6533b81ffe1ef96bd12788a7

RESEARCH PRODUCT

An energy residual-based approach to gradient effects within the mechanics of generalized continua

subject

description

AbstractGeneralized continua exhibiting gradient effects are addressed through a method grounded on the energy residual (ER)-based gradient theory by the first author and coworkers. A main tool of this theory is the Clausius-Duhem inequality cast in a form differing from the classical one only by a nonstandard extra term, the (nonlocality) ER, required to satisfy the insulation condition (its global value has to vanish or to take a known value). The ER carries in the nonlocality features of the mechanical problem through a strain-like rate field, being the specific nonlocality source, and a concomitant higher-order long-range stress (or microstress) field. The thermodynamic restrictions on the constitutive equations are determined by the latter inequality with no need for microstress equilibrium equations, whereas the principle of virtual power (PVP) is left in a standard format. The derived state equations include a set of partial differential equations involving the nonlocality-source strain-like quantity and the related long-range stress, as well as the associated higher-order boundary conditions determined by the insulation condition. Second-grade materials within gradient elasticity, gradient plasticity and crystal plasticity, as well as materials with microstructure (micromorphic and Cosserat materials) are considered to derive the pertinent constitutive equations. The proposed ER-based approach to gradient effects is shown to constitute a more straightforward and “economic” way to formulate the relevant constitutive equations than the PVP-based one.