Showing 1–17 of 17 results for author: Reina, C

On a structure preserving closure of Langevin dynamics

Authors: Travis Leadbetter, Prashant K. Purohit, Celia Reina

Abstract: Given a particle system obeying overdamped Langevin dynamics, we demonstrate that it is always possible to construct a thermodynamically consistent macroscopic model which obeys a gradient flow with respect to its non-equilibrium free energy. To do so, we significantly extend the recent Stochastic Thermodynamics with Internal Variables (STIV) framework, a method for producing macroscopic thermodyn… ▽ More Given a particle system obeying overdamped Langevin dynamics, we demonstrate that it is always possible to construct a thermodynamically consistent macroscopic model which obeys a gradient flow with respect to its non-equilibrium free energy. To do so, we significantly extend the recent Stochastic Thermodynamics with Internal Variables (STIV) framework, a method for producing macroscopic thermodynamic models far-from-equilibrium from the underlying mesoscopic dynamics and an approximate probability density of states parameterized with so-called internal variables. Though originally explored for Gaussian probability distributions, we here allow for an arbitrary choice of the approximate probability density while retaining a gradient flow dynamics. This greatly extends its range of applicability and automatically ensures consistency with the second law of thermodynamics, without the need for secondary verification. We demonstrate numerical convergence, in the limit of increasing internal variables, to the true probability density of states for both a multi-modal relaxation problem, a protein diffusing on a strand of DNA, and for an externally driven particle in a periodic landscape. Finally, we provide a reformulation of STIV with the quasi-equilibrium approximations in terms of the averages of observables of the mesostate, and show that these, too, obey a gradient flow. △ Less

Submitted 9 June, 2025; originally announced June 2025.

Integrated Experiment and Simulation Co-Design: A Key Infrastructure for Predictive Mesoscale Materials Modeling

Authors: Shailendra P. Joshi, Ashley Bucsek, Darren C. Pagan, Samantha Daly, Suraj Ravindran, Jaime Marian, Miguel A. Bessa, Surya R. Kalidindi, Nikhil C. Admal, Celia Reina, Somnath Ghosh, Jorge Vinals, Ellad B. Tadmor

Abstract: The design of structural & functional materials for specialized applications is being fueled by rapid advancements in materials synthesis, characterization, manufacturing, with sophisticated computational materials modeling frameworks that span a wide spectrum of length & time scales in the mesoscale between atomistic & continuum approaches. This is leading towards a systems-based design methodolo… ▽ More The design of structural & functional materials for specialized applications is being fueled by rapid advancements in materials synthesis, characterization, manufacturing, with sophisticated computational materials modeling frameworks that span a wide spectrum of length & time scales in the mesoscale between atomistic & continuum approaches. This is leading towards a systems-based design methodology that will replace traditional empirical approaches, embracing the principles of the Materials Genome Initiative. However, several gaps remain in this framework as it relates to advanced structural materials:(1) limited availability & access to high-fidelity experimental & computational datasets, (2) lack of co-design of experiments & simulation aimed at computational model validation,(3) lack of on-demand access to verified and validated codes for simulation and for experimental analyses, & (4) limited opportunities for workforce training and educational outreach. These shortcomings stifle major innovations in structural materials design. This paper describes plans for a community-driven research initiative that addresses current gaps based on best-practice recommendations of leaders in mesoscale modeling, experimentation & cyberinfrastructure obtained at an NSF-sponsored workshop dedicated to this topic. The proposal is to create a hub for Mesoscale Experimentation and Simulation co-Operation (hMESO)-that will (I) provide curation and sharing of models, data, & codes, (II) foster co-design of experiments for model validation with systematic uncertainty quantification, & (III) provide a platform for education & workforce development. It will engage experimental & computational experts in mesoscale mechanics and plasticity, along with mathematicians and computer scientists with expertise in algorithms, data science, machine learning, & large-scale cyberinfrastructure initiatives. △ Less

Submitted 12 March, 2025; originally announced March 2025.

