High-order tetrahedral finite elements applied to large deformation analysis of functionally graded rubber-like materials

• Published in: Applied mathematical modelling Vol. 37; no. 20-21; pp. 8757 - 8775
• Main Authors: Pascon, J.P., Coda, H.B.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.11.2013
• Subjects: Constitutive relationships; Dynamical systems; Finite displacements and finite strains; Finite element method; Functionally graded materials; Functionally gradient materials; High-order tetrahedral finite elements; Mathematical analysis; Mathematical models; Nonlinear dynamics; Rubber-like materials; Static and isothermal analysis; Strain; Finite displacements and finite strains; Rubber-like materials; Functionally graded materials; High-order tetrahedral finite elements; Static and isothermal analysis
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2013.03.062

In this paper, high-order tetrahedral finite elements are employed to analyze structures and solids composed of functionally graded rubber-like materials under finite displacements, finite strains, statically applied forces and isothermal conditions. In order to do so, the following concepts are used: geometrically nonlinear analysis, Green–Lagrange strain tensor, second Piola–Kirchhoff stress tensor, hyperelastic constitutive relations, isoparametric solid tetrahedral finite elements of any order of approximation, and functionally graded materials. The equilibrium of the body is achieved via the Principle of the Stationary Total Potential Energy. The elements are fully integrated via Gaussian quadratures, and the resultant processing time is reduced by means of parallel techniques. To solve the nonlinear system of equations, the Newton–Raphson iterative procedure is employed. The proposed formulation is validated by benchmark problems such as: the Cook’s membrane and the thick cylinder. Other interesting simulation, the Cook’s block is proposed in order to evaluate high strain gradient situations. The results show that, in the context of the present study, locking-free behavior is obtained with simple mesh refinement.