the same physical phenomena, yet they are distinct from one another. The overarching objective of this work is to bring all of these models together by laying down a unified framework of Navier-Stokes Cahn-Hilliard models. Our development is based on three principles: (1) there is only one system of balance laws based on continuum mixture theory that describes the physical model, (2) there is only one natural energy-dissipation law that leads to quasi-incompressible Navier-Stokes Cahn-Hilliard models, (3) variations between the models only appear in the constitutive choices. A further aim of our work is to highlight the inconsistency of existing volume-averaged velocity based models with respect to mixture theory, and to present a consistent rectification. Moreover, we identify the mobility to be of degenerate type and illustrate that a non-degenerate mobility leads to incompatibility of Navier-Stokes Cahn-Hilliard models in the limit of the single-fluid regime. The framework presented in this work now completes the fundamental exploration of alternate non-matching density Navier-Stokes Cahn-Hilliard models that utilize a single momentum equation for the mixture velocity, but leaves open room for further sophistication in the energy functional and constitutive dependence.