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For crystal plasticity formulation neglecting the strain gradients at dislocation scale, backstresses are necessary to satisfy mesoscopic stress equilibrium and compatibility requirements. Backstresses in a material point those between neighboring points treated separately. Physically can dynamically induce either hardening or softening effects adjust of slip systems, whereas sum stresses resul...

Abstract: In this paper, with the help of the Hardy and Dedekind sums we will give many properties of the sum B1(h, k), which was defined by Cetin et al. Then we will give the connections of this sum with the other well-known finite sums such as the Dedekind sums, the Hardy sums, the Simsek sums Y(h, k) and the sum C1(h, k). By using the Fibonacci numbers and two-term polynomial relation, we wi...