Journal ref: Mechanics of Materials 2025

Bridging statistical mechanics and thermodynamics away from equilibrium: a data-driven approach for learning internal variables and their dynamics

Authors: Weilun Qiu, Shenglin Huang, Celia Reina

Abstract: Thermodynamics with internal variables is a common approach in continuum mechanics to model inelastic (i.e., non-equilibrium) material behavior. While this approach is computationally and theoretically attractive, it currently lacks a well-established statistical mechanics foundation. As a result, internal variables are typically chosen phenomenologically and lack a direct link to the underlying p… ▽ More Thermodynamics with internal variables is a common approach in continuum mechanics to model inelastic (i.e., non-equilibrium) material behavior. While this approach is computationally and theoretically attractive, it currently lacks a well-established statistical mechanics foundation. As a result, internal variables are typically chosen phenomenologically and lack a direct link to the underlying physics which hinders the predictability of the theory. To address these challenges, we propose a machine learning approach that is consistent with the principles of statistical mechanics and thermodynamics. The proposed approach leverages the following techniques (i) the information bottleneck (IB) method to ensure that the learned internal variables are functions of the microstates and are capable of capturing the salient feature of the microscopic distribution; (ii) conditional normalizing flows to represent arbitrary probability distributions of the microscopic states as functions of the state variables; and (iii) Variational Onsager Neural Networks (VONNs) to guarantee thermodynamic consistency and Markovianity of the learned evolution equations. The resulting framework, called IB-VONNs, is tested on two problems of colloidal systems, governed at the microscale by overdamped Langevin dynamics. The first one is a prototypical model for a colloidal particle in an optical trap, which can be solved analytically, and thus ideal to verify the framework. The second problem is a one-dimensional phase-transforming system, whose macroscopic description still lacks a statistical mechanics foundation under general conditions. The results in both cases indicate that the proposed machine learning strategy can indeed bridge statistical mechanics and thermodynamics with internal variables away from equilibrium. △ Less

Submitted 29 January, 2025; originally announced January 2025.

A statistical mechanics derivation and implementation of non-conservative phase field models for front propagation in elastic media

Authors: Travis Leadbetter, Prashant K. Purohit, Celia Reina

Abstract: Over the past several decades, phase field modeling has been established as a standard simulation technique for mesoscopic science, allowing for seamless boundary tracking of moving interfaces and relatively easy coupling to other physical phenomena. However, despite its widespread success, phase field modeling remains largely driven by phenomenological justifications except in a handful of instan… ▽ More Over the past several decades, phase field modeling has been established as a standard simulation technique for mesoscopic science, allowing for seamless boundary tracking of moving interfaces and relatively easy coupling to other physical phenomena. However, despite its widespread success, phase field modeling remains largely driven by phenomenological justifications except in a handful of instances. In this work, we leverage a recently developed statistical mechanics framework for non-equilibrium phenomena, called Stochastic Thermodynamics with Internal Variables (STIV), to provide the first derivation of a phase field model for front propagation in a one dimensional elastic medium without appeal to phenomenology or fitting to experiments or simulation data. In the resulting model, the variables obey a gradient flow with respect to a non-equilibrium free energy, although notably, the dynamics of the strain and phase variables are coupled, and while the free energy functional is non-local in the phase field variable, it deviates from the traditional Landau-Ginzburg form. Moreover, in the systems analyzed here, the model accurately captures stress induced nucleation of transition fronts without the need to incorporate additional physics. We find that the STIV phase field model compares favorably to Langevin simulations of the microscopic system and we provide two numerical implementations enabling one to simulate arbitrary interatomic potentials. △ Less

Submitted 23 December, 2024; originally announced December 2024.

Statistical-Physics-Informed Neural Networks (Stat-PINNs): A Machine Learning Strategy for Coarse-graining Dissipative Dynamics

