Frank and Ora Lee Marble Professor of Aeronautics and Mechanical Engineering

Research

My main interest lies in understanding and modeling the behavior of materials and structures across length and time scales, ranging from atomistic to macroscopic, and over a variety of conditions, from quasistatic to extremes of pressure, temperature and rate of deformation. I am particularly interested in multiscale aspects of material behavior and the structure/property relation, including the development and evolution of microstructure during deformation and its role in shaping the macroscopic response of materials and structures.

I am also interested in understanding the limits of usability of materials, e.g., formability limits, failure mechanisms, fatigue life prediction, plastic deformation, fracture and fragmentation, material and structural instabilities, and others. From a methodological point of view, the main goal is to develop mathematical and computational methods enabling the application of high-fidelity multiscale material models to engineering systems, with a particular view to predicting their behavior under operational conditions with quantified uncertainties. Modern nonlinear analysis and high-performance computing are two disciplines that I find particularly useful in that regard and that have provided, and continue to provide, the basis and the focus for much of my work.

Some of the currently funded research projects that I am involved in at Caltech are:

  • US National Institutes of Health (NIH): Oncotripsy, Molecular Functional Ultrasound for Non-Invasive Imaging and Image-Guided Recording and Modulation of Neural Activity. Ultrasonic neuromodulation (UNM) is among the most significant new technologies being developed for hu-man neuroscience because it can provide non-invasive control of neural activity in deep-brain regions with mil-limeter spatial precision. This capability complements human imaging techniques for studying brain connectivity and function in basic and clinical applications. However, despite a surge of interest in UNM, the lack of knowledge about its mechanisms and recent findings of off-target sensory effects accompanying direct neuromodulation pose significant challenges to the use of this technology in human neuroscience. To overcome these challenges, we leverage a mechanistic understanding of ultrasonic neuromodulation to engineer methods for direct, spatially selective control of human brain function.

Other research projects that I am currently involved in are:

