Journal of AppliedMath

Background seismicity and seismic correlations

Bogdan Felix Apostol — 2025-01-03

The law of energy accumulation in the earthquake focus is presented, together with the temporal, energy and magnitude distributions of regular, background earthquakes. The background seismicity is characterized by two parameters—the seismicity rate and the Gutenberg-Richter parameter, which can be extracted by fitting the empirical earthquake distributions. Time-magnitude and temporal correlations are presented, and the information they can provide is discussed. For foreshocks the time-magnitude correlations can be used to forecast (with limitations) the mainshock. The temporal correlations indicate a decrease of the Gutenberg-Richter parameter for small magnitudes, in agreement with empirical observations for foreshocks. On the other hand, the aftershocks may be viewed as independent earthquakes with changed seismic conditions, so they may exhibit an increase of this parameter, also in accordance with empirical observations. The roll-off effect for small magnitudes and the modified Gutenberg-Richter distribution are discussed for temporal corralations, and the derivation of the Bath’s law is briefly reviewed.

Fatigue damage model of neoprene rubber sandwiched with bi-directional carbon fabric

Krishna Nair — 2025-02-19

Fatigue is a phenomenon that occurs in materials when they are subjected to repetitive or cyclic loading, which can lead to the accumulation of damage over a time. The purpose of the present study is to develop a fatigue damage model incorporating experimental test results of axial tension and fatigue that utilizes the principles of continuum damage mechanics (CDM) to predict the damage accumulation in composite. Experimental testing in axial tensile tests involves dumbbell specimens of neoprene rubber sandwiched with bi-directional carbon fabric to constitute a composite material with the help of which material constants C₁₀, C₂₀, and C₃₀ parameters are evaluated by the curve-fitting method. Fatigue tests were conducted for different displacements, from which constants s₀ and S₀ were figured out using a linear regression method. A mathematical model is developed, and MATLAB is used to relate stress and strain in Yeoh’s strain energy function to describe the nonlinear elastic behavior of elastomers incorporating material parameters evaluated by axial tensile tests and fatigue tests. The MATLAB script was run in ANSYS with this modified Yeoh hyperelastic model for evaluation of damage in composite and compared with damage evaluated by image processing software in scanning electron microscope (SEM) images for validation purposes.

Wronskian representations of the solutions to the Burgers’ equation

Pierre Gaillard — 2025-02-25

A representation of the solutions to the Burgers’ equation by the Wronskiens is given. For this, we use particular polynomials and we obtain a very efficient method to construct solutions to this equation. We deduce rational solutions from the latter equation. We explicitly build solutions for first orders.