Authors: Shenglin Huang, Zequn He, Nicolas Dirr, Johannes Zimmer, Celia Reina

Abstract: Machine learning, with its remarkable ability for retrieving information and identifying patterns from data, has emerged as a powerful tool for discovering governing equations. It has been increasingly informed by physics, and more recently by thermodynamics, to further uncover the thermodynamic structure underlying the evolution equations, i.e., the thermodynamic potentials driving the system and… ▽ More Machine learning, with its remarkable ability for retrieving information and identifying patterns from data, has emerged as a powerful tool for discovering governing equations. It has been increasingly informed by physics, and more recently by thermodynamics, to further uncover the thermodynamic structure underlying the evolution equations, i.e., the thermodynamic potentials driving the system and the operators governing the kinetics. However, despite its great success, the inverse problem of thermodynamic model discovery from macroscopic data is in many cases non-unique, meaning that multiple pairs of potentials and operators can give rise to the same macroscopic dynamics, which significantly hinders the physical interpretability of the learned models. In this work, we propose a machine learning framework, named as Statistical-Physics-Informed Neural Networks (Stat-PINNs), which further encodes knowledge from statistical mechanics and resolves this non-uniqueness issue for the first time. The framework is here developed for purely dissipative isothermal systems. It only uses data from short-time particle simulations to learn the thermodynamic structure, which can be used to predict long-time macroscopic evolutions. We demonstrate the approach for particle systems with Arrhenius-type interactions, common to a wide range of phenomena, such as defect diffusion in solids, surface absorption and chemical reactions. Stat-PINNs can successfully recover the known analytic solution for the case with long-range interaction and discover the hitherto unknown potential and operator governing the short-range interaction cases. We compare our results with an analogous approach that solely excludes statistical mechanics, and observe that, in addition to recovering the unique thermodynamic structure, statistical mechanics relations can increase the robustness and predictability of the learning strategy. △ Less

Submitted 10 December, 2023; originally announced December 2023.

A statistical mechanics framework for constructing non-equilibrium thermodynamic models

Authors: Travis Leadbetter, Prashant K. Purohit, Celia Reina

Abstract: Far-from-equilibrium phenomena are critical to all natural and engineered systems, and essential to biological processes responsible for life. For over a century and a half, since Carnot, Clausius, Maxwell, Boltzmann, and Gibbs, among many others, laid the foundation for our understanding of equilibrium processes, scientists and engineers have dreamed of an analogous treatment of non-equilibrium s… ▽ More Far-from-equilibrium phenomena are critical to all natural and engineered systems, and essential to biological processes responsible for life. For over a century and a half, since Carnot, Clausius, Maxwell, Boltzmann, and Gibbs, among many others, laid the foundation for our understanding of equilibrium processes, scientists and engineers have dreamed of an analogous treatment of non-equilibrium systems. But despite tremendous efforts, a universal theory of non-equilibrium behavior akin to equilibrium statistical mechanics and thermodynamics has evaded description. Several methodologies have proved their ability to accurately describe complex non-equilibrium systems at the macroscopic scale, but their accuracy and predictive capacity is predicated on either phenomenological kinetic equations fit to microscopic data, or on running concurrent simulations at the particle level. Instead, we provide a framework for deriving stand-alone macroscopic thermodynamics models directly from microscopic physics without fitting in overdamped Langevin systems. The only necessary ingredient is a functional form for a parameterized, approximate density of states, in analogy to the assumption of a uniform density of states in the equilibrium microcanonical ensemble. We highlight this framework's effectiveness by deriving analytical approximations for evolving mechanical and thermodynamic quantities in a model of coiled-coil proteins and double stranded DNA, thus producing, to the authors' knowledge, the first derivation of the governing equations for a phase propagating system under general loading conditions without appeal to phenomenology. The generality of our treatment allows for application to any system described by Langevin dynamics with arbitrary interaction energies and external driving, including colloidal macromolecules, hydrogels, and biopolymers. △ Less

Submitted 13 September, 2023; originally announced September 2023.

Predicting the unobserved: a statistical mechanics framework for non-equilibrium material response with quantified uncertainty

Authors: Shenglin Huang, Ian R. Graham, Robert A. Riggleman, Paulo Arratia, Steve Fitzgerald, Celia Reina

Abstract: Can far-from-equilibrium material response under arbitrary loading be inferred from equilibrium data and vice versa? Can the effect of element transmutation on mechanical behavior be predicted? Remarkably, such extrapolations are possible in principle for systems governed by stochastic differential equations, thanks to a set of exact relations between probability densities for trajectories derived… ▽ More Can far-from-equilibrium material response under arbitrary loading be inferred from equilibrium data and vice versa? Can the effect of element transmutation on mechanical behavior be predicted? Remarkably, such extrapolations are possible in principle for systems governed by stochastic differential equations, thanks to a set of exact relations between probability densities for trajectories derived from the path integral formalism [1, 2, 3]. In this article, we systematically investigate inferences (in the form of ensemble-averages) drawn on system/process S based on stochastic trajectory data of system/process S~, with quantified uncertainty, to directly address the aforementioned questions. Interestingly, such inferences and their associated uncertainty do not require any simulations or experiments of S. The results are exemplified over two illustrative examples by means of numerical simulations: a one-dimensional system as a prototype for polymers and biological macromolecules, and a two-dimensional glassy system. In principle, the approach can be pushed to the extreme case where S~ is simply comprised of Brownian trajectories, i.e., equilibrium non-interacting particles, and S is a complex interacting system driven far from equilibrium. In practice, however, the "further" S~ is from S, the greater the uncertainty in the predictions, for a fixed number of realizations of system S~. △ Less

