Continuum Field Research Articles

Quantized Axial Charge of Staggered Fermions and the Chiral Anomaly.

In the 1+1D ultralocal lattice Hamiltonian for staggered fermions with a finite-dimensional Hilbert space, there are two conserved, integer-valued charges that flow in the continuum limit to the vector and axial charges of a massless Dirac fermion with a perturbative anomaly. Each of the two lattice charges generates an ordinary U(1) global symmetry that acts locally on operators and can be gauged individually. Interestingly, they do not commute on a finite lattice and generate the Onsager algebra, but their commutator goes to zero in the continuum limit. The chiral anomaly is matched by this non-Abelian algebra, which is consistent with the Nielsen-Ninomiya theorem. We further prove that the presence of these two conserved lattice charges forces the low-energy phase to be gapless, reminiscent of the consequence from perturbative anomalies of continuous global symmetries in continuum field theory. Upon bosonization, these two charges lead to two exact U(1) symmetries in the XX model that flow to the momentum and winding symmetries in the free boson conformal field theory.

Anisotropic interactions for continuum modeling of protein-membrane systems.

In this work, a model for anisotropic interactions between proteins and cellular membranes is proposed for large-scale continuum simulations. The framework of the model is based on dynamic density functional theory, which provides a formalism to describe the lipid densities within the membrane as continuum fields while still maintaining the fidelity of the underlying molecular interactions. Within this framework, we extend recent results to include the anisotropic effects of protein-lipid interactions. As applications, we consider two membrane proteins of biological interest: a RAS-RAF complex tethered to the membrane and a membrane embedded G protein-coupled receptor. A strong qualitative and quantitative agreement is found between the numerical results and the corresponding molecular dynamics simulations. Combining the scope of continuum level simulations with the details from molecular level particle simulations enables research into protein-membrane behaviors at a more biologically relevant scale, which crucially can also be accessed via experiment.

Density-Nematic Coupling in Isotropic Solution of DNA: Multiscale Model.

Monte Carlo simulations of isotropic solutions of double-stranded DNA (deoxyribonucleic acid) are performed using the well-established oxDNA model. By comparing the fluctuation amplitudes with theoretical predictions, the parameters of a generic macroscopic model of an isotropic linear polymer solution/melt are determined. A multiscale continuum field model is thus obtained, corresponding to the full specificity of the isotropic phase of double-stranded DNA in the usual B-form as perceived at the macroscopic level. Present research is particularly focused on the coupling between spatial concentration/density variations of the polymer and the emerging nematic orientation order of the chains. This rather unfamiliar, only recently described phenomenon, inherent to linear polymers, is outlined and interpreted. Quantitative predictions are provided for the degree of nematic order induced by concentration gradients in isotropic solutions of double-strandedDNA.

Micromechanics-based variational phase-field modeling of fatigue fracture

In this paper, we extend the micromechanics-based phase-field model to simulate fatigue failure. The coupling of a micromechanics-based framework with the phase-field approach helps to differentiate between failure modes, by distinguishing between open and closed microcracks. This integrated framework links continuum field variables, such as plastic strain and damage variable, to micromechanical mechanisms like frictional sliding and microcrack opening. We first improve the algorithm’s stability during loading–unloading in the tensile regime through a modification of the plasticity evolution equations. Next, we incorporate fatigue damage accumulation and deterioration due to cyclic loading into the micromechanics-based phase-field model. A fatigue degradation function, driven by free energy accumulation, is introduced to degrade the fracture energy upon reaching a specified threshold during cyclic loading. Various cyclic loads are applied to benchmark tests, both with and without imperfections (e.g. holes, inclusions, voids), under plane strain conditions to capture diverse failure modes. The results demonstrate the model’s capability to accurately describe tensile, shear, and mixed-mode fracture under cyclic loading. Furthermore, the model effectively simulates key features of fatigue behavior, including crack nucleation, growth, and coalescence.

