arXiv subjects

Alexander S. Balankin

Publications and source records attributed to Alexander S. Balankin.

8 recordsLinked to original sources

arXiv2014

Toward the mechanics of fractal materials: mechanics of continuum with fractal metric

This paper is devoted to the mechanics of fractal materials. A continuum framework accounting for the topological and metric properties of fractal domains in heterogeneous media is developed. The kinematics of deformations is elucidated and the symmetry of the Cauchy stress tensor is established. The mapping of mechanical problems for fractal materials into the corresponding problems for the fractal continuum is discussed. Stress and strain distributions in elastic fractal bars are analyzed. Some features of acoustic wave propagation and localization in scale-invariant media are briefly discussed. The effect of fractal correlations in the material microstructure on the crack mechanics is revealed. It is shown that the fractal nature of heterogeneity can either delay or assist the crack initiation and propagation, depending on the interplay between metric and topological properties of the fractal domain.

cond-mat.mtrl-sci↗

arXiv2009

Topological crossovers in the forced folding of self-avoiding matter

We study the scaling properties of forced folding of thin materials of different geometry. The scaling relations implying the topological crossovers from the folding of threedimensional plates to the folding of two-dimensional sheets, and further to the packing of one-dimensional strings, are derived for elastic and plastic manifolds. These topological crossovers in the folding of plastic manifolds were observed in experiments with predominantly plastic aluminum strips of different geometry. Elasto-plastic materials, such as paper sheets during the (fast) folding under increasing confinement force, are expected to obey the scaling force-diameter relation derived for elastic manifolds. However, in experiments with paper strips of different geometry, we observed the crossover from packing of one-dimensional strings to folding two dimensional sheets only, because the fractal dimension of the set of folded elasto-plastic sheets is the thickness dependent due to the strain relaxation after a confinement force is withdrawn.

cond-mat.mtrl-sci↗

arXiv2008

Power law scaling of lateral deformations with universal Poissons index for randomly folded thin sheets

We study the lateral deformations of randomly folded elastoplastic and predominantly plastic thin sheets under the uniaxial and radial compressions. We found that the lateral deformations of cylinders folded from elastoplastic sheets of paper obey a power law behavior with the universal Poissons index nu = 0.17 pm 0.01, which does not depend neither the paper kind and sheet sizes, nor the folding confinement ratio. In contrast to this, the lateral deformations of randomly folded predominantly plastic aluminum foils display the linear dependence on the axial compression with the universal Poissons ratio nu_e = 0.33 pm 0.01. This difference is consistent with the difference in fractal topology of randomly folded elastoplastic and predominantly plastic sheets, which is found to belong to different universality classes. The general form of constitutive stress-deformation relations for randomly folded elastoplastic sheets is suggested.

cond-mat.soft↗

arXiv2008

Dynamic scaling approach to study time series fluctuations

We propose a new approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval plays the role of time variable, whereas the physical time is treated as the analog of spatial variable. In this way we found that the fluctuations of many real-world time series satisfy the analog of the Family-Viscek dynamic scaling ansatz. This finding permits to use the powerful tools of kinetic roughening theory to classify, model, and forecast the fluctuations of real-world time series.

physics.data-an↗

arXiv2008

Entropic rigidity of a crumpling network in a randomly folded thin sheet

We have studied experimentally and theoretically the response of randomly folded hyperelastic and elastoplastic sheets on the uniaxial compression loading and the statistical properties of crumpling networks. The results of these studies reveal that the mechanical behavior of randomly folded sheets in the one-dimensional stress state is governed by the shape dependence of the crumpling network entropy. Following up on the original ideas by Edwards for granular materials, we derive an explicit force-compression relationship which precisely fits the experimental data for randomly folded matter. Experimental data also indicate that the entropic rigidity modulus scales as the power of the mass density of the folded ball with universal scaling exponent.

cond-mat.stat-mech↗

arXiv2005

The concept of multifractal elasticity

A new type of elasticity of random (multifractal) structures is suggested. A closed system of constitutive equations is obtained on the basis of two proposed phenomenological laws of reversible deformations of multifractal structures. The results may be used for predictions of the mechanical behavior of materials with multifractal microstructure, as well as for the estimation of the metric, information, and correlation dimensions using experimental data on the elastic behavior of materials with random microstructure.

cond-mat.mtrl-sci↗

arXiv2005

Anomalous roughness with system size dependent local roughness exponent

We note that in a system far from equilibrium the interface roughening may depend on the system size which plays the role of control parameter. To detect the size effect on the interface roughness, we study the scaling properties of rough interfaces formed in paper combustion experiments. Using paper sheets of different width λL, we found that the turbulent flame fronts display anomalous multi-scaling characterized by non universal global roughness exponent αand the system size dependent spectrum of local roughness exponents,ξ_q, whereas the burning fronts possess conventional multi-affine scaling. The structure factor of turbulent flame fronts also exhibit unconventional scaling dependence on λThese results are expected to apply to a broad range of far from equilibrium systems, when the kinetic energy fluctuations exceed a certain critical value.

cond-mat.stat-mech↗

arXiv2005

Devils staircase like behavior of the range of random time series associated with the tangled nature of evolution

We present empirical evidence that the range of random time series associated with the tangled nature model of evolution exhibits a devils staircase like behavior characterized by logarithmic trend and the universal multi-affine spectrum of scaling exponents xi_c of q leq q_c moments of q-order height-height correlations, whereas for q > q_c the moments behaves logarithmically.

physics.soc-ph↗