Submitted 12 October, 2021; originally announced October 2021.

Relationships among structure, memory, and flow in sheared disordered materials

Authors: K. L. Galloway, E. G. Teich, X-g Ma, Ch. Kammer, I. R. Graham, N. C. Keim, C. Reina, D. J. Jerolmack, A. G. Yodh, P. E. Arratia

Abstract: A fundamental challenge for disordered solids is predicting macroscopic yield from the microscopic arrangements of constituent particles. Yield is accompanied by a sudden and large increase in energy dissipation due to the onset of plastic rearrangements. This suggests that one path to understanding bulk rheology is to map particle configurations to their mode of deformation. Here, we perform labo… ▽ More A fundamental challenge for disordered solids is predicting macroscopic yield from the microscopic arrangements of constituent particles. Yield is accompanied by a sudden and large increase in energy dissipation due to the onset of plastic rearrangements. This suggests that one path to understanding bulk rheology is to map particle configurations to their mode of deformation. Here, we perform laboratory experiments and numerical simulations that are designed to do just that: 2D dense colloidal systems are subjected to oscillatory shear, and particle trajectories and bulk rheology are measured. We quantify particle microstructure using excess entropy. Results reveal a direct relation between excess entropy and energy dissipation, that is insensitive to the nature of interactions among particles. We use this relation to build a physically-informed model that connects rheology to microstructure. Our findings suggest a framework for tailoring the rheological response of disordered materials by tuning microstructural properties. △ Less

Submitted 13 May, 2021; originally announced May 2021.

How to find the evolution operator of dissipative PDEs from particle fluctuations?

Authors: Xiaoguai Li, Nicolas Dirr, Peter Embacher, Johannes Zimmer, Celia Reina

Abstract: Dissipative processes abound in most areas of sciences and can often be abstractly written as $\partial_t z = K(z) δS(z)/δz$, which is a gradient flow of the entropy $S$. Although various techniques have been developed to compute the entropy, the calculation of the operator $K$ from underlying particle models is a major long-standing challenge. Here, we show that discretizations of diffusion opera… ▽ More Dissipative processes abound in most areas of sciences and can often be abstractly written as $\partial_t z = K(z) δS(z)/δz$, which is a gradient flow of the entropy $S$. Although various techniques have been developed to compute the entropy, the calculation of the operator $K$ from underlying particle models is a major long-standing challenge. Here, we show that discretizations of diffusion operators $K$ can be numerically computed from particle fluctuations via an infinite-dimensional fluctuation-dissipation relation, provided the particles are in local equilibrium with Gaussian fluctuations. A salient feature of the method is that $K$ can be fully pre-computed, enabling macroscopic simulations of arbitrary admissible initial data, without any need of further particle simulations. We test this coarse-graining procedure for a zero-range process in one space dimension and obtain an excellent agreement with the analytical solution for the macroscopic density evolution. This example serves as a blueprint for a new multiscale paradigm, where full dissipative evolution equations --- and not only parameters --- can be numerically computed from particles. △ Less

Submitted 15 November, 2018; v1 submitted 15 May, 2018; originally announced May 2018.

Computing diffusivities from particle models out of equilibrium

Authors: Peter Embacher, Nicolas Dirr, Johannes Zimmer, Celia Reina

Abstract: A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have Gaussian fluctuations but is otherwise allowed to undergo arbitrary out of equilibrium evolutions. This could be potentially relevant for particle data obtained from e… ▽ More A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have Gaussian fluctuations but is otherwise allowed to undergo arbitrary out of equilibrium evolutions. This could be potentially relevant for particle data obtained from experimental applications. The key idea underlying the method is that finite, yet large, particle systems formally obey stochastic partial differential equations of gradient flow type satisfying a fluctuation-dissipation relation. The strategy is here applied to three classic particle models, namely independent random walkers, a zero range process and a symmetric simple exclusion process in one space dimension, to allow the comparison with analytic solutions. △ Less

Submitted 14 March, 2018; v1 submitted 30 September, 2017; originally announced October 2017.

