Crack enucleation and propagation in embrittled materials. Numerical simulations, multiscale analysis, plasticity analogies, real-life applications. Within the theoretical and computational analysis of multi-scale fracture mechanics we are devoting research efforts in the area of crack propagation in brittle and quasi-brittle materials by means of standard dissipative system analogies, advanced variational formulations, and numerical algorithms for crack growth. These studies, fueled by a long-term cooperation with the Cornell Fracture Group and more recently by a cooperation with internationally renowned enterprises, are undergoing a vibrant development. A recent theoretical investigation provided a computational breakthrough, which has the potential to track 3D crack growth in embrittled materials very efficiently and on a firm theoretical basis. Extensions have been carried out for layered materials and, most interesting, for the multi-scale and multi-physics fracture processes induced by diffusion of species in solids. Selected publications: - A. Salvadori, P. Wawrzynek, F. Fantoni, Fracture propagation in brittle materials as a standard dissipative process: effective crack tracking algorithms based on a viscous regularization, Journal of the Mechanics and Physics of Solids 127 (2019) 221–238 - Silvia Agnelli, Francesco Baldi, Fabio Bignotti, Alberto Salvadori, Isabella Peroni, Fracture characterization of hyperelastic polyacrylamide hydrogels, Engineering Fracture Mechanics 203 (2018) 54–65 - M. Zammarchi, F. Fantoni, A. Salvadori, P. Wawrzynek, High Order Boundary and Finite Elements for 3D Fracture Propagation in Brittle Materials, Comput. Methods Appl. Mech. Engrg. 315 (2017) 550-583 - Salvadori A., Fantoni F., Fracture propagation in brittle materials as a standard dissipative process: general theorems and crack tracking algorithms, Journal of The Mechanics and Physics of Solids, 95, (2016), 681-696 - Bosco E., Kouznetsova V.G., Coenen E.W.C., Geers M.G.D., Salvadori A., Multiscale computational homogenization-localization modelling of microscale damage towards macroscopic failure: describing non-uniform fields across discontinuity., Comput Mech (2014) 54:299-319 - Salvadori A., Fantoni F., On a 3D crack tracking algorithm and its variational nature., Journal of the European Ceramic Society 34 (2014) 2807-2821, - Salvadori A., Fantoni F., Weight function theory and variational formulations for three-dimensional plane elastic cracks advancing, International Journal of Solids and Structures, 51 (2014) 1030-1045 - Salvadori A., Fantoni F., Minimum theorems in 3D incremental linear elastic fracture mechanics, International Journal of Fracture, Volume 184, Issue 1 (2013), 57-74 - Salvadori, A., Giacomini, A., The most dangerous flaw orientation in brittle materials and structures, International Journal of Fracture, Volume 183, Issue 1 (2013), 19-28, - Salvadori, A., Wawrzynek, P., Ingraffea, A., Energy dissipation in the mixed mode growth of cracks at the interface between brittle materials. International Journal of Fracture: Volume 181, Issue 2 (2013), 257-271 - Salvadori, A., Crack kinking in brittle materials, Journal of the Mechanics and Physics of Solids, 58 (2010) 1835-1846 - Salvadori A., A plasticity framework for (linear elastic) fracture mechanics, Journal of the Mechanics and Physics of Solids, 56 (2008) 2092-2116 More at http://m4lab.unibs.it/Fracture.html

Effective material properties and multiphysics behavior of granular materials. Data-driven analysis in co-designed experimental, theoretical, and numerical investigations of effective material properties in granular materials have been performed. Specifically, the Young's modulus for cold compacted powder materials has been targeted. Co-designed experimental, theoretical, and numerical investigations aiming at estimating the value of the Young's modulus for cold compacted powder materials have been undertaken. The concept of image-based modeling has been used to reconstruct the morphology of the powder structure with high fidelity. Analyses on aluminum powder pellets provide significant understanding of the microstructural mechanisms that preside the increase of the elastic properties with compaction. The role of the stress percolation path and its evolution during material densification has been highlighted and a scaling law for the surface contact area between powder particles has been proposed. At the same time high-performance computing analyses of Reverse Taylor impact tests on solid pellets, at strains in the order of 7000s-1 modeled with large strain crystal plasticity were successfully dealt with. Finally, a new visco-plastic model for granular materials is under development. This model accounts for the rate dependence, elasto-plastic coupling, pressure sensitivity, and transition to full solid state. The model has been implemented, verified, and validated against experimental analyses available in the literature for copper powder compounds. width= Selected publications: - Salvadori A., Lee S., Gillman A., Matous K., Shuck C., Mukasyan A., Beason M., Gunduz I.E., Son S.F., Numerical and experimental analysis of the Young's modulus of cold compacted powder materials, Mechanics of Materials, 112 (2017) 56-70 Krairi A., Matouš K, Salvadori A., A poro-viscoplastic constitutive model for granular materials at finite strains, International Journal of Solids and Structures 135 (2018) 289–300,

Materials science enhanced by machine learning. We are currently working to investigate the role of machine learning algorithms in predicting the overall response of non linear elastic and inelastic composite materials, moving from the geometric and constitutive properties of their microstructures. Replacing computationally expensive homogenization techniques with machine learning algorithms could reveal to be extremely promising given the importance of composites in numerous engineering sectors. Composite materials in fact can be tailored to meet specific design requirements and their use is becoming increasingly attractive to fulfill industry needs due to their mechanical and physico-chemical properties. It is worth emphasizing that the capability to make full use of extensive data is of fundamental importance in the application of machine learning to materials science research. In this regard numerous efforts have made by the scientific community in order to discover ways to overcome the shortcomings that both computational simulations and experimental measurements could involve in terms of time and costs. For example with the introduction of the Materials Genome Initiative (www.mgi.gov) in 2011 and the coming of the big data era, a great work has been done to collect extensive data sets on materials properties in order to provide a fast access to the properties of know materials. Machine learning is a powerful tool for discovering patterns in such a framework and in recent years the modeling of complex relations between physical factors and materials properties has proved to be successful thanks to machine learning techniques. The application of machine learning in materials science concerns mainly material properties prediction, at the macro and micro scales, the discovery of new materials, and numerous other purposes such as process optimization, density functions approximations, monitoring of batteries and prediction of fatigue crack growth rate to cite a few.

Mechanics of Energy Storage Materials: multiscale and multiphysics modeling of Li-ion batteries. 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. width= 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. width= 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. This innovative strategy in modeling ESM received interest both on the academic and industrial sides. More at http://m4lab.unibs.it/Li-ion.html

Mechanobiology : A vibrant area of my research concerns the mechanics of cells and applications to angiogenesis, metastatization, tumor growth, in strong cooperation with the Patient-based and preventive medicine (MPP) lab @ UNIBS. We develop predictive science through modeling and computational simulations of biological processes, stemming from rigorous thermodynamic formulations, numerical analysis in high performance computing frameworks, verification and validation against experimental evidences. More at http://m4lab.unibs.it/Mechanobiology.html

Multi-scale characterization of high strenght steels. This project falls within the funded proposal "SteelPro 4.0 - Sviluppo di acciai speciali attraverso innovazioni nella realizzazione del processo di fabbricazione, caratterizzazione dei materiali e controllo integrato dell'intera filiera produttiva". We aim at modeling the overall response of high strength steels from the microscopic realistic description of multi-phase material behavior, making use of accurate TEM and SEM phase reconstruction, computational homogenization strategies coupled with crystal plasticity in large strains, high performance computing.