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This paper presents an overview of modeling fractal media by continuum mechanics using the method of dimensional regularization. The basis of this method is to express the balance laws for fractal media in terms of fractional integrals and, then, convert them to integer‐order integrals in conventional (Euclidean) space. Following an account of this method, we develop balance laws of fractal media...
We give a complete general answer to the problem, recurrent in continuum mechanics, of determining the number and type of symmetry classes of an odd‐order tensor space. This kind of investigation was initiated for the space of elasticity tensors. Since then, this problem has been solved for other kinds of physics such as photoelectricity, piezoelectricity, flexoelectricity, and strain‐gradient elasticity...
The classical continuum model does not describe the mechanical behaviour of cellular materials. To model the size‐dependent mechanical properties of these materials, the extended continuum models such as the micropolar approach can be used. The reference data is extracted from the virtual experiments performed on an artificial open‐cell foam specimens. With the proper set of the Cosserat parameters...
This paper deals with the buckling of a column which is modeled by some finite rigid segments and elastic rotational springs and relating its solution to continuum nonlocal elasticity. This problem, which can be referred to Hencky's chain, can serve as a basic model to rigorously investigate the effect of the microstructure on the buckling behaviour of a simple equivalent continuum structural model...
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