Abstract

A novel continuum mechanics theory of deformable solids accounts for large deformations, nonlinear elasticity, inelastic deformation mechanisms, microstructure changes, and time-dependent fields. This theory incorporates concepts from Finsler differential geometry, and it provides a diffuse interface description of surfaces associated with evolving microstructure. Physical mechanisms include fractures, twinning, phase transitions, and inelastic shearing, with cleavage planes, twin boundaries, phase boundaries, and slip planes the associated surfaces. An internal state vector of pseudo-Finsler space is viewed as an order parameter. Governing equations are derived in the context of finite kinematics, balances of momentum and energy, and either Euler- Lagrange equations or Ginzburg-Landau kinetic laws. Jump conditions pertinent to shock loading, analogs of the Rankine-Hugoniot equations, are obtained. Metric tensors vary isotropically with internal state via a conformal transformation in most applications to date, but more general Finsler metrics depending on direction are admissible. When a conventional Euclidean rather than pseudo- Finsler metric is used, the theory reduces to a variational phase-field model.

Problems solved semi-analytically treat single crystals of magnesium and boron carbide in 1D or 2D. Comparisons with data from experiments or atomic simulations validate results. Finite element methods consider 3D problems for heterogeneous polycrystals, including high-toughness ceramic composites B4C-TiB2 and diamond-SiC. Results demonstrate effects of phase volume fractions, phase morphologies, grain sizes, activity of inelastic deformation mechanisms, and amorphous grain boundary films on strength.

Bio

John D. Clayton has served as a staff member at the US Army Research Laboratory since 2003. As a team leader in multi-scale mechanics and impact physics, he conducts fundamental research in the mechanics and failure of solid materials. Recent work has further addressed soft tissue biomechanics. He has also mentored many junior scientists, post-doctoral scholars, and graduate students.

Dr. Clayton obtained a PhD from the Georgia Institute of Technology in 2002. He has authored four books and over 75 journal articles on various topics in solid mechanics, physics, materials science, and applied mathematics. He serves on the editorial boards of several scientific journals and has been an active member of the American Academy of Mechanics, the American Physical Society, and the American Society of Mechanical Engineers. Honors include the Baltimore Federal Executive Board Career Silver Medal (2016), the Army Special Act Award (2014), twice the ARL Award for Publication of the Year (2011, 2017), five ARL Director’s Research Initiative Awards during the period 2004-2014, and the National Research Council post-doctoral fellowship (2003). He was elected a Fellow of the Army Research Laboratory in 2016 and a Fellow of the American Society of Mechanical Engineers in 2017. Dr. Clayton served as visiting research faculty at the Courant Institute of Mathematical Sciences in New York in the Spring of 2016 and at Columbia University in New York in the Fall of 2016. He has taught a graduate course on finite element methods at the University of Maryland, College Park, annually since 2015.