Keywords: delamination, buckling, multiscale computation, domain decomposition method, LaTIn solver.

The LaTIn strategy [1] splits the structure into volume substructures separated by surface interfaces which both are mechanical entities. Consequently, the reference problem resulting from the chosen mesomodel is substructured naturally, and the cohesive interfaces of the model are handled within the interfaces of the domain decomposition. For computational efficiency, three scales are introduced to solve the problem:

• The microscale corresponds to small wavelength phenomena, which occur between neighbouring substructures.
• The macroscale corresponds to the permanent verification of a weak equilibrium over the whole structure. This feature, which grants the scalability of the method, is realized through the definition of few macro degrees of freedom per interface which have to satisfy continuity conditions and which are linked by an automatically constructed homogenized behaviour.
• The number of substructures being dependent on the number of plies, it may become very large. Substructures are then gathered into super-substructures and a primal domain decomposition method [2] is applied to solve the macro problem. The third scale (supermacro) problem is classically introduced when balancing the supersubstructures with respect to rigid body modes.

This framework is highly user controlled. In order to conduct our computations, the following parameters have to be established:

• The influence of neighbouring subdomains is represented by so called "search directions". These have to be adapted to the aspect ratio of the neighbouring structure by the introduction of well-chosen anisotropic coefficients.
• Because of the loss of stiffness induced by buckling and delamination, macro-stiffness might become irrelevant and the macroscopic operators and search directions have to be adapted.
• The supermacroproblem is solved using a projected preconditioned conjugate gradient method, which implies a convergence threshold to be set up.

These improvements make the multiscale analysis of slender structures subject to buckling possible with an efficient treatment of delamination.

1

P. Ladevèze, "Nonlinear Computational Structural Mechanics - New Approaches and Non-Incremental Methods of Calculation", Springer Verlag, 1999.

2

J. Mandel, "Balancing Domain Decomposition", Communications in Numerical Methods in Engineering, 9, 233-241, 1993. doi:10.1002/cnm.1640090307

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