2014/09/19 by Alexander S. Balankin, Balankin, Alexander S.
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Composite Material Mechanics #Elasticity and Wave Propagation #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci)
paper · pdf · doi:10.48550/arxiv.1409.5829
openalex publication_date 2014/09/19 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
This paper is devoted to the mechanics of fractal materials. A continuum\nframework accounting for the topological and metric properties of fractal\ndomains in heterogeneous media is developed. The kinematics of deformations is\nelucidated and the symmetry of the Cauchy stress tensor is established. The\nmapping of mechanical problems for fractal materials into the corresponding\nproblems for the fractal continuum is discussed. Stress and strain\ndistributions in elastic fractal bars are analyzed. Some features of acoustic\nwave propagation and localization in scale-invariant media are briefly\ndiscussed. The effect of fractal correlations in the material microstructure on\nthe crack mechanics is revealed. It is shown that the fractal nature of\nheterogeneity can either delay or assist the crack initiation and propagation,\ndepending on the interplay between metric and topological properties of the\nfractal domain.\n