Efficient Implementation of Lattice Discrete Particle Models for Quasi-brittle and Polymer Materials

  • Kruis, Jaroslav (Czech Technical University)
  • Vorel, Jan (Czech Technical University)
  • Koudelka, Tomas (Czech Technical University)

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This paper concerns with the second order time dependent problems which emerge in connection with the use of lattice discrete particle models (LDPM). The LDPM require very short time steps and therefore an explicit time integration methods are used. The explicit methods use a diagonal matrix and therefore the solution of a system of algebraic equations is very easy. Unfortunately, the explicit methods are conditionally stable which requires the time step to be smaller than a limit value. The limit length of the time step is usually not known or its determination is a very computationally demanding task and therefore only estimates are used. There are many problems, where the use of a fine mesh on the whole domain and a short time step during the whole time period studied are inefficient. The use of different lengths of time steps is called multi-time step methods or sub-cycling. A new opportunity for the multi-time step methods emerged in connection with parallel computers and domain decomposition methods. This contribution concerns with sub-cycling algorithm with two time steps. The shorter time step is used in the area where nonlinear behaviour is concentrated while longer time step is used in the remaining part of the domain. A modified finite difference method was used for time integration of lattice discrete particle models. In some cases, the method requires time steps similar to the time step needed in the standard finite difference method otherwise it diverges. Therefore, different method based on the Lagrange multipliers was implemented and used.