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One of the greatest challenges facing the electric power industry is how to deliver the energy in a useable form as a higher-value product, especially in the area of renewable energy and electric road transportation. By storing the power produced from immense renewable sources off-peak (e.g., daytime for solar energy) and releasing it during on-peak periods, energy storage can transform low-value, unscheduled power into high-value "green" products. Similarly, adequate energy storage is mandatory to promote the large scale market of Electric Vehicles (EVs). It is now generally accepted that among the various possible choices, the most suitable energy storage carriers are electrochemical batteries, namely portable devices capable to deliver the stored chemical energy as electrical energy with high conversion efficiency and without any gaseous emission.

Lithium (Li) ion batteries currently have the highest energy storage density of any rechargeable battery technology and are the power sources of choice for consumer market. However, the present Li-ion batteries, although commercial realities, are not yet at such a technological level to support Renewable Energy Plants, as well as to efficiently power EVs. Major advances may be obtained only by moving towards new materials, as also pointed out in the "European Strategic Energy Technology (SET) Plan, 2007", the following "SET Plan Materials Road Map, 2011" as well as the recent (2013) recommendations on their implementation.
Materials for batteries with lower cost, higher safety level, and higher energy density are the focus of the present project. Theoretical and computational modeling provides the ability to predict, tailor and shape their properties. The present project may provide a significant contribution to advance the quality of European science in the fundamental area of energy storage materials.

Directly resolving all scales and modeling all particles in the electrodes is not feasible. Instead, the nano-scale effects are incorporated into the micro-scale problem through constitutive models that are derived from advanced homogenization methods. A computational homogenization approach has been recently proposed by myself in four papers on ISI journals and is nowadays in a mature implementation phase. A new model, based on the notion of trapping, has been formulated for the lithiation process. At the same time, the quality of the reconstruction of the morphology of the electrodes structure has great impact to the final solution. Image-based (data-driven) modeling of the fine structure has recently been achieved (see Fig. 1). In both regards, the cooperation with supercomputing centers is vital. The complexity of the analysis calls for high performance computing, to which great efforts is currently devoted: specific code has been written using the open finite element library deal.ii and two grants have been awarded for HPC implementation (see below). This innovative strategy in modeling ESM received interest both on the academic and industrial sides.


Joint PhD fellowship between the Universities of Brescia (Italy) and Notre Dame (USA) on the subject of Co-designed modeling and experimental investigations on electrodes modified with lithiated organic ligands. The student, who must have graduated in a non-Italian institution, will be co-advised by Prof. A. Salvadori (UNIBS) and J. Schaefer (ND). The candidate will work at the forefront of experimental and modeling in the vibrant area of next generation of energy storage materials. The position requires the willingness of working in an interdisciplinary team. A background in solid mechanics and thermodynamics, knowledge of nonlinear finite element methods and ability to use FEM codes, preferably ABAQUS, is positively considered. If interested, please contact alberto.salvadori(at) A copy of a CV, eligibility to work in Italy and in the USA, and a description of research interests is mandatory. Further information and administrative facts can be found at

Selected publications:

- Salvadori A., McMeeking R., Grazioli D., Magri M., A coupled model of transport-reaction-mechanics with trapping. Part I - small strain analysis., Journal of the Mechanics and Physics of Solids, 114 (2018), 1-30
- Grazioli, D., Magri,M., Salvadori A., Computational modeling of Li-ion batteries, Computational Mechanics, Review Article December 2016, 58 (2016), 889-909
- Salvadori A., Grazioli D., Geers M.G.D., Governing equations for a two-scale analysis of Li-ion battery cells, International Journal of Solids and Structures, 59 (2015) 90-109
- Salvadori A., Grazioli D., Geers M.G.D., Danilov D., Notten P., A multiscale-compatible approach in modeling ionic transport in the electrolyte of (Lithium ion) batteries, Journal of Power Sources 293 (2015) 892-911
- Salvadori A., Grazioli D., Magri M., Geers M.G.D., Danilov D., Notten P., On the role of saturation in modeling ionic transport in the electrolyte of (Li-ion) batteries. Journal of Power Sources 294 (2015) 696-710
- Salvadori A., Bosco E., Grazioli D., A computational homogenization approach for Li-ion battery cells. Part 1 - Formulation, Journal of the Mechanics and Physics of Solids, 65 (2014) 114-137

Ph.D. thesis (available upon request):

- Magri M., A theory for the analysis of electro-chemo-mechanical systems and its application to Li-ion batteries, 2018
- Grazioli D., Multiscale and Multiphysics Modeling of Li-Ion Battery Cells, 2015
- Bosco E., Computational homogenization formulations for localization and multiphysics phenomena in energy storage materials, 2013

Further achievements and awards:

HPC-Europa3 Transnational Access programme 2018 - "Virtual batteries: multiscale, multiphysics, and HPC for the next generation of energy storage materials"

CINECA - HPC LISA award 2016-2018 "HPC Simulations for the design of Li-ion batteries under extreme conditions."

MARIE CURIE ACTIONS - Intra-European Fellowships (IEF) Call:
Swelling and Fracturing in Lithium Batteries electrodes during Charging/Discharging Cycles (LiSF)

awarded in 2011 by CARIPLO - UniBs - MITMechE Faculty Exchange Program
awarded in 2012 by CARIPLO - UniBs - MITMechE Faculty Exchange Program
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