@Penn
NonEquilibrium Mechanics Laboratory
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Extrapolating material response into the farfromequilibrium realm
Despite their ubiquity and technological importance, the understanding of farfromequilibrium material behavior remains at its infancy. Here, we propose a strategy to extrapolate material behavior with quantified uncertainty to distinct loading conditions or material systems. This includes, as a specific example, the prediction of the farfromequilibrium behavior from equilibrium trajectory data, like the emergence of caging in glassformers from the liquid phase.
Publications:

S. Huang, I. R. Graham, R. A. Riggleman, P. Arratia, S. Fitzgerald, and C. Reina. Predicting the unobserved: a statistical mechanics framework for nonequilibrium material response with quantified uncertainty. Under review [arxiv]
Computational homogenization for elastic wave propagation.
Computational multiscale techniques, such as FE2 methods, take advantage of the separation of length scales to deliver efficient numerical strategies capable of capturing both the local and effective material behavior. They were originally developed for the quasistatic setting based on microtomacro relations that enable the appropriate coupling between the two different scales. Here, we extend these relations to the discrete and dynamic setting to simulate wave propagation in dispersive media at a reduced computational cost.
Publications:

C. Liu, C. Reina. Dynamic homogenization of resonant elastic metamaterials with space/time modulation. Computational Mechanics, 64.1 (2019): 147161. [web]

C. Liu, C. Reina. Variational coarsegraining procedure for dynamic homogenization. Journal of the Mechanics and Physics of Solids, 104 (2017): 187206. [web]

C. Liu, C. Reina. Discrete averaging relations for micro to macro transition. Journal of Applied Mechanics, 838 (2016): 081006. [web]
Kinematics of finite elastoplasticity.
The kinematic description of large elastoplastic deformations was conjectured in the 1950's to be of the form F=FeFp, where the total deformation F is decomposed multiplicatively into its elastic (Fe) and plastic (Fp) contributions. It has since then become a standard assumption in the continuum modeling of elastoplasticity, as well as general inelastic phenomena, including growth, damage, viscoelasticity, thermoelasticity and phase transformations. However, the absence of a rigorous justification for this decomposition has lead to numerous debates and controversies. Here, we use tools from the calculus of variations to perform rigorous multiscale analyses from discrete dislocations to a continuum formulation and make precise the necessary and sufficient conditions for the validity of F=FeFp (or F=FeFi, in the general inelastic setting).
Publications:

C. Reina, L. F. Djodom, M. Ortiz and S. Conti. Kinematics of elastoplasticity: Validity and limits of applicability of F= FeFp for general threedimensional deformations. Journal of the Mechanics and Physics of Solids, 121 (2018): 99113. [web]

C. Reina and S. Conti. Incompressible inelasticity as an essential ingredient for the validity of the kinematic decomposition F=FeFi. Journal of the Mechanics and Physics of Solids, 107 (2017): 322342. [web]

C. Reina, A. Schlomerkemper and S. Conti. Derivation of F=FeFp as the continuum limit of crystalline slip. Journal of the Mechanics and Physics of Solids, 89 (2016): 231254. [web]

C. Reina and S. Conti. Kinematic description of crystal plasticity in the finite kinematic framework: a micromechanical understanding of F=FeFp. Journal of the Mechanics and Physics of Solids, 67 (2014): 4061. [web]
Continuum modeling of nonequilibrium phenomena.
The modeling of dissipative evolution equations remains a major challenge in continuum mechanics and is primarily based on phenomenological constitutive relations. Our efforts in this area are multifaceted and encompass

Machine learning strategy for the discovery of continuum evolution equations. Here, we propose a variational learning strategy for the discovery of nonequilibrium equations, through the variational action density from which these equations may be derived. The strategy is based on the socalled Onsager’s variational principle, which may be written as a function of the free energy and dissipation potential, and utilizes neural network architectures that strongly guarantee thermodynamic consistency.
Publications:
S. Huang, Z. He, B. Chem and C. Reina. Variational Onsager Neural Networks (VONNs): A thermodynamicsbased variational learning strategy for nonequilibrium PDEs. Journal of the Mechanics and Physics of Solids (2022): under review. Preprint available on arxiv. [web]