  • Ministerio de Ciencia, Innovación y Universidades (Spain), project "Plataforma Computacional para el Disenho Integrado de Materiales de Altas Prestaciones para la Industria de las Energias Limpias," coordinated by Pilar Ariza (University of Seville). The project focuses on the development of computational tools for the analysis of hydrogen storage mechanisms in magnesium within the framework of the emerging hydrogen economy.
  • Junta de Analucia (Conserjeria de Economia y Conocimiento), project on "Estudio de Materiales Reforzados con Grafeno para su Aplicacion en Sistemas de Almacenamiento de Energia" (REINSTOMAT), coordinated by Pilar Ariaza and Hector Cifuentes (University of Seville). The project is concerened with the development of advanced concrete formulations including embedded graphene particles for application in energy storage systems.
  • DFG grant on "Multiobjective Topology Optimization of Anode Structures for Lithium-Ion Batteries", coordinated by Kerstin Weinberg (uni-Siegen). The goal of the project is to develop an optimization tool for the design of silicon anodes within lithium-ion batteries. To this end, competing design requirements must be incorporated in an adequate optimization strategy. The large volume expansion upon lithiation requires conventional topology optimization to be extended to full finite kinematics. The maximization of electrical conduction through the structure while preserving structural integrity are competing design objectives. Additionally, the strength, structural integrity and life expectancy of the batteries are to be maximized. To this end, the topology optimization protocol needs to account for accumulated damage. With these objectives in mind, we develop numerical tools for the design of battery anodes using multi-objective topology optimization.
  • Franco-German (ANR-DFG) PRCI project on "Direct Data-Driven Computational Mechanics for Anelastic Material Behaviours" (D3MecA), coordinated by L. Stainier (ECN), in collaboration with CNRS, RWTH (Steafnie Reese, lead) and uni-Bonn. The objectives of this project are to implement and assess data-driven (DD) approaches to inelasticity in a framework able to handle cases oriented towards industrial applications: use of actual, noisy and possibly incomplete, experimental data, complex 3D geometries and loading, efficiency and robustness of solvers, uncertainty quantification. An additional objective is to provide an online platform allowing to share the methodology and the associated data with the scientific community.
  • Research Council of Norway project on "Multiscale Hydrogen Embrittlement Assessment for Subsea Conditions" (M-HEAT), coordinated by Zhilian Zhang (NTNU). Driven by the prioritized industrial needs of structural integrity and life extension, and powered by multiscale simulations and experiments, the M-HEAT project aims to establish quantitative hydrogen embrittlement tools for engineering materials exposed to subsea conditions, by deriving mechanism-based hydrogen-induced failure criteria and forging the transferability from lab scale tests to industrial components.
  • UK Engineering and Physical Sciences Research Council project on "Tribology as and Enabling Technology (TRENT)”, coordinated by Ardian Morina (University of Leeds). The key aim of TRENT is to introduce tribology as an enabling technology in the engineering of intelligent systems for manufacturing and robotics. This is facilitated through collaboration with teams from Norway (NTNU); Germany (Max Planck) and the US (Caltech). Our study has the potential to have significant impact across a number of application areas (for example, transport, healthcare, energy (nuclear, offshore etc.) and both focus areas are pivotal to delivery on the Industrial Strategy and to EPSRC themes as highlighted in the case for support. This will only achieved through a well-defined strategy for dissemination to, and collaboration with academia and industry.
  • DFG SFB 1060 project on "The Mathematics of Emergent Effects", coordinated by Stefan Mueller (uni-Bonn), subproject A05 "From Pair Potentials to Macroscopic Plasticity". This project is concerned with the study of plasticity, damage and fracture in solids, with emphasis on energetic methods, the derivation of effective macroscopic models from microscopic or mesoscopic assumptions, the development of mathematical tools, their application to specific problems, and on the study of concrete materials. Mathematically, the main tools are G convergence, rigidity estimates for gradient fields and the theory of functions of bounded deformation.
  • Mercator Fellow in DFG Research Training Group GRK 2423 (FRASCAL) on "Fracture across Scales: Integrating Mechanics, Materials Science, Mathematics, Chemistry and Physics", coordinated by Paul Steinmann (FAU), subproject on "Adaptivity in the Dynamics Simulation of Fracture Mechanics". The aim of this project is the development of spatial and temporal mesh adaption strategies for different regularized fracture theories, with particular focus on phase-field modeling.
  • Mercator Fellow in DFG Collaborative Research Centre/Transregio 87 (SFB-TR 87) on "Pulsed High Power Plasmas for the Synthesis of Nanostructured Functional Layers," coordinated by Peter Awakowicz (RUB). The project investigates how plasma behaves on certain surfaces and which interactions result from this behavior. The main focus is on pulsed plasmas, which are partially supported by magnetic fields and show promise for synthesising intelligent coating systems in the future. The project addresses fundamental questions of plasma physics from the atoms in the gaseous phase down to performance characteristics of coated material surfaces. Plasma can be used to coat materials and thus protect them from wear. Such coatings can also increase the storage capacities of computers and thus also make mobile phones smaller. The diverse properties and fields of use of plasma offer the opportunity to develop innovative materials.
  • DFG Schwerpunktprogramm on "Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials" (SPP 2256), project on "Mathematical analysis of microstructure in supercompatible alloys", coordinated by Sergio Conti and Stefan Mueller (uni-Bonn). The project is concrened with the microstructures of newly discovered supercompatible alloys, focusing initially on the energetics and geometry of curved macroscopic interfaces, which are not possible without supercompatibility. We explore hysteresis in supercompatibile alloys using the recently developed approach of data-driven elasticity, which offers a new perspective on relaxation and phase transitions. We also investigate situations where microstructure is geometrically possible but energetically not necessary.
  • DFG Schwerpunktprogramm on "Robust Coupling of Continuum-biomechanical In Silico Models to Establish Active Biological System Models for Later Use in Clinical Applications – Co-design of Modelling, Numerics and Usability" (SPP 2311), project on "Multiscale Modelling of Ultrasound Neuromodulation in the Human Brain – From Neuron to Brain", coordinated by Marc-Andre Keip and Metin Sitti (uni-Stuttgart). The project aims to develop a mechanistic understanding of ultrasonic neuromodulation enabling the engineering of methods for direct, spatially selective control of human brain function. Methodologically, the overarching objective of the proposed work is to develop a multiscale hierarchy of electromechanical models that provides a fundamental understanding, as well as a modeling and predictive capability, of how ultrasonic excitation results in brain activity and neuromodulation.