An approach to generalized one-dimensional self-similar elasticity

作者：Michelitsch Thomas M^*; Maugin Gerard A; Rahman Mujibur; Derogar Shahram; Nowakowski Andrzej F; Nicolleau Franck C G A

来源：International Journal of Engineering Science, 2012, 61: 103-111.

DOI：10.1016/j.ijengsci.2012.06.014

• Self-similarity
• Fractals
• Elasticity
• Laplacian
• Fractional integrals
• Nonlocality

We employ a self-similar Laplacian in the one-dimensional infinite space and deduce a model for one-dimensional self-similar elasticity. As a consequence of self-similarity this Laplacian assumes the non-local form of a self-adjoint combination of fractional integrals. The linear elastic constitutive law becomes a non-local convolution with the elastic modulus function being a power-law kernel. We outline some principal features of a linear self-similar elasticity theory in one dimension. We find an anomalous behavior of the elastic modulus function reflecting a regime of critically slowly decreasing interparticle interactions in one dimension. The approach can be generalized to the n (n = 1,2,3) dimensional physical space (Michelitsch, Maugin, Nowakowski, Nicolleau, %26 Rahman, to be published).

• 出版日期2012-12