Physicsbased datadriven approaches for the discovery of continuum equations. Here, we leverage infinite dimensional fluctuationdissipation relations and fluctuation theorems valid far away from equilibrium to fully learn from data the PDEs governing the system's evolution.
Publications:
S. Huang, C. Sun, P. K. Purohit and C. Reina. Harnessing fluctuation theorems to discover free energy and dissipation potentials from nonequilibrium data. Journal of the Mechanics and Physics of Solids (2021): 104323. [web]
X. Li, N. Dirr, P. Embacher, J. Zimmer and C. Reina. Harnessing fluctuations to discover dissipative evolution equations. Journal of the Mechanics and Physics of Solids, 131 (2019): 240251. [web]
P. Embacher, N. Dirr, J. Zimmer, C. Reina. Computing diffusivities from particle models out of equilibrium. Proceedings of the Royal Society A, 474 (2018): 220170694. [web]

The foundational understanding of the continuum equations of motion and their thermodynamic structure, from systems governed by Hamiltonian dynamics. Here, we observed from data the inherent spatial and temporal scale separation (i.e., the existence of slow and fast degrees of freedom), and show how the reversible or dissipative nature of the system at the continuum scale emerges as a function of that scale separation.
Publications:
M. Klar, K. Matthies, C. Reina and J. Zimmer. Secondorder fastslow dynamics of nonergodic Hamiltonian systems: Thermodynamic interpretation and simulation. Physica D: accepted. [arxiv]
X. Li and C Reina. Simultaneous spatial and temporal coarsegraining: From atomistic models to continuum elastodynamics. Journal of the Mechanics and Physics of Solids, 130 (2019): 118140. [web]

Connections between the geometry of dissipative gradient flows, the principle of maximum entropy production, large deviation principles for stochastically augmented evolution equations and fluctuationdissipation relations.
Publications:
C. Reina and J. Zimmer. Entropy production and the geometry of dissipative evolution equations. Physical Review E, 92 (2015): 052117. [web]
Design of elastic metamaterials.
Internal resonances are widely used in elastic metamaterials to generate subwavelength bandgaps, where no waves propagate. However, these bandgaps tend to be very narrow, severely limiting their applicability. Drawing inspiration from biological materials, we have explored the role of hierarchical architectures and softness as important and rich mechanisms for bandgap widening. Jointly with the group of Prof. Raney, we have fabricated an additively manufactured soft resonant metamaterial with a gapmidgap ratio of 81.8%, greatly surpassing metamaterials of the same class found in the literature.
Publications:

B. Chem, Y. Jian, C. Liu, J. R. Raney and C. Reina. Dynamic behavior of soft resonant metamaterials: experiments and simulations. Journal of Applied Physics, 129 (2021): 135104. [web]

C. Liu, C. Reina. Broadband locally resonant metamaterials with graded hierarchical architecture. Journal of Applied Physics, 123 (2018): 095108. [web]
Modeling of amorphoustocrystalline transformation.
Phase change materials (PCMs) can exhibit ultrafast phase transformations and are considered as promising candidates for nonvolatile memory devices. Yet, a full understanding of this nonequilibrium process is still lacking. Here, we develop a thermodynamically consistent atomisticphase field models for the understanding of the nanocrystallization of amorphous Ge, a base element of many PCMs.
Publications:

L. Sandoval, C. Reina and J. Marian. Formation of Nanotwin Networks during HighTemperature Crystallization of Amorphous Germanium. Scientific Reports, 5 (2015): 17251. [web]

C. Reina, L. Sandoval and J. Marian. Mesoscale computational study of the nanocrystallization of amorphous Ge via a selfconsistent atomistic  phase field model. Acta Materialia, 77 (2014): 335351. [web]
Damage via void nucleation and growth.
Damage and failure by voids occur in a wide range of materials ranging from biological tissue to polymers and metals. We have developed multiscale models and simulations that transfer information all the way from the quantum level to the continuum scale using kinetic Monte Carlo methods, multiscale finite element techniques and estimates from quasicontinuum simulations.
Publications:

C. Reina, B. Li, K. Weinberg and M. Ortiz. A micromechanical model of distributed damage due to void growth in general materials and under general deformation histories. International Journal for Numerical Methods in Engineering, 93 (2013): 575611. [web]

C. Reina, J. Marian and M. Ortiz. Nanovoid nucleation by vacancy aggregation and vacancycluster coarsening in highpurity metallic single crystals. Physical Review B, 84 (2011): 104117. [web]