Internal Length Gradient (ILG) Material Mechanics Across Scales and Disciplines

Abstract

Abstract A combined theoretical/numerical/experimental program is outlined for extending the internal length gradient (ILG) approach to consider time lags, stochasticity, and multiphysics couplings. Through this extension, it is possible to discuss the interplay between deformation internal lengths (ILs) and ILs induced by thermal, diffusion, or electric field gradients. Size-dependent multiphysics stability diagrams are obtained, and size-dependent serrated stress–strain curves are interpreted through combined gradient-stochastic models. When differential equations are not available for describing material behavior, a Tsallis nonextensive thermodynamic formulation is employed to characterize statistical properties. A novel multiscale coarse-graining technique, the equation-free method (EFM), is suggested for bridging length scales, and the same is done for determining ILs through novel laboratory tests by employing specimens with fabricated gradient micro-/nanostructures. The extension of ILG framework to consider fractional derivatives and fractal media is explored. Three apparently different emerging research areas of current scientific/technological/biomedical interest are discussed: (i) plastic instabilities and size effects in nanocrystalline (NC)/ultrafine grain (UFG) and bulk metallic glass (BMG) materials; (ii) chemomechanical damage, electromechanical degradation, and photomechanical aging in energetic materials; (iii) brain tissue and neural cell modeling. Finally, a number of benchmark problems are considered in more detail. They include gradient chemoelasticity for Li-ion battery electrodes; gradient piezoelectric and flexoelectric materials; elimination of singularities from crack tips; derivation of size-dependent stability diagrams for shear banding in BMGs; modeling of serrated size-dependent stress–strain curves in micro-/nanopillars; description of serrations and multifractal patterns through Tsallis q -statistics; and an extension of gradient elasticity/plasticity models to include fractional derivatives and fractal media.