Thermoelastic diffusion based on a nonlocal three-phase-lag diffusion model with double porosity structure

This work aims to develop a new diffusion-elasticity-based model using Eringen’s nonlocal elasticity theory under the purview of the three-phase-lag (TPL) model of hyperbolic thermoelasticity. This problem is treated in the context of a double porosity structure in a homogeneous, isotropic thermoelastic medium. By considering the phase laggings of the diffusion flux vector and using nonlocal continuum mechanics, new constitutive and field equations are derived. The problem is solved by employing the normal mode analysis technique which gives the exact results of all the physical variables. To illustrate the theoretical results, different physical quantities are calculated numerically and presented graphically with respect to distance and time. The influences of different thermoelastic models like TPL (three-phase-lag model), GN-III (Green-naghdi model), DPL (dual-phase-lag model), LS (Lord-Shulman model), and CT (coupled thermoelasticity) on the physical quantities are shown graphically. Additionally, the effects of nonlocal parameters, double voids, and diffusion on the physical quantities are represented graphically. Some limiting and particular cases are also derived from the governing equations and those results have been compared with the existing results available in the literature. Some 3D surface curves are also presented to study the impact of diffusion, nonlocality, and double voids on various physical quantities.

Investigation of surface roughness effects on the dynamic performance of electromagnetic nano-resonators

Here, we expose the influence of surface roughness on the dynamics of electromagnetic nano-resonators. To this end, the continuum field equations of an electromechanical nano-resonator subjected to an external magnetic flux are formulated. The developed model considers surface integrity, including surface roughness, waviness, and altered layer. Also, the influence of residual stresses of the extreme surfaces of the resonator is incorporated in the proposed model. It was revealed that the surface roughness significantly tailors the dynamic stability of the resonator, as the voltage that onsets the pull-in instability of the resonator decreases as the surface roughness increases, which thus indicates the necessity of particular calibrations of nano-resonators for surface roughness. To investigate the problem and the effect of factors such as magnetic field intensity, roughness, and beam surface thickness on the pull-in voltage, we have performed an analysis using the Taguchi method and analysis of variance. The results show that the intensity of the magnetic field has the most significant effect on pull-in voltage. Also, the more accurate results show on the resonance frequency; with the increase of the input voltage to the beam, the impact of increasing the intensity of the magnetic field and other factors increases. The rest of the paper proposes a linear and non-linear model to express the pull-in voltage according to the investigated factors.

Identification of the continuum field structure at multiple scale levels.

For continuum fields such as turbulence, analyses of the field structure offer insights into their kinematic and dynamic properties. To ensure the analyses are quantitative rather than merely illustrative, two conditions are essential: space-filling and structure quantification. A pertinent example is the dissipation element (DE) structure, which is however susceptible to noisy interference, rendering it inefficient for extracting the large-scale features of the field. In this study, the multi-level DE structure is proposed based on the multi-level extremal point concept. At a given scale level, the entire field can be decomposed into the corresponding space-filling and non-overlapping DEs, each characterized by its length scale l and the scalar difference Δϕ between its two extremal points. We will first elaborate on the fundamental principles of this method. Results from an artificially constructed two-scale field indicate that the decomposed units adequately represent the geometry of the original field. In examining the fractal Brownian motion, a structure function equivalent ⟨Δϕ|l⟩ and an energy spectrum equivalent are introduced. The scaling relation derived from ⟨Δϕ|l⟩ corresponds with the Hurst number. Furthermore, the multi-level DE structure distinctly reveals the two different inertial ranges in two-dimensional turbulence. Overall, this novel structure identification approach holds significant potential for complex analyses concerning the field geometry.

Continuum field theory of three-dimensional topological orders with emergent fermions and braiding statistics

Continuum field theory of three-dimensional topological orders with emergent fermions and braiding statistics

Atmospheric Interactions of Ejecta on Earth and Mars Including the Effect of Vaporization

Atmospheres play an important role in ejecta deposition after an impact event. Many impact experiments and simulations neglect the effect of atmospheres. We simulate ejecta plumes created by craters with transient diameters of 2 and 20 km on Mars and Earth, to show the effect atmospheric density and crater size have on the strength of the interaction. The interaction of ejecta with an atmosphere is explored in this study using a two-fluid hydrocode that simultaneously simulates ejecta and atmospheres as coupled, continuum fields to correctly capture the transfer of mass, energy, and momentum between the two. Here, we study the effect of vaporization of plume material as well as the effect of the bow shock. We find that only the fastest ejecta is vaporized with a peak vaporized mass of 2.5 × 105 kg, 3.5 s after the impact in our 2 km diameter terrestrial crater. Terrestrial meteorites are preferentially formed from the fastest ejecta. However, that fastest ejecta is mostly vaporized in our simulations, so to form a terrestrial meteorite, there must be a sufficiently large impact for solid material to be ejected and not vaporize. Thus, we place a lower limit of 33 km on the size of crater needed to generate terrestrial meteorites, but the crater size needed could be substantially larger. The bow shocks in our simulations result in lofting of ejecta, especially vaporized material, in the wake of the impactor.

