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Exploring the chaotic behavior of quasistatic strength and fatigue tests for structural laminates of composite materials

Frederico F. Bittencourt and Euvaldo F. Cabral Jr.

Vol. 13 (2025), No. 4, 417–435
Abstract

Carbon-fiber-reinforced epoxy polymers (CFRP), a high-performance composite material, have been extensively studied. The initiation damage and progression process in strength and fatigue tests for these materials and the definition of strength and final failure are poorly understood since many considerable effects are disregarded under necessary hypothetical simplifications during simulations. This work investigates the behavior of CFRP under quasistatic tests, utilizing numerical simulations to explore physical phenomena through the explicit integration of finite element models. Various experimental modeling and evaluation tests were carried out, and many phenomena typical of chaotic dynamic systems were observed. Clear evidence is presented for the chaotic behavior of even a simple, physically discrete lumped element mass model chosen as a minimalistic simplification of such laminates. The null hypothesis of a nonchaotic case is tested and confirmed using Student’s t-test.

Keywords
chaos theory, dynamical systems, mechanical engineering, composite materials
Mathematical Subject Classification
Primary: 34D08, 34D45, 34H10, 37C29, 70K05
Secondary: 37-11, 37C05, 37C20, 37C25, 65P20
Milestones
Received: 4 January 2025
Revised: 28 April 2025
Accepted: 29 May 2025
Published: 19 September 2025

Communicated by Emilio Barchiesi
Authors
Frederico F. Bittencourt
Departamento de Física Aplicada
Universidade de São Paulo
São Paulo, SP Brazil
Euvaldo F. Cabral Jr.
IME (Rio de Janeiro, RJ) and Polytechnical School
University of São Paulo
São Paulo, SP
Brazil