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Application of the hp-FEM for Hyperelastic Problems with Isotropic Damage

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Computational Modeling, Optimization and Manufacturing Simulation of Advanced Engineering Materials

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 49))

Abstract

This work presents a damage formulation applied to hyperelastic materials in order to capture the Mullins effect, observed in rubber-like materials and biological tissues. A mixed (u/p) formulation with a pressure projection procedure is used with the hp-FEM to overcome the volumetric locking. The isotropic damage model uses a scalar variable that evolves coupled with the maximum attained equivalent strain. This damage variable defines a stress reduction factor, which describes the softening behavior. Cyclic loading tests were performed to reproduce the Mullins effect. Convergence analyses were made for compressible and nearly-incompressible materials imposing smooth solutions. The results presented a spectral convergence rate for the p-refinement. In the case of near-incompressibility, the material showed locking-free characteristics.

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Notes

  1. 1.

    In practical cases, there are small residual stresses, characterizing hysteresis. However, idealized models do not account for these stresses, as well as temperature and viscosity effects.

  2. 2.

    For compressible materials with damage, the reduction factor \((1-D)\) of Eq. 97 is applied to W, rather than \(\bar{W}\).

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Authors and Affiliations

  1. University of Campinas, Cidade Universitária Zeferino Vaz, Rua Mendeleyev, 200, Campinas, 13083-860, Brazil

    Jorge L. Suzuki & Marco L. Bittencourt

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  1. Jorge L. Suzuki
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  2. Marco L. Bittencourt
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Correspondence to Marco L. Bittencourt .

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Editors and Affiliations

  1. Department of Mechanical Engineering, Santa Catarina State Uni. - UDESC, Joinville, Santa Catarina, Brazil

    Pablo Andrés Muñoz-Rojas

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Suzuki, J.L., Bittencourt, M.L. (2016). Application of the hp-FEM for Hyperelastic Problems with Isotropic Damage. In: Muñoz-Rojas, P. (eds) Computational Modeling, Optimization and Manufacturing Simulation of Advanced Engineering Materials. Advanced Structured Materials, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-319-04265-7_6

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  • DOI: https://doi.org/10.1007/978-3-319-04265-7_6

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  • Online ISBN: 978-3-319-04265-7

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