Vol. 7, No. 10, 2012

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ISSN: 1559-3959
Internal structures and internal variables in solids

Jüri Engelbrecht and Arkadi Berezovski

Vol. 7 (2012), No. 10, 983–996
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 reaction-diffusion 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.

Keywords
microstructured solids, dual internal variables, generalized continua, microtemperature
Milestones
Received: 26 September 2012
Revised: 10 December 2012
Accepted: 24 December 2012
Published: 1 March 2013
Authors
Jüri Engelbrecht
Centre for Nonlinear Studies
Institute of Cybernetics at Tallinn University of Technology
Akadeemia tee 21
12618 Tallinn
Estonia
Arkadi Berezovski
Centre for Nonlinear Studies
Institute of Cybernetics at Tallinn University of Technology
Akadeemia tee 21
12618 Tallinn
Estonia