Physics-informed neural network frameworks for crack simulation based on minimized peridynamic potential energy

Physics-informed neural networks (PINNs), which are promising tools for solving nonlinear equations in the absence of labeled data, have been successfully applied for continuum field approximation in fluid mechanics, solid mechanics, thermodynamics, and other scientific and engineering problems. However, it is equally necessary to solve discontinuous problems such as cracking behaviors in structures and materials, which are challenging to describe using partial differential equations in traditional solid mechanics frameworks. In this work, PINNs are established with the constraint of integral–differential equations in bond-based peridynamic to simulate crack initiation and propagation behaviors in quasi-brittle plates. To solve the cracking behaviors, the initial displacements of the plate are determined by minimizing the total potential energy through the optimization of global network parameters. The subsequent displacements during crack initiation or propagation are characterized by transfer learning to accelerate convergence. The simulated crack paths for four cases with or without precracks are consistent with those obtained in existing studies based on experiments or numerical simulations. Moreover, the effects of network regularization and neuron scales on the nonlinear displacement characterization performance are investigated.

Toupin–Mindlin first strain‐gradient elasticity for cubic and isotropic materials at small scales

AbstractThe Toupin–Mindlin anisotropic first strain‐gradient elasticity is a generalized continuum field theory valid at small scales. The field theoretical framework, the constitutive tensors, and the material parameters are given for anisotropic, cubic, and isotropic materials in first strain gradient elasticity. Since the characteristic lengths are in the unit‐range of Ångström, first strain‐gradient elasticity leads to Ångström mechanics, in a straightforward manner.

Strain gradient viscoelasticity theory of polymer networks

A physically-based strain gradient viscoelasticity theory is proposed specially for polymer networks, accounting for the strain gradient effect and the history-dependent behavior, where the microstructure-dependence and history-dependence of stress and hyperstress are interpreted physically and quantitatively. The chain representation of the Helmholtz free energy density is transferred to the strain gradient continuum field representation through the geometric (spatial) connection between the chain stretch ratio and the continuum deformation measure. The necessity of using strain gradients to characterize asymmetric deformation of the microstructure of polymer networks serves as the origin of microstructure-dependent hyperstress, which is work-conjugated to the strain gradient field. The free energy per chain is assumed history-dependent to account for chain-environment interactions (e.g., friction between segments), which ultimately results in the history-dependent behavior of polymeric solids. A general constitutive relation is provided, which together with the assumed network structure, gives a concrete one. It is shown that independent of the assumed network structure, the stress, and the hyperstress share the same dimensionless relaxation function. A strain gradient viscoelastic constitutive relation based on the eight-chain network is applied to the analysis of polymer nanocomposites, where the complex moduli are rationally defined and calculated numerically. It is found that the strain gradient effect can be viewed as an amplifier that transforms the strain-induced stress into the effective stress.

Strain Localization Patterns and Thrust Propagation in 3‐D Discrete Element Method (DEM) Models of Accretionary Wedges

AbstractHigh‐resolution three‐dimensional discrete element method (DEM) simulations of sandbox‐scale models of accretionary wedges suggest thrusts follow a variety of propagation processes and orientations depending on a number of factors. These include the stage of development of the wedge (precritical vs. critical), basal friction, and type of thrust (forward vs. backward‐vergent). In terms of propagation processes, two clear mechanisms are identified. The first involves propagation from the décollement to the wedge top, similar to the standard model of thrust propagation seen in many kinematic models, and in the second, thrusts grow downward from an initial nucleation point just below the top surface of the wedge as well as upward from the décollement joining in the middle. In terms of orientation, forward‐vergent thrusts initially form at Roscoe (θR = 45° − Ψ/2) or Arthur orientations (θA = 45° − (ϕ + Ψ)/4), and over greater shortening, rotate into Coulomb orientations (θC = 45° − ϕ/2). To arrive at these results, a wide array of continuum parameters and fields were extracted from the DEM simulations, including stress, strain, strain rate, kinetic energy, Mohr‐Coulomb parameters, and proximity to yielding using the Drucker‐Prager criterion to visualize thrust nucleation and propagation. Lastly, the advantages and disadvantages of these continuum proxies for discerning failure in the granular assembly are considered, and the spatial and temporal relationship between proximity to yielding and strain localization (both pre‐peak and subsequent persistent shear banding) in the granular model of an accretionary wedge is explored.

