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Size-dependent rigidities of nanosized torsional elements. (English) Zbl 1040.74007
Summary: A theory for the prediction of the size dependence of torsional rigidities of nanosized structural elements is developed. It is shown that, to a very good approximation, the torsional rigidity \(D\) of a nanosized bar differs from the prediction of standard continuum mechanics \(D_c\) as (\(D-D_c)/D_c= Ah_0/a\), where \(A\) is a non-dimensional constant, \(a\) is the size scale of the cross-section of the bar, and \(h_0\) is a material length equal to the ratio of surface elastic constant to bulk elastic constant. The theory developed is compared with direct atomistic calculations (“numerical experiment”) of the torsional rigidity bars made of several FCC metals modeled using the embedded atom method. Very good agreement is obtained between theory and simulation. The framework presented here can aid the development of design methodologies for nanoscale structural elements without the need for full scale atomistic simulations.

MSC:
74A60 Micromechanical theories
74M25 Micromechanics of solids
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