Surface phenomena of gradient materials

Abstract

The behavior of third gradient materials is analyzed. They possess stress tensor fields of second, third and fourth order. Starting from the principle of virtual power, we derive the admissible boundary conditions. Those on free surfaces can only be obtained by the application of the divergence theorem of surfaces. On the other hand, such an application to fictitious internal cuts makes no sense although it is usually practiced. We prove that some of the boundary conditions on a free surface may be interpreted as the equilibrium conditions of a shell. So a crust shell exists on such a surface and a beam exists where patches of the surface meet. On the other hand, no such shells or beams can be found with fictitious surfaces in the interior of a continuum. Our finding does not depend on any specific constitutive assumption.

Nonlocal continuum mechanics structures: The virtual powers method vs the extra fluxes topic

“…Therefore this approach therefore just pierces the target of the important hyper-boundary conditions topic, strictly related to the applicability of complex mechanical structures in a wide range of phenomena, see e.g. [2,3].…”

“…Higher-order boundary problems yield new and interesting insights in their applicability, since they are able to describe typical surface singularities of nano-technologies, see e.g. [2,3]. Inspired by the evergreen great attention towards these smart materials, we aim in going back to the issue upstream, concerning the right thermodynamic approach to derive governing PDEs equations for nonlocal theories and related boundary conditions.…”

System Identification using Self-Adaptive Filtering Applied to Second-Order Gradient Materials

“…This is particular true for materials with micro-structure, functionally graded materials, and metamaterials [3][4][5][6][7][8]. Furthermore, finite gradient plasticity [8][9] and theories for gradient fluids [10][11][12] became blossoming fields of research in the last decades. Because of the broad range of research in this field, the list of references is restricted to recent publications.…”

System Identification Using Self-Adaptive Filtering Applied to Second-Order Gradient Materials

“…This is particularly true for materials with a micro-structure, functionally graded materials, and metamaterials [3][4][5][6][7][8]. Furthermore, finite gradient plasticity [9,10] and theories for gradient fluids [11][12][13] became blossoming fields of research in the last few decades. Because of the broad range of research in this field, the list of references is restricted to recent publications.…”