Title: Strain Localization, Lyapunov Stability, and Internal Length in Continuum Mechanics

Abstract: Classical continuum mechanics is formulated through balance laws for mass, momentum, angular momentum, and energy, together with thermodynamic restrictions, yet these equations are written without an explicit internal length reflecting material heterogeneity. In problems involving material instability, strain softening, and localization, this omission becomes especially significant: numerical simulations exhibit mesh dependence and localization zones of vanishing thickness, despite experimental evidence for deformation bands of finite size.

In this talk, I revisit this issue from the viewpoint of Lyapunov stability and present a new continuum field theory that I call the Padé-enriched continuum. The central idea is that an internal length should not be introduced only afterward, through constitutive modeling, to recover mesh-independent computations and finite localization widths. Rather, it should emerge from governing equations that capture the underlying heterogeneous structure of materials with sufficient fidelity. From this perspective, micromorphic continua, as well as weakly and strongly nonlocal constitutive theories, remain valuable, but their primary role should be to describe actual material behavior across scales, not merely to regularize strain localization.

Bio: Madura Pathirage is an Assistant Professor in the Gerald May Department of Civil, Construction and Environmental Engineering at the University of New Mexico, where he leads the Theoretical and Applied Fracture Mechanics research group. He earned his PhD in Mechanics, Materials, and Structures from Northwestern University in 2020 and held postdoctoral appointments at the University of Pau and Pays de l’Adour in France and at Northwestern University. His research combines analytical and computational methods to understand fracture and multi-physics processes in quasi-brittle materials under a wide range of loading conditions. He has co-authored articles in PNAS, JMPS, and other leading journals in applied mechanics, fracture mechanics, and the physics of solids. He is a recipient of the ORAU Ralph E. Powe Junior Faculty Enhancement Award and is an active member of the Engineering Mechanics Institute of ASCE and the U.S. Association for Computational Mechanics.