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Numerical Approach to a Model for Quasistatic Damage with Spatial BV -Regularization

  • Sören Bartels
  • Marijo Milicevic
  • Marita ThomasEmail author
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 27)

Abstract

We address a model for rate-independent, partial, isotropic damage in quasistatic small strain linear elasticity, featuring a damage variable with spatial BV -regularization. Discrete solutions are obtained using an alternate time-discrete scheme and the Variable-ADMM algorithm to solve the constrained nonsmooth optimization problem that determines the damage variable at each time step. We prove stability of the method and show that a discrete version of a semistable energetic formulation of the rate-independent system holds. Moreover, we present our numerical results for two benchmark problems.

Notes

Acknowledgements

This work was carried out within the project Finite element approximation of functions of bounded variation and application to models of damage, fracture, and plasticity within the DFG Priority Programme SPP 1748 “Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretisation Methods, Mechanical and Mathematical Analysis.”

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Sören Bartels
    • 1
  • Marijo Milicevic
    • 1
  • Marita Thomas
    • 2
    Email author
  1. 1.Department of Applied Mathematics, Mathematical InstituteUniversity of FreiburgFreiburg i. Br.Germany
  2. 2.Weierstrass-Institute for Applied Analysis and StochasticsBerlinGermany

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