Orlando Susarrey Huerta

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.

Fractal Geometry and Mechanics of Randomly Folded Thin Sheets

This work is devoted to the statistical geometry of crumpling network and its effect on the geometry and mechanical properties of randomly folded materials. We found that crumpling networks in randomly folded sheets of different kinds of paper exhibit statistical self-similarity characterized by the universal fractal dimension DN = 1.83 ± 0.03. The balance of bending and stretching energy stored in the folded creases determines the fractal geometry of folded sheets displaying intrinsically anomalous self-similarity with the universal local fractal dimension Dl = 2.67 ± 0.05 and the material dependent global fractal dimension D < Dl. Moreover, we found that the entropic rigidity of crumpling network governs the mechanical behavior of randomly crumpled sheets under uniaxial compression.

Mechanics of Randomly Folded Thin Materials

In this work, the mechanical properties of randomly folded thin sheets in the hydrostatic and non-hydrostatic stress states were studied. It is pointed out that under the hydrostatic compression the sheet, rigidity is governed by the volume dependence of its enthalpy, whereas in a non-hydrostatic stress state, the rigidity of folded sheets is controlled by the shape dependence of the Edwards entropy of the network of crumpling creases. Furthermore, the stress relaxation in folded sheets after uni-axial compression was studied. It was found that stress relaxation in folded elasto-plastic sheets differs from this in the folded predominantly plastic sheets and obeys an unusual relaxation law with the universal characteristic exponent.

Failure Stress in Notched Paper Sheets

In this work the crack initiation stress of notched specimens of filter paper is studied. The paper in the microstructure has a random array in their fibers while macroscopically it behaves anisotropically. The self-affine crack mechanics is used to study the size effect in the tensile behavior of this kind of paper under the presence of several conditions of geometrical notches. While in the traditional fracture mechanics the crack initiation stress is a material parameter when is reached a critical level at the crack tip, in the self-affine crack mechanics, depends moreover of the resulting tortuosity of the crack. Four geometrical arrangements in two sizes we considered: centered circular notch, centered lineal notch, sided circular notches and without notch at 10 and 300 mm width with a relation 2a/w = 0.25 under the same loading conditions. In this, the without notch specimens present the higher stress, all other notched specimens presented a similar crack initiation stress about 1 % of difference among them, and the crack growth is not affected by the geometry of notch. In spite of this difference, no one of the specimens reach the theoretical stress concentration of 3 such as predicted the classical stress theory.

Self-Affine Crack Pattern in Filter Paper Sheets

In this work the self-affine crack pattern in Filter Paper sheets is studied. This paper has a well-defined anisotropy of mechanical properties associated with visible preferable orientation of fibers in the machine direction. Fracture behavior is in essence brittle, the rupture lines have self-affine invariance, and the stresses ahead of the straight notch follow a power-law behavior. The roughness exponent value is of H = 0.50 0.01, different from the suggested universal value H = 0.8. The classical theory has demonstrated that, in materials such as metal, there is a relationship between the size and the starting crack stress, which does not happen in this material. The tests show that the starting crack stress from stress-strain behavior curves remains stable for the different specimen sizes w and crack length size. Moreover, different types of geometric groove, circular and linear, and without a crack, were tested and show almost the same behavior.