An information-analytical system for finite-difference modeling of dynamic stress concentrations in composite materials under impact, tension, and bending loads
Year: 2026
Type: article
Abstract: Composite materials (CM) are widely used in aerospace, transportation, and civil engineering due to their high specific strength, stiffness, and wear resistance. However, predicting their dynamic mechanical response under non-stationary loading conditions remains a significant challenge. Stress fields often exhibit singularities at corner points, contact discontinuities, and dissimilar material interfaces, which cannot be accurately resolved using classical homogenization approaches or conventional finite element methods (FEM). This paper presents a second-order accurate computational framework for analyzing the behavior of CM within a unified strip-halfplane configuration. Three mechanical scenarios are investigated: impact resistance (Problem A), tensile strength (Problem B), and bending behavior (Problem C). The proposed framework employs an explicit finite difference method (FDM) based on the method of spatial characteristics and a splitting technique. The numerical scheme is implemented in Python 3.12.3 using NumPy and Matplotlib libraries. A dedicated algorithm is developed to compute stress and velocity fields at singular points and is validated through a three-level grid convergence study. The results indicate that the stress concentration ratio at the singular point P reaches 3.0 times the applied boundary load in Problem A. Under tensile loading in Problem B, the normalized maximum normal stress, σ11k , attains a value of 0.63 at point P. Furthermore, sensitivity analysis reveals that the extremal stresses in the half-plane material vary by a factor of 3.0 for strip embedment depths of 5h, 10h, and 15h. Grid convergence is confirmed with a root mean square error (RMSE) of 4.3 × 10⁻³ between the medium and fine grids. The observed order of convergence at the singular point P is 1.2, which is consistent with the second-order accuracy of the trapezoidal bicharacteristic integration scheme. These findings provide quantitative reference data for the design and analysis of composite structures containing strip inclusions subjected to impact, tensile, and bending loads.
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7166718245