Computational homogenization of heterogeneous media under dynamic loading

Authors: Chenchen Liu, Celia Reina

Abstract: A variational coarse-graining framework for heterogeneous media is developed that allows for a seamless transition from the traditional static scenario to a arbitrary loading conditions, including inertia effects and body forces. The strategy is formulated in the spirit of computational homogenization methods (FE$^2$) and is based on the discrete version of Hill's averaging results recently derive… ▽ More A variational coarse-graining framework for heterogeneous media is developed that allows for a seamless transition from the traditional static scenario to a arbitrary loading conditions, including inertia effects and body forces. The strategy is formulated in the spirit of computational homogenization methods (FE$^2$) and is based on the discrete version of Hill's averaging results recently derived by the authors. In particular, the traditional static multiscale scheme is proved here to be equivalent to a direct homogenization of the principle of minimum potential energy and to hold exactly under a finite element discretization. This perspective provides a unifying variational framework for the FE$^2$ method, in the static setting, with Dirichlet or Neumann boundary conditions on the representative volume element; and it directly manifests the approximate duality of the effective strain energy density obtained with these two types of boundary conditions in the sense of Legendre transformation. Its generalization to arbitrary loading conditions and material constitutive relations is then immediate through the incremental minimum formulation of the dynamic problem à la Radovitzky and Ortiz (1999), which, in the discrete setting, is in full analogy to the static problem. These theoretical developments are then translated into an efficient multiscale FE$^2$ computational strategy for the homogenization of a microscopic explicit dynamics scheme, with two noteworthy properties. Firstly, each time incremental problem can be solved exactly with a single Newton-Raphson iteration with a constant Hessian, regardless of the specific non-linearities or history-dependence of the micro-constituents' behavior. Secondly, the scheme concurrently solves for the microscopic and macroscopic degrees of freedom, in contrast to standard approaches based on sequential or nested minimizations. △ Less

Submitted 8 October, 2015; originally announced October 2015.

Comments: Due to the limitation "The abstract field cannot be longer than 1,920 characters", the abstract here is shorter than that in the PDF file

Discrete averaging relations for micro to macro transition

Authors: Chenchen Liu, Celia Reina

Abstract: The well-known Hill's averaging theorems for stresses and strains as well as the so-called Hill-Mandel principle of macrohomogeneity are essential ingredients for the coupling and the consistency between the micro and macro scales in multiscale finite element procedures (FE$^2$). We show in this paper that these averaging relations hold exactly under standard finite element discretizations, even i… ▽ More The well-known Hill's averaging theorems for stresses and strains as well as the so-called Hill-Mandel principle of macrohomogeneity are essential ingredients for the coupling and the consistency between the micro and macro scales in multiscale finite element procedures (FE$^2$). We show in this paper that these averaging relations hold exactly under standard finite element discretizations, even if the stress field is discontinuous across elements and the standard proofs based on the divergence theorem are no longer suitable. The discrete averaging results are derived for the three classical types of boundary conditions (affine displacement, periodic and uniform traction boundary conditions) using the properties of the shape functions and the weak form of the microscopic equilibrium equations. The analytical proofs are further verified numerically through a simple finite element simulation of an irregular representative volume element undergoing large deformations. Furthermore, the proofs are extended to include the effects of body forces and inertia, and the results are consistent with those in the smooth continuum setting. This work provides a solid foundation to apply Hill's averaging relations in multiscale finite element methods without introducing an additional error in the scale transition due to the discretization. △ Less

Submitted 22 September, 2015; originally announced September 2015.