Coarse-grained methods for heterogeneous vesicles with phase-separated domains: Elastic mechanics of shape fluctuations, plate compression, and channel insertion

We develop coarse-grained particle approaches for studying the elastic mechanics of vesicles with heterogeneous membranes having phase-separated domains. We perform simulations both of passive shape fluctuations and of active systems where vesicles are subjected to compression between two plates or subjected to insertion into narrow channels. Analysis methods are developed for mapping particle configurations to continuum fields with spherical harmonics representations. Heterogeneous vesicles are found to exhibit rich behaviors where the heterogeneity can amplify surface two-point correlations, reduce resistance during compression, and augment vesicle transport times in channels. The developed methods provide general approaches for characterizing the mechanics of coarse-grained heterogeneous systems taking into account the roles of thermal fluctuations, geometry, and phase separation.

Short–Range Variation of Humus and Carbonate Profiles of Arable Chernozems (Key Site in Belgorod Region)

The short-range variation of soil properties is a particular expression of the spatial soil variability; it is non-directional short-periodic (in the range of a few meters) changes in soil-profile features. The short-range variation of soil properties is aimed to characterize the continuum nature of soil cover instead of the discrete (as in the soil cover pattern theory), thus the soil cover is presented by a continuum field of various soil properties, and the boundaries of the selected soil properties ranges may or may not coincide with the soil taxonomic boundaries. The study is based on soil data of three parallel transects (length 240 m) in the watershed, perpendicularly crossing the 60-year-old shelterbelt in their central part. The sampling step was 10 m on agricultural fields, 6 – under the shelterbelt; In total, the features of the humus (the content of organic carbon in the 0–20 cm layer, the thickness of the humus horizon and profile) and carbonate (the effervescence depth, the carbonate content in the effervescence layer and the horizon of maximum accumulation of carbonates) profiles were studied at 75 points. It was revealed that the parameters of the humus and carbonate profiles of soils have periodic changes with a step of 6–10 meters. The parameters of the humus profile are characterized by lower coefficients of variation (less than 30%) than the parameters of the carbonate profile of soils (more than 50%). The growth of trees on agrochernozems (Haplic Chernozem (Aric)) for 60 years led to the formation of new taxonomic components (postagrogenic agrochernozems (Haplic Chernozem)), characterized by a smaller lateral variation in soil properties compared to arable soils. In total, 3 types of soils are found within the studied area: agrochernozem (64 points; Haplic Chernozem (Aric, Loamic, Pachic)), clay-illuvial agrochernozem (7 points; Luvic Chernozem (Aric, Loamic, Pachic) and Luvic Chernic Phaeozem (Aric, Loamic, Pachic, Loamic, Pachic)) and agrochernozems, clay-illuvial quasigley (4 points; Luvic Stagnic Chernic Phaeozem (Aric, Loamic, Pachic)), including 8 subtypes.

Emergent higher-symmetry protected topological orders in the confined phase of U(1) gauge theory

