Multi-phase field approach to tensile fracture and compressive
crushing in grained heterogeneous materials

BIO
Pietro Lenarda received his Master’s Degree in Mathematics at the University of Florence and his PhD in Computational Mechanics at IMT School for Advanced Studies Lucca, Italy. After a post-doc at the Italian Institute of Technology in Genoa at the Laboratory for Computational Nanomedicine, he became a Tenure Track Assistant Professor at IMT School for Advanced Studies Italy in 2023 within the Multiscale Analysis of Material (MUSAM) research unit directed by Prof. Marco Paggi.

He has been a visiting fellow at the University of Oxford, UK (2016), at the University of Seville, Spain (2022), and at the University Campus Bio-Medico of Rome (2017 and 2022).

His research focuses on computational methods for numerical solutions of nonlinear coupled phenomena in continuum mechanics, with particular applications to phase-field variational formulations for fracture mechanics.

ABSTRACT

Multi-phase field approach to tensile fracture and compressive crushing in grained heterogeneous materials

The variational phase-field approach to brittle fracture is extended to deal with the simultaneous interplay of two failure mechanisms affecting grained heterogeneous materials in compression—fracture in tension and crushing in compression. The problem is addressed within the context of a multi-phase field variational approach, with two independent damage variables associated with each failure mechanism.

The proposed computational method, implemented in the open-source FEniCS finite element software, is applied to 2D mesoscale models of concrete specimens in compression. The predicted trends for specimens with different aspect ratios and varying degrees of lateral confinement are consistent with experimental results on apparent compressive strength and with typically observed failure patterns.

Abstract:

For three centuries, Western thought lived under Newton’s clockwork paradigm—a
worldview of predictability, control, and linear causation. It shaped institutions from
Madison’s checks and balances to Taylor’s scientific management, defining modernity.
But successive scientific revolutions—statistical thermodynamics, relativity, quantum
mechanics, evolution, game theory, DNA, and AI—revealed a radically different
universe: dynamic, probabilistic, and deeply complex. We have shifted from Newton’s
clocks to what Popper called a “cloud world,” marked by emergence, interdependence,
and irreducible uncertainty.

This talk traces how these revolutions reshaped our understanding of reality and
explores their leadership implications: why navigating 21st-century challenges demands
embracing complexity, cultivating resilience, and designing organizations that work with,
rather than against, dynamic systems.

Bio:

Julio Mario Ottino is a researcher, engineering scientist, academic leader, educator, artist, and author. He is Founder and Co-Director of the Northwestern Institute on Complex Systems, McCormick Institute Professor of Engineering, W.P. Murphy Professor of Chemical Engineering, with a courtesy appointment in Mechanical Engineering at the McCormick School of Engineering, and Professor of Management and Organizations at Northwestern at the Kellogg School of Management in Northwestern University. Widely recognized as a world authority on mixing, chaos, and complexity, he has been a Guggenheim Fellow and is a member of the National Academy of Engineering, the National Academy of Sciences, and the American Academy of Arts and Sciences. As Dean of Engineering, he launched major university-wide initiatives, programs, degrees, and centers spanning design, energy and sustainability, synthetic biology, human–computer interaction, and entrepreneurship. His most recent book, The Nexus (MIT Press, 2022) was a category winner in Engineering and Technology, from the Association of American Publishers

Abstract:

We provide an overview of a recent NASA University Leadership Initiative project entitled “Development of an Ecosystem for Qualification of Additive Manufacturing Processes and Materials in Aviation”. This work demonstrated the dependence of fatigue on defect structures in AM Ti-6Al-4V. Our current NASA Science & Technology Research Institute “Institute for Model-Based Qualification & Certification of Additive Manufacturing (IMQCAM)” is creating a numerical digital twin (DT) for predicting fatigue as a function of process parameters. The key result of a systematic variation across power-velocity space was that the defect number density was anti-correlated with fatigue life. The fatigue-based process window was much narrower compared to typical reports and explainable in terms of observed variations based on spatter rates and intermittent lack of melt pool overlap. We report on recent developments in modeling microstructure, texture and pores along with variations in heat treatment. We conclude that establishing a qualified materials process is feasible via an efficient survey of a limited domain of process space. Linking models together in the DT requires substantial effort in terms of data exchange. In terms of predictability of fatigue, the limited data suggests that the scatter in life is smallest in the long crack (Paris Law) regime, intermediate for short cracks and largest for crack nucleation. This provides an important background for Uncertainty Quantification (UQ), which is a major focus for the IMQCAM team and which has already revealed a significant sensitivity to compositional variations, for example.

Support from multiple agencies is gratefully acknowledged, including NASA, DOE/BES, DOE/NNSA, ONR, NSF, OEA, Commonwealth of Pennsylvania, and Ametek. I am indebted to my many collaborators.

Bio:

I have been a member of the faculty at Carnegie Mellon University since 1995. I am also the Co-Director of the NextManufacturing Center on additive manufacturing. Previously, I worked for the University of California at the Los Alamos National Laboratory. I spent nine years in management with four years as a Group Leader (and then Deputy Division Director) at Los Alamos, followed by five years as Department Head at CMU (up to 2000). I have been a Fellow of ASM since 1996, Fellow of the Institute of Physics (UK) since 2004 and Fellow of TMS since 2011. I received the Cyril Stanley Smith Award from TMS in 2014, was elected as Member of Honor by the French Metallurgical Society in 2015 and then became the US Steel Professor of Metallurgical Engineering and Materials Science in 2017. I received Cyril Stanley Smith Award from the International Conference on Recrystallization and Grain Growth in 2019 and the Hans Bunge Award from the Intl. Conf. on Textures of Materials (ICOTOM) in 2024. I was an International Francqui Professor (Belgium) in 2022 and I received the ASM Gold Medal and was promoted to University Professor, both in 2024. My research focuses on processing-microstructure-properties relationships with interests in additive manufacturing, the measurement and prediction of microstructural evolution, the relationship between microstructure and properties, especially three-dimensional effects, texture & anisotropy and the use of synchrotron x-rays.