Events

Representing general three-dimensional states of residual stress

Residual stresses are ubiquitous and stem from diverse, complex sources; consequently, characterization is essential yet challenging. 

Most existing theoretical approaches assume a prescribed constitutive response. In contrast, we develop a framework for characterizing residual stresses in arbitrary solids that is independent of their origins and of material properties. We obtain a family of residual stress bases, each comprising elements that can be linearly combined to represent any square-integrable residual stress field. Our construction involves minimizing a quadratic functional of the stress gradient, which reduces the task to an eigenvalue problem whose eigenfunctions constitute the basis elements. Three applications are presented: (a) interpolation, (b) fitting, and (c) representation of arbitrary residual stresses. The choice of basis can be tailored to the problem. 

Stresses induced by self-equilibrated surface tractions—relevant to most stationary objects in the absence of gravity—will also discussed. In this extension, additional boundary terms arise; the outcome is tensor-valued bases for systematic representation of arbitrary equilibrated stresses, with applications to stress-based variational principles and to the design of structures and materials with optimally distributed stresses.

Eliot Fried

Eliot Fried received his PhD in Applied Mechanics from the California Institute of Technology in 1991, followed by postdoctoral fellowships from the National Science Foundation. He subsequently held tenured faculty appointments at the University of Illinois at Urbana--Champaign, Washington University in St. Louis, McGill University (Tier I Canada Research Chair in Interfacial and Defect Mechanics), and the University of Washington, before joining the Okinawa Institute of Science and Technology as Professor and Head of the Mechanics and Materials Unit. His honors include a National Science Foundation Research Initiation Award, a fellowship at the Center for Advanced Study at Illinois, and a Critical Research Initiative grant from the same institution. His research concerns mechanics, thermodynamics, and geometry. Apart from the seminar topic, his current work includes the analysis of unstretchable surfaces subject to edge loads, coupling of surface reaction--diffusion processes with bulk strain and diffusion, and new families of under-constrained linkages. Applied directions include diamond films on glass for sensing and nanofluidics, exact geometrical constructions of developable surfaces, and devices for natural fiber processing, such as spinning yarn from banana pseudostem fibers. He is a co-inventor on two U.S. patents and a co-applicant on two additional patents, including one concerning laser-written nanochannels and another on yarn produced by a fiber-spinning machine developed in his group.