We consider compact ${U}^{\ensuremath{\kappa}}(1)$ gauge theory in $3+1$ dimensions with a general $2\ensuremath{\pi}$-quantized topological term ${\ensuremath{\sum}}_{I,J=1}^{\ensuremath{\kappa}}\frac{{K}_{IJ}}{4\ensuremath{\pi}}{\ensuremath{\int}}_{{M}^{4}}{F}^{I}\ensuremath{\wedge}{F}^{J}$, where $K$ is an integer symmetric matrix with even diagonal elements and ${F}^{I}=d{A}^{I}$. At energies below the gauge charges' gaps but above the monopoles' gaps, this field theory has an emergent ${\mathbb{Z}}_{{k}_{1}}^{(1)}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{{k}_{2}}^{(1)}\ifmmode\times\else\texttimes\fi{}\ensuremath{\cdots}$ 1-symmetry, where ${k}_{i}$ are the diagonal elements of the Smith normal form of $K$ and ${\mathbb{Z}}_{0}^{(1)}$ is regarded as a $U(1)$ 1-symmetry. In the ${U}^{\ensuremath{\kappa}}(1)$ confined phase, the boundary can have a phase whose infrared (IR) properties are described by Chern-Simons field theory. Such a phase has a ${\mathbb{Z}}_{{k}_{1}}^{(1)}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{{k}_{2}}^{(1)}\ifmmode\times\else\texttimes\fi{}\ensuremath{\cdots}$ 1-symmetry that can be anomalous. To show these results, we develop a bosonic lattice model whose IR properties are described by this continuum field theory, thus acting as its ultraviolet completion. The lattice model in the aforementioned limit has an exact ${\mathbb{Z}}_{{k}_{1}}^{(1)}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{{k}_{2}}^{(1)}\ifmmode\times\else\texttimes\fi{}\ensuremath{\cdots}$ 1-symmetry. We find that the short-range entangled gapped phase of the lattice model, corresponding to the confined phase of the ${U}^{\ensuremath{\kappa}}(1)$ gauge theory, is a symmetry protected topological (SPT) phase for the ${\mathbb{Z}}_{{k}_{1}}^{(1)}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{{k}_{2}}^{(1)}\ifmmode\times\else\texttimes\fi{}\ensuremath{\cdots}$ 1-symmetry, whose SPT invariant is $\phantom{\rule{1.0pt}{0ex}}{e}^{\phantom{\rule{1.0pt}{0ex}}i\phantom{\rule{1.0pt}{0ex}}\ensuremath{\pi}{\ensuremath{\sum}}_{I,J}{K}_{IJ}{\ensuremath{\int}}_{{\mathcal{M}}^{4}}{B}_{I}\ensuremath{\smile}{B}_{J}+{B}_{I}\underset{1}{\ensuremath{\smile}}\phantom{\rule{1.0pt}{0ex}}d{B}_{J}}\phantom{\rule{1.0pt}{0ex}}{e}^{\phantom{\rule{1.0pt}{0ex}}i\phantom{\rule{1.0pt}{0ex}}\ensuremath{\pi}{\ensuremath{\sum}}_{I<J}{K}_{IJ}{\ensuremath{\int}}_{{\mathcal{M}}^{4}}\phantom{\rule{1.0pt}{0ex}}d{B}_{I}\underset{2}{\ensuremath{\smile}}\phantom{\rule{1.0pt}{0ex}}d{B}_{J}}$. Here, the background $\mathbb{R}/\mathbb{Z}$-valued 2-cochains ${B}_{I}$ satisfy $\phantom{\rule{1.0pt}{0ex}}d{B}_{I}={\ensuremath{\sum}}_{I}{B}_{I}{K}_{IJ}=0\phantom{\rule{3.33333pt}{0ex}}mod\phantom{\rule{0.28em}{0ex}}1$ and describe the symmetry twist of the ${\mathbb{Z}}_{{k}_{1}}^{(1)}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{{k}_{2}}^{(1)}\ifmmode\times\else\texttimes\fi{}\ensuremath{\cdots}$ 1-symmetry. We apply this general result to a few examples with simple $K$ matrices. We find the nontrivial SPT order in the confined phases of these models and discuss its classifications using the fourth cohomology group of the corresponding 2-group.

Quantum simulation of weak-field light-matter interactions

Simulation of the interaction of light with matter, including at the few-photon level, is important for understanding the optical and optoelectronic properties of materials, and for modeling next-generation non-linear spectroscopies that use entangled light. At the few-photon level the quantum properties of the electromagnetic field must be accounted for with a quantized treatment of the field, and then such simulations quickly become intractable, especially if the matter subsystem must be modeled with a large number of degrees of freedom, as can be required to accurately capture many-body effects and quantum noise sources. Motivated by this we develop a quantum simulation framework for simulating such light-matter interactions on platforms with controllable bosonic degrees of freedom, such as vibrational modes in the trapped ion platform. The key innovation in our work is a scheme for simulating interactions with a continuum field using only a few discrete bosonic modes, which is enabled by a Green's function (response function) formalism. We develop the simulation approach, sketch how the simulation can be performed using trapped ions, and then illustrate the method with numerical examples. Our work expands the reach of quantum simulation to important light-matter interaction models and illustrates the advantages of extracting dynamical quantities such as response functions from quantum simulations.

