MATHEMATICAL MODELING IN DEFORMABLE SOLID MECHANICS: THEORY, FORMULAS, AND ANALYSIS

Abstract

This article presents a systematic description of the main mathematical models of deformable solid mechanics (DSM). The stress tensor, generalized Hooke’s law, Euler–Bernoulli model, and failure criteria are provided along with analytical solutions. All formulas are numbered and accompanied by detailed explanations. Theoretical results are illustrated with graphs computed in Python/Matplotlib: stress–strain diagrams, beam deflection profiles, Kirsch stress contour fields, and failure surfaces. A comparative analysis table is provided for steel, aluminum, and CFRP materials.