On the constitutive modeling of reinforced rubber in a broad frequency domain

• Published in: Zeitschrift für angewandte Mathematik und Mechanik 2010-05, Vol.90 (5), p.418-435
• Main Authors: Suwannachit, A., Nackenhorst, U.
• Format: Article
• Language: English
• Subjects: complex modulus; Mullins effect; pseudo-elasticity; Rubber elasticity; viscoelasticity
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.200900360

A constitutive model for the numerical simulation of rubber behavior in a wide frequency range is presented. The combination between the well known Simo's viscoelastic model and a pseudo‐elastic approach enables for the modeling of inelastic effects at low frequencies, such as nonlinear elasticity, hysteretic behavior, and damage (Mullins effect). The constitutive formulation is derived in detail with an aim of the finite element implementation. Because mechanical response at high frequencies is usually characterized by complex modulus, the developed viscoelastic damage model is extended to high‐frequency analysis. A key idea is the decomposition of the deformation gradient into linear and nonlinear part. The nonlinear part is associated with inelastic deformations established at low frequencies, while the linear contribution plays an important role for dynamic analysis at high frequencies. As a result, the steady‐state response of rubber at a certain static deformation is evaluated and consequently leads to the numerical solution for complex modulus. The computational efficiency of the proposed model can be seen from a good agreement with experimental data. A constitutive model for the numerical simulation of rubber behavior in a wide frequency range is presented. The combination between the well known Simo's viscoelastic model and a pseudo‐elastic approach enables for the modeling of inelastic effects at low frequencies. The constitutive formulation is derived in detail with an aim of the finite element implementation. The developed viscoelastic damage model is extended to high‐frequency analysis. A key idea is the decomposition of the deformation gradient into linear and nonlinear part. The nonlinear part is associated with inelastic deformations established at low frequencies, while the linear contribution plays an important role for dynamic analysis at high frequencies. As a result, the steady‐state response of rubber at a certain static deformation is evaluated and consequently leads to the numerical solution for complex modulus. The computational efficiency of the proposed model can be seen from a good agreement with experimental data.