Investigating cohesive sediment dynamics in open waters via grain-resolved simulations

Cohesive particulate flows play an important role in environmental fluid dynamics, as well as in a wide variety of civil and process engineering applications. However, the scaling laws, constitutive equations and continuum field descriptions governing such flows are currently less well understood than for their non-cohesive counterparts. Grain-resolved simulations represent an essential tool for addressing this shortcoming, along with theoretical investigations, laboratory experiments and field studies. Here we provide a tutorial introduction to simulations of fine-grained sediments in viscous fluids, along with an overview of some representative insights that this approach has yielded to date. After a brief review of the key physical concepts governing van der Waals forces as the main cohesive effect for subaqueous sediment suspensions, we discuss their incorporation into particle-resolved simulations based on the immersed boundary method. We subsequently describe simulations of cohesive particles in several model turbulent flows, which demonstrate the emergence of a statistical equilibrium between the growth and break-up of aggregates. As a next step, we review the influence of cohesive forces on the settling behaviour of dense suspensions, before moving on to submerged granular collapses. Throughout the article, we highlight open research questions in the field of cohesive particulate flows whose investigation may benefit from grain-resolved simulations.

Chiral nonreciprocal elasticity and mechanical activity

There has been significant recent interest in creating, modeling, and exploiting the novel functionality afforded by odd elastic solids, which are a specific class of active matter whose behavior cannot be described by a free energy function. As a result, the mechanical behavior of such solids can be described by a non-symmetric elasticity tensor which means they can be mechanically active, and thus do work on their surroundings through quasistatic deformation cycles without energetic gain or loss terms explicitly appearing in the solid’s equation of state. However, previous incarnations of such solids have required the usage of active elements coupled with robotic machinery powered by independent external energy sources to operate. As such, it is unclear whether the non-symmetric elasticity of these solids can be developed using only passive elements that do not require the usage of energy sources, and furthermore how nonreciprocity in elastic media enables non-symmetric elasticity in elastic solids or mechanical activity. In this work, we propose the notion of chiral, nonreciprocal elasticity, which represents a generic route to enabling 2D, isotropic elastic solids exhibiting non-symmetric elasticity. Chiral, nonreciprocal elasticity describes elastic behaviors that result from coupling chirality with nonreciprocity—specifically, (1) the modulation of the elastic properties depending on the mode and direction of deformation and (2) the nonreciprocal coupling of different deformation fields, both of which enable the solid to exhibit a non-symmetric elasticity tensor. To motivate this, we introduce an isotropic 2D chiral metamaterial made of passive chiral elements that, by exploiting local geometric asymmetry, behaves in a chiral, nonreciprocal elastic fashion. We derive, based on the mechanics of a discrete model of this chiral element, the resulting continuum field equations and constitutive relationships that capture the chiral, nonreciprocal elastic behavior. Then, we establish a thermodynamic framework of energy balance and conservation of chiral, nonreciprocal elastic solids, based on which we demonstrate the ability of the proposed chiral metamaterial to act as a source of mechanical work when used in specific quasistatic deformation cycles, though no energy is dissipated by its passive elements. Finally, we demonstrate through numerical finite element simulations the practical implementation of the deformation cycles, while elucidating the specific conditions needed for the chiral metamaterial to exhibit linear, chiral nonreciprocal elastic behavior throughout the deformation cycle, and thus reveal mechanical activity.

Simulation of strain induced abnormal grain growth in aluminum alloy by coupling crystal plasticity and phase field methods

A mesoscale modeling methodology is proposed to predict the strain induced abnormal grain growth in the annealing process of deformed aluminum alloys. Firstly, crystal plasticity finite element (CPFE) analysis is performed to calculate dislocation density and stored deformation energy distribution during the plastic deformation. A modified phase field (PF) model is then established by extending the continuum field method to consider both stored energy and local interface curvature as driving forces of grain boundary migration. An interpolation mapping approach is adopted to transfer the stored energy distribution from CPFE to PF efficiently. This modified PF model is implemented to a hypothetical bicrystal firstly for verification and then the coupled CPFE-PF framework is further applied to simulating the 2D synthetic polycrystalline microstructure evolution in annealing process of deformed AA3102 aluminum alloy. Results show that the nuclei with low stored energy embedded within deformed matrix tend to grow up, and abnormal large grains occur when the deformation is close to the critical plastic strain, attributing to the limited number of recrystallized nuclei and inhomogeneity of the stored energy.