Micromorphic and micropolar continuum theories can be derived from the classical equations of continuum mechanics by introducing a local averaging technique into a mixed variational principle. This approach delivers the geometrically nonlinear strain measures, the equilibrium equations and the constitutive relations of the microcontinuum theory in a natural, variationally consistent way. It also allows to evaluate the residuum of the locally averaged theory with respect to the underlying classical continuum mechanics, and shows that the microcontinuum can be understood as a special kind of a representative volume element. © Springer-Verlag Berlin Heidelberg 2011.
A variationally consistent derivation of microcontinuum theories
Eremeyev V.;
2011-01-01
Abstract
Micromorphic and micropolar continuum theories can be derived from the classical equations of continuum mechanics by introducing a local averaging technique into a mixed variational principle. This approach delivers the geometrically nonlinear strain measures, the equilibrium equations and the constitutive relations of the microcontinuum theory in a natural, variationally consistent way. It also allows to evaluate the residuum of the locally averaged theory with respect to the underlying classical continuum mechanics, and shows that the microcontinuum can be understood as a special kind of a representative volume element. © Springer-Verlag Berlin Heidelberg 2011.
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