A LATIN-based model reduction approach for the simulation of cycling damage

Abstract

The objective of this article is to introduce a new method including model order reduction for the life prediction of structures subjected to cycling damage. Contrary to classical incremental schemes for damage computation, a non-incremental technique, the LATIN method, is used herein as a solution framework. This approach allows to introduce a PGD model reduction technique which leads to a drastic reduction of the computational cost. The proposed framework is exemplified for structures subjected to cyclic loading, where damage is considered to be isotropic and micro-defect closure effects are taken into account. A difficulty herein for the use of the LATIN method comes from the state laws which can not be transformed into linear relations through an internal variable transformation. A specific treatment of this issue is introduced in this work.

Large time increment approach for fatigue damage computations

“…The presented LATIN-PGD method has been extended in [2] to predict damage evolution of 2D structures undergoing nonproportional fatigue loading. This method is promising to conduct fatigue damage analysis.…”

“…In this case, the global stage is nonlinear and it is not straightforward to solve such a problem. This is why, it was suggested by [2] to incorporate the nonlinear elastic state law in the local step such that the global stage remains linear. The quantities of interest are represented as s and the starting point s i ∈ A is assumed to be known, typically from an elastic initialisation.…”

“…The convergence of the method is shown in Fig.4. With only three PGD pairs the relative error as defined in [2] can be minimised to approximately 10 −9 within 25 LATIN iterations. The generated PGD time and space functions are plotted in Fig.5.…”

“…LATIN has been well established to compute several types of problems including different material nonlinearities other than damage which leads to a non-linear state equation. An extension of the method has been introduced by [2] to tackle fatigue damage and then to benefit from a promising numerical framework for fatigue damage computations.…”

A Model Reduction Technique in Space and Time for Fatigue Simulation

“…It has been developed for solving plasticity and visco-plasticity problems and shown a drastic decrease of the computational cost compared to a classical approach [33][34][35]. Here an extended version is used for (visco-)plastic problems with damage that incorporates micro-defects closure effects [36].…”