Non-classical and non-local continuum mechanics and constitutive theories


Karan Surana, University of Kansas

J. N. Reddy, Texas A&M University

Arun Srinivasa, Texas A&M University

Debashish Roy, Indian Institute of Science

Aaron D. Joy, University of Maine



The broad aim of this symposium is to reflect on the current state of continuum theories and identify short- and long-term research opportunities and goals – theoretical, computational as well as complementary experimental – with the objective of identifying thermodynamically consistent macroscopic non-classical and non-local continuum theories for solid and flent continua. The field of classical continuum theories addresses a large majority of theoretical and practical questions that arise in day-to-day engineering science. However, they appear less than satisfactory when applied to certain modern engineered materials and structures that require consideration of additional physics, involving multiple scales in general and the microstructural information in particular, in the theories and/or their computational models. Unlike classical continuum mechanics, non-classical continuum theories a field theoretic description for the microstructural features, including defect distributions that generally precipitate inelastic response, and adopt certain nonequilibrium aspects of thermodynamics in framing the constitutive relations. Reorganizations of the defect microstructure, induced by external stimuli such as mechanical loading, typically necessitate non-local modeling to account for long-range interactions and in the appropriate accomplishment of upscaling. The symposium will consist of presentations on non-classical and non-local continuum theories and models, including applications of these ideas to beams, plates, shells, composite structures, architected materials, functionally graded materials, fracture mechanics, plasticity, compressible and incompressible fluid continua, and other emerging topics in continuum mechanics.

Titles and abstracts are invited from interested colleagues on new theoretical developments in the field theoretic representation of the defect microstructure, related conservation and balance laws, and the constitutive theories for solid and fluent continua. Granular mechanics, homogenization methods and associated constitutive theories are also within the scope of this symposium. Works related to purely theoretical developments, computational studies for model problems as well as experimental works are also welcome in the symposium. In addition, theoretical work and applications related to non-equilibrium thermodynamics are also encouraged.