Formation of Nanotwin Networks during High-Temperature Crystallization of Amorphous Germanium

Authors: Luis A. Sandoval, Celia Reina, Jaime Marian

Abstract: Germanium is an extremely important material used for numerous functional applications in many fields of nanotechnology. In this paper, we study the crystallization of amorphous Ge using atomistic simulations of critical nano-metric nuclei at high temperatures. We find that crystallization occurs by the recurrent transfer of atoms via a diffusive process from the amorphous phase into suitably-orie… ▽ More Germanium is an extremely important material used for numerous functional applications in many fields of nanotechnology. In this paper, we study the crystallization of amorphous Ge using atomistic simulations of critical nano-metric nuclei at high temperatures. We find that crystallization occurs by the recurrent transfer of atoms via a diffusive process from the amorphous phase into suitably-oriented crystalline layers. We accompany our simulations with a comprehensive thermodynamic and kinetic analysis of the growth process, which explains the energy balance and the interfacial growth velocities governing grain growth. For the $\langle111\rangle$ crystallographic orientation, we find a degenerate atomic rearrangement process, with two zero-energy modes corresponding to a perfect crystalline structure and the formation of a $\Sigma3$ twin boundary. Continued growth in this direction results in the development a twin network, in contrast with all other growth orientations, where the crystal grows defect-free. This particular mechanism of crystallization from amorphous phases is also observed during solid-phase epitaxial growth of $\langle111\rangle$ semiconductor crystals, where growth is restrained to one dimension. We calculate the equivalent X-ray diffraction pattern of the obtained nanotwin networks, providing grounds for experimental validation. △ Less

Submitted 14 July, 2015; originally announced July 2015.

Entropy production and the geometry of dissipative evolution equations

Authors: Celia Reina, Johannes Zimmer

Abstract: Purely dissipative evolution equations are often cast as gradient flow structures, $\dot{\mathbf{z}}=K(\mathbf{z})DS(\mathbf{z})$, where the variable $\mathbf{z}$ of interest evolves towards the maximum of a functional $S$ according to a metric defined by an operator $K$. While the functional often follows immediately from physical considerations (e.g., the thermodynamic entropy), the operator… ▽ More Purely dissipative evolution equations are often cast as gradient flow structures, $\dot{\mathbf{z}}=K(\mathbf{z})DS(\mathbf{z})$, where the variable $\mathbf{z}$ of interest evolves towards the maximum of a functional $S$ according to a metric defined by an operator $K$. While the functional often follows immediately from physical considerations (e.g., the thermodynamic entropy), the operator $K$ and the associated geometry does not necessarily so (e.g., Wasserstein geometry for diffusion). In this paper, we present a variational statement in the sense of maximum entropy production that directly delivers a relationship between the operator $K$ and the constraints of the system. In particular, the Wasserstein metric naturally arises here from the conservation of mass or energy, and depends on the Onsager resistivity tensor, which, itself, may be understood as another metric, as in the Steepest Entropy Ascent formalism. This new variational principle is exemplified here for the simultaneous evolution of conserved and non-conserved quantities in open systems. It thus extends the classical Onsager flux-force relationships and the associated variational statement to variables that do not have a flux associated to them. We further show that the metric structure $K$ is intimately linked to the celebrated Freidlin-Wentzell theory of stochastically perturbed gradient flows, and that the proposed variational principle encloses an infinite-dimensional fluctuation-dissipation statement. △ Less

Submitted 4 November, 2015; v1 submitted 1 July, 2015; originally announced July 2015.

Journal ref: Phys. Rev. E 92, 052117 (2015)

Derivation of $\mathbf{F}=\mathbf{F}^e\mathbf{F}^p$ as the continuum limit of crystalline slip

Authors: Celia Reina, Anja Schlömerkemper, Sergio Conti

Abstract: In this paper we provide a proof of the multiplicative kinematic description of crystal elastoplasticity in the setting of large deformations, i.e. $\mathbf{F}=\mathbf{F}^e\mathbf{F}^p$, for a two dimensional single crystal. The proof starts by considering a general configuration at the mesoscopic scale, where the dislocations are discrete line defects (points in the two-dimensional description us… ▽ More In this paper we provide a proof of the multiplicative kinematic description of crystal elastoplasticity in the setting of large deformations, i.e. $\mathbf{F}=\mathbf{F}^e\mathbf{F}^p$, for a two dimensional single crystal. The proof starts by considering a general configuration at the mesoscopic scale, where the dislocations are discrete line defects (points in the two-dimensional description used here) and the displacement field can be considered continuous everywhere in the domain except at the slip surfaces, over which there is a displacement jump. At such scale, as previously shown by two of the authors, there exists unique physically-based definitions of the total deformation tensor $\mathbf{F}$ and the elastic and plastic tensors $\mathbf{F}^e$ and $\mathbf{F}^p$ that do not require the consideration of any non-realizable intermediate configuration and do not assume any a priori relation between them of the form $\mathbf{F}=\mathbf{F}^e\mathbf{F}^p$. This mesoscopic description is then passed to the continuum limit via homogenization i.e., by increasing the number of slip surfaces to infinity and reducing the lattice parameter to zero. We show for two-dimensional deformations of initially perfect single crystals that the classical continuum formulation is recovered in the limit with $\mathbf{F}=\mathbf{F}^e\mathbf{F}^p$, $\det \mathbf{F}^p= 1$ and $\mathbf{G}=\text{Curl}\ \mathbf{F}^p$ the dislocation density tensor. △ Less

