Engineering Transactions, 65, 1, pp. 209–215, 2017

Dynamical Systems Approach of Internal Length in Fractional Calculus

Peter Balazs BEDA
Budapest University of Technology and Economics

Conventionally, non-local properties are included in the constitutive equations in the form of strain gradient-dependent terms. In case of the second gradient dependence an internal material length can be obtained from the critical eigenmodes in instability problems. When non-locality is included by using fractional calculus, a generalized strain can be defined. Stability investigation can be also performed and internal length effects can be studied by analysing the critical eigenspace. Such an approach leads to classical results for second gradient, but new phenomena appear in the first gradient case
Keywords: rate and gradient dependence; fractional calculus; static and dynamic internal length
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DOI: 10.24423/engtrans.703.2017