Theoretical principles for computing local-gradient thermomechanical systems with allowance for subsurface phenomena

Abstract

Existing models for deformable solids that incorporate subsurface inhomogeneities [1, 2] usually are based on introducing a subsurface layer (shell) whose characteristics differ from those of the main material. A classification has been given [3] of results obtained from a bulk local-gradient approach. This paper continues that research and deals with deriving an equation system for the quantitative description of coupled physicomechanical fields in the presence of local strain gradients. We consider a thermoelastic system K, present in an inertial medium K, + (thermostat) and interacting with it. A conceptively distinguished subsystem K C K, is put biectively into relationship with a region X(r) in three-dimensional euclidean space such that the boundary elements k E OK relate to elements x(r) E OX(r) in the surface of region X(r). The equation system is formulated in the Lagrangian coordinate system k ~ [ ~ {g~}, (i) in which we take the region of space X(ro) as the specified set of elements (, while the Lagrangian coordinates {(i} are the coordinates of the points X(ro) E X(ro). The conservation equation for the total energy for the subsystem K at time r is [4]