The Development of a Piezoelectric Defect Detection Device Through Mathematical Modeling Applied to Polymer Composite Materials

Abstract

In this research article, the focus is on examining the strength characteristics of polymer composite materials under various stress states. The investigation into the material dissolution process is conducted in two distinct stages. Initially, the article employs a criterion approach to derive explicit formulas for the latent decay time (incubation period) of materials, considering singular, exponential and Abelian kernels of the damage operator. In the subsequent stage, the classical strength condition is applied to establish a Volterra type integral equation, which characterizes the damage process for hereditary materials. These resulting differential equations are then solved with appropriate initial conditions. The study utilizes the obtained results to create time- dependent graphs of the damage parameter and performs comparisons. A piezoelectric defect detection device for polymer composite materials has been proposed through the application of mathematical modeling.