Internal structures and internal variables in solids

Abstract

The response of many materials (metals, alloys, composites, etc.) to external loading may be essentially influenced by an existing or emerging internal structure at smaller scales which must be taken into account. For this purpose the concept of dual internal variables can be used in order to describe the effect of internal fields. In this paper it is shown that dual internal variable theory is sufficiently general to model cases like micromorphic elasticity and the influence of microtemperature. Based on the material (canonical) balance equations for material momentum and energy, this approach extends single internal variable theory. The resulting governing equations are not limited by first-order reactiondiffusion equations, as is typical for single internal variable theory. Hyperbolic governing equations for internal variables provide the description of the interaction of waves at the macro and microlevels.

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“…Berezovski et al [2011b] have used the dual internal variable concept [Ván et al 2008] in addition to canonical equations (9) and (13). In this case, for example, the governing equation for the internal variable α (identified as the microdeformation tensor) is obtained by satisfying inequality (14) [Engelbrecht and Berezovski 2012]:…”

“…Bearing in mind microstructured materials, it is possible to use the concept of internal variables to construct mathematical models for governing the wave motion. This is achieved by the dual internal variable theory [Ván et al 2008], which permits modelling of the dissipation effects due to the microstructure in thermoelastic solids [Berezovski et al 2011b;Engelbrecht and Berezovski 2012]. The dissipation is associated with microtemperature, i.e., fluctuations of temperature due to the difference of thermal characteristics of the macro-and microstructure in a solid.…”

On modelling of wave propagation in microstructured solids

“…For the sake of simplicity, we focus on one-dimensional problems only. The full three-dimensional theory is presented in [ 10,11 ].…”

On the role of micro-inertia in enriched continuum mechanics

“…Although various generalized continuum models have been introduced to describe dispersion (see the pioneering works [1,2]; for a review of the use of enriched models in the dynamics of heterogeneous materials we refer to [3]), it is still not completely clear whether such dispersive properties can be attributed to the constitutive assumptions which are made on the strain energy density or to the choice of the micro-inertia terms which can be introduced.…”