Submitted 25 April, 2015; originally announced April 2015.

Journal ref: J. Mech. Phys. Solids 89 (2016), 231-254

Mesoscale computational study of the nano-crystallization of amorphous Ge via a self-consistent atomistic - phase field coupling

Authors: Celia Reina, Luis Sandoval, Jaime Marian

Abstract: Germanium is the base element in many phase-change materials, i.e. systems that can undergo reversible transformations between their crystalline and amorphous phases. They are widely used in current digital electronics and hold great promise for the next generation of non-volatile memory devices. However, the ultra fast phase transformations required for these applications can be exceedingly compl… ▽ More Germanium is the base element in many phase-change materials, i.e. systems that can undergo reversible transformations between their crystalline and amorphous phases. They are widely used in current digital electronics and hold great promise for the next generation of non-volatile memory devices. However, the ultra fast phase transformations required for these applications can be exceedingly complex even for single component systems, and a full physical understanding of these phenomena is still lacking. In this paper we study nucleation and growth of crystalline Ge from amorphous thin films at high temperature using phase field models informed by atomistic calculations of fundamental material properties. The atomistic calculations capture the full anisotropy of the Ge crystal lattice, which results in orientation dependences for interfacial energies and mobilities. These orientation relations are then exactly recovered by the phase field model at finite thickness via a novel parametrization strategy based on invariance solutions of the Allen-Cahn equations. By means of this multiscale approach, we study the interplay between nucleation and growth and find that the relation between the mean radius of the crystallized Ge grains and the nucleation rate follows simple Avrami-type scaling laws. We argue that these can be used to cover a wide region of the nucleation rate space, hence facilitating comparison with experiments. △ Less

Submitted 12 December, 2013; originally announced December 2013.

Kinematic description of crystal plasticity in the finite kinematic framework: a micromechanical understanding of F=FeFp

Authors: Celia Reina, Sergio Conti

Abstract: The plastic component of the deformation gradient plays a central role in finite kinematic models of plasticity. However, its characterization has been the source of extended debates in the literature and many important issues still remain unresolved. Some examples are the micromechanical understanding of F=FeFp with multiple active slip systems, the uniqueness of the decomposition, or the charact… ▽ More The plastic component of the deformation gradient plays a central role in finite kinematic models of plasticity. However, its characterization has been the source of extended debates in the literature and many important issues still remain unresolved. Some examples are the micromechanical understanding of F=FeFp with multiple active slip systems, the uniqueness of the decomposition, or the characterization of the plastic deformation without reference to the so-called intermediate configuration. In this paper, we shed some light to these issues via a two-dimensional kinematic analysis of the plastic deformation induced by discrete slip surfaces and the corresponding dislocation structures. In particular, we supply definitions for the elastic and plastic components of the deformation gradient as a function of the active slip systems without any a priori assumption on the decomposition of the total deformation gradient. These definitions are explicitly and uniquely given from the microstructure and do not make use of any unrealizable intermediate configuration. These quantities are then passed to the continuous limit via homogenization, i.e., by increasing the number of slip surfaces to infinity and reducing the lattice parameter to zero. This continuum limit is computed for several illustrative examples, where the well-known multiplicative decomposition of the total deformation gradient is recovered. Additionally, by similar arguments, an expression of the dislocation density tensor is obtained as the limit of discrete dislocation densities. △ Less

Submitted 4 December, 2013; originally announced December 2013.

Journal ref: J. Mech. Phys. Solids, 67:40-61, 2014