Study of Instabilities in Hyperelastic Laminates

• Grant number: 13/00644-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2013
• End date: September 30, 2015
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: Adair Roberto Aguiar
• Grantee: Edmar Borges Theóphilo Prado
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Phenomena like softening and strain localization are intrinsically nonlinear and, in the case of hyperelastic materials, are related to the loss of, respectively, convexity and ellipticity of the Hessian of the strain energy function. In general, the solutions of the associated problems are not known. Analytical methods, such as the homogenization methods, and numerical methods, such as the Finite Element Method (FEM), are used to search for approximate solutions to these problems. These approximate solutions may not correspond to a stable and, therefore, realistic solution of the associated nonlinear problem, and other stable solutions may exist. We wish to use our expertise in both asymptotic homogenization and finite element methods in the approximate analysis of problems involving laminates with distinct hyperelastic phases. We shall obtain sequences of approximate solutions and shall investigate the convergence properties of these sequences. We shall use stability criteria to determine whether the associated solutions are physically possible. This research finds applications in various fields of engineering, which include the optimum design of supports in Civil Engineering and the development of new materials with lamellar microstructure.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

AGUIAR, ADAIR R.; PEREZ-FERNANDEZ, LESLIE D.; PRADO, EDMAR B. T.. Analytical and numerical investigation of failure of ellipticity for a class of hyperelastic laminates. EUROPEAN JOURNAL OF MECHANICS A-SOLIDS, v. 61, p. 110-121, JAN-FEB 2017. (13/00644-5)