Abstract:

In this lecture, mass lumped, rate-type C continuous finite element models of arbitrarily higher order using shear deformable beam, plate, and shell elements are discussed. Higher-order elements provide true curvature, improved performance in bending and buckling, and avoid hourglass modes and numerical locking without ad hoc treatments. Historically, first-order shear deformation finite elements have been predominant in explicit finite element codes because of difficulties achieving robust and reliable mass-lumping. We spatially discretize using a standard weak-form 0 Galerkin finite element approximation and optimal C Lagrange shape functions of arbitrarily higher order and integrate throughout time using a central-difference method and a lumped mass matrix. Several numerical examples of nonlinear finite deformation demonstrating the accuracy and utility of the lumped-mass elements developed are presented.

Bio:

Dr. Reddy is a Distinguished Professor, Regents’ Professor, and the holder of the O’Donnell Foundation Chair IV in Mechanical Engineering at Texas A&M University. He is known for his significant contributions to the field of applied mechanics through the authorship of many textbooks (25) and journal papers (>800). His pioneering works on the development of shear deformation theories have had a major impact and have led to new research developments and applications. In recent years, Reddy's research has focused on the development of locking-free shell finite elements and nonlocal and non-classical continuum mechanics problems dealing with architected materials and structures and damage and fracture in solids. Dr. Reddy has received some of the highest awards, including the Leonardo da Vinci Award from the European Academy of Sciences, the IACM Congress (Gauss-Newton) Medal from the International Association of Computational Mechanics, and the SP Timoshenko Medal from American Society of Mechanical Engineers, He is a member eight national academies.

ABOUT JAN D. ACHENBACH:

Jan D. Achenbach was the Walter P. Murphy Professor and Distinguished McCormick School
Professor Emeritus-in-Service at the McCormick School of Engineering and Applied Science at Northwestern University until his death in August, 2020. He made distinguished contributions to many areas of applied mechanics including fracture mechanics, wave propagation, and quantitative nondestructive evaluation. During his tenure spanning nearly six decades at the McCormick School of Engineering, Prof. Achenbach mentored over 40 Ph.D. students and countless postdocs, many of whom became leaders in industry and academia. His innovations in non-destructive evaluation, such as ultrasonic approaches for inspecting DC-9 aircraft wings without disassembly improved aircraft reliability, saving lives and millions of dollars. Prof. Achenbach received top honors from many professional organizations such as ASME, ASCE, and SES. He was a member of both the National Academy of Engineering and National Academy of Sciences, an elected fellow of the American Academy of Arts and Sciences, and a recipient of both the U.S. National Medal of Technology and the National Medal of Science.

Abstract:

The functioning of Li metal-solid state batteries (LMSSB) requires that interfacial contact between the Li metal anode and the solid electrolyte (SE) be maintained during cycling. A reduction in contact area during Li stripping will increase the local current density during subsequent Li plating, fostering dendrite nucleation. The contact area is influenced by the rate of Li transport within the anode towards the interface. Relevant transport mechanisms include diffusion and creep, with faster rates of these processes resulting in improved performance. Given the importance of these transport modes, predicting them as a function of the anode’s microstructure, stress state, and temperature will be helpful in the design of LMSSB. Here, the rates of diffusion and creep in Li are predicted using atomic scale simulations. A primary goal is to understand if and how Li microstructure impacts the performance of LMSSB. First, molecular dynamics is used to estimate the rate of Li diffusion along dislocations and in grain boundary triple junctions. By combining this data with that from a prior study of grain boundary diffusion, the dominant diffusion mechanisms and overall rates of self-diffusion in Li polycrystals are predicted as a function of grain size, grain shape, dislocation density, and temperature. A 1D continuum model for interfacial contact is parameterized using the computed diffusion data. The model predicts that high dislocation densities (~10 12 /cm 2 ) and/or small grain sizes (~10 m) enable achieving battery performance targets. Secondly, the dominant creep deformation mechanisms are predicted as a function of applied stress, grain size, and temperature. Grain boundary sliding and coble creep are observed to be the primary mechanisms for micron-sized grains. Finally, a kinetic lattice Monte Carlo model is developed to monitor the dynamics of Li voids as a function of interfacial thermodynamics and the presenceof grain boundaries.

Bio:

Don Siegel is Professor and Chair of the Walker Department of Mechanical Engineering at the University of Texas at Austin. He also has appointments in the Oden Institute for Computational Engineering and Sciences and the Texas Materials Institute. At UT he is a Temple Foundation Endowed Professor and holds a Cockrell Family Chair for Departmental Leadership. Prior to joining UT in 2021, Prof. Siegel spent 12 years at the University of Michigan, with earlier posts in industry (Ford Motor Company) and at national laboratories (Sandia National Lab and the U.S. Naval Research Lab). Siegel is a computational materials scientist whose research targets the development of energy storage materials and lightweight alloys. He is a recipient of the NSF Career Award and a Gilbreth Lectureship from the National Academy of Engineering.

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