A simulation strategy for life time calculations of large, partially damaged structures

The present paper is motivated by the increasing concern to accomplish more realistic lifetime estimations of complex engineering structures. For this purpose the entire system and additional mechanisms like damage evolution or changes in the loading situation as well as in the surroundings have to be incorporated into such a long-term computation. Undoubtedly the finite element method represents a suitable tool to this end. But inspite of the fast development of computer technology the life time computation is still to complex to be carried out without advantageous and effective strategies to reduce computational cost.

In this contribution we present a discretisation strategy which takes into account that only small parts of a structure demand a non-linear analysis. Accordingly we strictly decompose our system on the structural level into non-linear and linear subsystems by an exact substructure technique. We are finally able to determine the entire system response by the solution of a number of small non-linear subsystems. Additionally, if it is required, the linear subsystems may be evaluated in a post processing calculation.

Further we may reduce the number of degrees-of-freedom of the linear subsystems, because they influence the evolution of damage only indirectly. Hence we join our proposed substructure strategy with projection-based model reduction techniques for linear second order systems, like modal truncation, Ritz vectors and the proper orthogonal decomposition [

1

]. An alternative approach of partial model reduction is e.g. presented by [

2

].

In the non-linear substructures we model the evolution of damage for ductile damage behaviour of metals taking into consideration large inelastic strains by the material model of [

3

]. At the material level we exploit the advantages of a formulation in principle axes in combination with the exponential mapping algorithm.

This material model is implemented into the computationally efficient Q1SP finite element formulation of [

4

], which is based on the concept of reduced integration with hourglass stabilisation.