Abstract
We derive two different effective models from a heterogeneous Cosserat continuum taking into account the Cosserat intrinsic length of the constituents. We pass to the limit using homogenization via periodic unfolding and in doing so we provide rigorous proof to the results introduced by Forest, Pradel, and Sab (Int. J. Solids Struct. 38 (26-27): 4585-4608 ’01). Depending on how different characteristic lengths of the domain scale with respect to the Cosserat intrinsic length, we obtain either an effective classical Cauchy continuum or an effective Cosserat continuum. Moreover, we provide some corrector type results for each case.
Highlights
In recent years it has been widely observed that mechanical properties of composite materials that are used in a variety of applications depend on different characteristic lengths
We point out that the authors in [9] provide a historical perspective and theoretical overview of higher grade continua. Regarding the latter, where one allows for additional degrees of freedom as in a Cosserat continuum, a series of works appeared in the late nineties addressing estimation of effective properties of heterogenous Cosserat materials taking into account size effects [13,14,15]
We derived effective models for a heterogeneous Cosserat continuum taking into account the Cosserat intrinsic length of the constituents by the method of homogenization and periodic unfolding
Summary
In recent years it has been widely observed that mechanical properties of composite materials that are used in a variety of applications depend on different characteristic lengths. Generalized continuum theories fall into two categories: higher grade theory that introduces higher gradients of the displacement field to the usual strain tensor and higher order theory that includes additional degrees of freedom Regarding the former there is a vast literature of deriving second grade models through constitutive modelling, dimensional reduction or homogenization techniques [9,16,18,19,35,37,39]. We point out that the authors in [9] provide a historical perspective and theoretical overview of higher grade continua Regarding the latter, where one allows for additional degrees of freedom as in a Cosserat continuum, a series of works appeared in the late nineties addressing estimation of effective properties of heterogenous Cosserat materials taking into account size effects [13,14,15].
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