The evolution of soft materials: interactions between mass addition and stress

Modeling the mechanical behavior of growing solid bodies with surface growth, where mass is added at the boundary of the body, is challenging using standard Lagrangian (or individual particle tracking) formulations, which are designed for situations with constant mass. Understanding observed failure and instabilities in diverse processes involving surface growth ranging from electrodeposition in batteries to melting and solidification in environmental applications and additive manufacturing, requires realistic models for studying the interaction between growth and stress. An Eulerian (or spatial) description of this problem enables mechanical modeling of growing solids by side-stepping the issue of the mass addition. Using a transport equation to determine the evolution of the deformation gradient enables computing the stress of the solid in an Eulerian setting. A free energy-based approach provides a unified and thermodynamically-consistent framework to study the thermomechanics of a growing solid by coupling the developed mechanical model with a thermal model. The Eulerian approach enables numerical modeling of the governing equations on a fixed discretization which avoids potential difficulties such as mesh entanglement and self-contact that arise in conventional Lagrangian approaches. Implementing this unified formulation in the open-source finite element framework FEniCS enables studying the role of thermo-mechanical stress in the distortion of 3D printed objects and glacial ablation.

Kiana Naghibzadeh is a Ph.D. candidate in Civil and Environmental Engineering at Carnegie Mellon University in Pittsburgh. She is broadly interested in using a combination of modeling and computation to discover the behavior of natural and architectured materials. Specifically, her current research focuses on modeling the dynamics of evolving systems which are motivated by applications in 3D printing, evolution in glaciers, and failure in batteries. In her future research, she will continue developing more realistic multiphysics models in combination with data science tools to study, predict, and understand the physics of real-world problems in biomechanics, advanced manufacturing, electrochemistry, and environmental engineering. Kiana received her BS and MS in Mechanical Engineering from Amirkabir University of Technology (Iran) in 2016 and 2018, respectively. She joined the Ph.D. program in Civil and Environmental Engineering at Carnegie Mellon University in 2019, where she also received her second MS in Computational Mechanics in 2021. Her research was recognized by the Neil and Jo Bushnell Fellowship in 2022 at Carnegie Mellon University and the Civil and Environmental Engineering Rising Stars Workshop at MIT in 2021. She received the Outstanding Teaching Assistant Award in 2021

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