One-step semi-implicit integration of general finite-strain plasticity models

Abstract

Using the Kröner–Lee elastic and plastic decomposition of the deformation gradient, a differential-algebraic system is obtained (in the so-called semi-explicit form). The system is composed by a smooth nonlinear differential equation and a non-smooth algebraic equation. The development of an efficient one-step constitutive integrator is the goal of this work. The integration procedure makes use of an explicit Runge–Kutta method for the differential equation and a smooth replacement of the algebraic equation. The resulting scalar equation is solved by the Newton–Raphson method to obtain the plastic multiplier. We make use of the elastic Mandel stress construction, which is power-consistent with the plastic strain rate. Iso-error maps are presented for a combination of Neo-Hookean material using the Hill yield criterion and a associative flow law. A variation of the pressurized plate is presented. The exact Jacobian for the constitutive system is presented and the steps for use within a structural finite element formulation are described .

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    Order 11, 22, 33, 12, 13, 23, 21, 31, 32.

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Acknowledgements

The authors acknowledge the support of FCT, through IDMEC, under LAETA, Project UIDB/50022/2020.

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Correspondence to P. Areias.

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Areias, P. One-step semi-implicit integration of general finite-strain plasticity models. Int J Mech Mater Des (2020). https://doi.org/10.1007/s10999-020-09510-0

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Keywords

  • Finite strain plasticity
  • Differential-algebraic system
  • Runge–Kutta method
  • Mandel stress