A Theory of Coupled Anisothermal Chemomechanical Degradation for Finitely-Deforming Composite Materials with Higher-Gradient Interactive Forces

Hall, Richard B.

doi:10.1007/978-3-319-41543-7_13

Cited by 1 publication

(4 citation statements)

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“…The constitutive relation for the interactive force is a higher order relation as it involves second‐order derivatives of the displacement fields. As indicated by Hall , the components of the interactive forces reflect a change of sign when the constituents are interchanged.…”

Section: Mixture Theory Governing Equationsmentioning

confidence: 98%

“…The constitutive relations for the mixture theory are obtained through maximization of the rate of dissipation constraint with respect to state variables

s [t] = ({}, {bold-italicF}^{m}, {bold-italicF}^{r}, ρ^{m}, ρ^{r}) [t]

. Details for this derivation can be seen in . Here, we present the summary of the constitutive relations, where the volume additivity constraint is not imposed.…”

Section: Mixture Theory Governing Equationsmentioning

confidence: 99%

“…Interactive force is required for force balance of a given constituent as obtained from both the surface tractions on a representative element and the interacting constituents within the element. Interactive force in the matrix domain under isothermal conditions is given by (15) and is a function of both matrix and fiber displacement fields. The constitutive relation for the interactive force is a higher order relation as it involves second-order derivatives of the displacement fields.…”

Section: Remarkmentioning

confidence: 99%

“…Although these constituent particles occupy different spatial points as the material deforms, the interactions between constituents are evaluated in the reference configuration using the composite particle. Hall and Rajagopal [14,15] proposed a mixture model for diffusion of chemically reacting fluids through anisotropic solids based on the maximization of the rate of entropy production constraint, considering anisotropic effective reaction rates and the limits of diffusion-dominated (diffusion of the reactants is far more rapid than the reaction) and reaction-dominated (the reaction is far more rapid than the diffusion of the reactants) processes. In the present work, the theory by Hall and Rajagopal [14,15] is enhanced to the case of a mixture of two interacting solid constituents, and an edge-stabilized method is developed to numerically model mixture-based fibrous composite systems.A general preface of the mixture theory is that the constituents are assumed to coexist over each other at every point in the domain, a condition that arises because of the volumetric homogenization of each constituent over the composite/mixture domain.…”

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confidence: 99%

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Edge stabilization and consistent tying of constituents at Neumann boundaries in multi‐constituent mixture models

Gajendran

Hall

Masud

2017

Numerical Meth Engineering

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Summary A mixture‐theory‐based model for multi‐constituent solids is presented where each constituent is governed by its own balance laws and constitutive equations. Interactive forces between constituents that emanate from maximization of entropy production inequality provide the coupling between constituent‐specific balance laws and constitutive models. The deformation of multi‐constituent mixtures at the Neumann boundaries requires imposing inter‐constituent coupling constraints such that the constituents deform in a self‐consistent fashion. A set of boundary conditions is presented that accounts for the non‐zero applied tractions, and a variationally consistent method is developed to enforce inter‐constituent constraints at Neumann boundaries in the finite deformation context. The new method finds roots in a local multiscale decomposition of the deformation map at the Neumann boundary. Locally satisfying the Lagrange multiplier field and subsequent modeling of the fine scales via edge bubble functions result in closed‐form expressions for a generalized penalty tensor and a weighted numerical flux that are free from tunable parameters. The key novelty is that the consistently derived constituent coupling parameters evolve with material and geometric nonlinearity, thereby resulting in optimal enforcement of inter‐constituent constraints. Various benchmark problems are presented to validate the method and show its range of application. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Mixture Theory Governing Equationsmentioning

confidence: 98%

“…The constitutive relations for the mixture theory are obtained through maximization of the rate of dissipation constraint with respect to state variables

s [t] = ({}, {bold-italicF}^{m}, {bold-italicF}^{r}, ρ^{m}, ρ^{r}) [t]

. Details for this derivation can be seen in . Here, we present the summary of the constitutive relations, where the volume additivity constraint is not imposed.…”

Section: Mixture Theory Governing Equationsmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

mentioning

confidence: 99%

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