A dynamic phase-field model for structural transformations and twinning: Regularized interfaces with transparent prescription of complex kinetics and nucleation. Part I: Formulation and one-dimensional characterization

Agrawal, Vaibhav; Dayal, Kaushik

doi:10.1016/j.jmps.2015.04.010

Cited by 30 publications

(14 citation statements)

References 46 publications

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“…where we have used that dφ i dt = 0 and dx dt = 0 per our quasistatic model. We have assumed that the boundary terms vanish for simplicity, but they can easily be accounted for following, e.g., [PF90,AD15a].…”

Section: F Compatibility With the Second Law Of Thermodynamicsmentioning

confidence: 99%

“…To ensure that the proposed model is consistent with the second law of thermodynamics, we first notice that in an isothermal setting it reduces to the requirement that the dissipation is non-negative for any process. 45 Following prior works, [46][47][48][49][50][51][52] we begin by taking the time derivative of the free energy from (3) to get:…”

Section: Compatibility With the Second Law Of Thermodynamicsmentioning

confidence: 99%

“…We have assumed that the boundary terms vanish for simplicity, but they can easily be accounted for following, prior works. 46,51 From Section 2.3, we can push back the balance of mass to the reference configuration to obtain:…”

Section: Compatibility With the Second Law Of Thermodynamicsmentioning

confidence: 99%

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Energetic formulation of large‐deformation poroelasticity

Karimi

Massoudi

Walkington

et al. 2022

Num Anal Meth Geomechanics

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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 phasechanging 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.

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Section: F Compatibility With the Second Law Of Thermodynamicsmentioning

confidence: 99%

Section: Compatibility With the Second Law Of Thermodynamicsmentioning

confidence: 99%

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Energetic formulation of large‐deformation poroelasticity

Karimi

Massoudi

Walkington

et al. 2022

Num Anal Meth Geomechanics

Self Cite

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“…This approach corresponds to static equilibrium with respect to stress fields and conjugate forces to order parameters; hence, propagation speeds of crack fronts and twin boundaries are not quantitatively reproduced. Phase field formulations fully accounting for inertia and time-dependent kinetics are discussed elsewhere for brittle fracture [ 35 , 36 ] and deformation twinning [ 37 , 38 ]. Elastic strain energy density is expressed in terms of a linearized strain tensor, a representation assumed sufficient for problems of brittle fracture addressed herein, to be contemplated further upon inspection of numerical results.…”

Section: Phase Field Theory: Bulk Grains and Matrix Materialsmentioning

confidence: 99%

A Multi-Scale Approach for Phase Field Modeling of Ultra-Hard Ceramic Composites

et al. 2021

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Diamond-silicon carbide (SiC) polycrystalline composite blends are studied using a computational approach combining molecular dynamics (MD) simulations for obtaining grain boundary (GB) fracture properties and phase field mechanics for capturing polycrystalline deformation and failure. An authentic microstructure, reconstructed from experimental lattice diffraction data with locally refined discretization in GB regions, is used to probe effects of local heterogeneities on material response in phase field simulations. The nominal microstructure consists of larger diamond and SiC (cubic polytype) grains, a matrix of smaller diamond grains and nanocrystalline SiC, and GB layers encasing the larger grains. These layers may consist of nanocrystalline SiC, diamond, or graphite, where volume fractions of each phase are varied within physically reasonable limits in parametric studies. Distributions of fracture energies from MD tension simulations are used in the phase field energy functional for SiC-SiC and SiC-diamond interfaces, where grain boundary geometries are obtained from statistical analysis of lattice orientation data on the real microstructure. An elastic homogenization method is used to account for distributions of second-phase graphitic inclusions as well as initial voids too small to be resolved individually in the continuum field discretization. In phase field simulations, SiC single crystals may twin, and all phases may fracture. The results of MD calculations show mean strengths of diamond-SiC interfaces are much lower than those of SiC-SiC GBs. In phase field simulations, effects on peak aggregate stress and ductility from different GB fracture energy realizations with the same mean fracture energy and from different random microstructure orientations are modest. Results of phase field simulations show unconfined compressive strength is compromised by diamond-SiC GBs, graphitic layers, graphitic inclusions, and initial porosity. Explored ranges of porosity and graphite fraction are informed by physical observations and constrained by accuracy limits of elastic homogenization. Modest reductions in strength and energy absorption are witnessed for microstructures with 4% porosity or 4% graphite distributed uniformly among intergranular matrix regions. Further reductions are much more severe when porosity is increased to 8% relative to when graphite is increased to 8%.

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“…There are distinct model parameters that correspond to each of these, i.e., we can specify the equilibrium response, the kinetics of interfaces, and the nucleation of interfaces independently. This model was proposed recently in [AD15a].…”

Section: Interface Motion In Existing Phase-field Modelsmentioning

confidence: 99%

Phase-Field Modeling and Peridynamics for Defect Dynamics, and an Augmented Phase-Field Model with Viscous Stresses

Chua,

Agrawal,

Breitzman

et al. 2021

Preprint

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This work begins by applying peridynamics and phase-field modeling to predict 1-d interface motion with inertia in an elastic solid with a non-monotone stress-strain response. In classical nonlinear elasticity, it is known that subsonic interfaces require a kinetic law, in addition to momentum balance, to obtain unique solutions; in contrast, for supersonic interfaces, momentum balance alone is sufficient to provide unique solutions. This work finds that peridynamics agrees with this classical result, in that different choices of regularization parameters provide different kinetics for subsonic motion but the same kinetics for supersonic motion. In contrast, conventional phase-field models coupled to elastodynamics are unable to model, even qualitatively, the supersonic motion of interfaces. This work identifies the shortcomings in the physics of standard phase-field models to be: (1) the absence of higher-order stress to balance unphysical stress singularities, and (2) the ability of the model to access unphysical regions of the energy landscape.Based on these observations, this work proposes an augmented phase-field model to introduce the missing physics. The augmented model adds: (1) a viscous stress to the momentum balance, in addition to the dissipative phase-field evolution, to regularize singularities; and (2) an augmented driving force that models the physical mechanism that keeps the system out of unphysical regions of the energy landscape. When coupled to elastodynamics, the augmented model correctly describes both subsonic and supersonic interface motion. The augmented model has essentially the same computational expense as conventional phase-field models and requires only minor modifications of numerical methods, and is therefore proposed as a replacement to the conventional phase-field models.

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A dynamic phase-field model for structural transformations and twinning: Regularized interfaces with transparent prescription of complex kinetics and nucleation. Part I: Formulation and one-dimensional characterization

Cited by 30 publications

References 46 publications

Energetic formulation of large‐deformation poroelasticity

Energetic formulation of large‐deformation poroelasticity

A Multi-Scale Approach for Phase Field Modeling of Ultra-Hard Ceramic Composites

Phase-Field Modeling and Peridynamics for Defect Dynamics, and an Augmented Phase-Field Model with Viscous Stresses

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