An enhanced nonlinear multi-scale strategy for the simulation of buckling and delamination on 3D composite plates

Summary A multiscale extension for a parallel noninvasive mixed domain decomposition method is presented. After briefly exposing our noninvasive implementation of the Latin method, we present how the scalability of the algorithm is obtained by the partial verification of the constitutive law of the interfaces. We propose a new interpretation of the classical macrostrategy that imposes the overall balance of interface's forces. We also propose a new study of the macrostrategy that consists in enforcing the coarse continuity of the interfaces' displacement.

Section: Numerical Examplesmentioning

confidence: 99%

“…The choice of the macrobasis is crucial. The optimal one is difficult to choose and complex as it depends on all the characteristics of the problem to be solved …”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A parallel noninvasive multiscale strategy for a mixed domain decomposition method with frictional contact

Oumaziz

Gosselet

Boucard

et al. 2018

“…When one wishes to choose an invariant scalar (or tensor in case of anisotropy) for each interface, it can be beneficial to use a coarse model for its estimation. 26 A possibility to better model short-range interaction between interface nodes is to use Ventcell conditions, instead of simple Robin conditions 27 ; this enables to recover the same sparsity for the impedance as for the stiffness of the subdomain. An extreme strategy is to use (scalar) Robin conditions on the Riesz' image of the normal flux leading to a fully populated impedance matrix.…”

Section: Quick Reviewmentioning

confidence: 99%

A new impedance accounting for short‐ and long‐range effects in mixed substructured formulations of nonlinear problems

Negrello

Gosselet

Rey

2018

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance) which can increase the convergence rate. The optimal value for this parameter is usally too expensive to be computed exactly in practice: an approximate version has to be sought, along with a compromise between efficiency and computational cost. In the context of parallel algorithms for solving nonlinear structural mechanical problems, we propose a new heuristic for the impedance which combines short and long range effects at a low computational cost.

“…An alternative to fully 3D computations is a multiscale formulation applying the so-called FE 2 approach. 36 At the integration points of the macro scale, representative volume elements (RVEs) are introduced. In case of thin structures, the RVEs often extend through the total thickness of the shell.…”

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confidence: 99%

A shell element for the prediction of residual load‐carrying capacities due to delamination

Gruttmann

Knust

2019

This paper deals with layered plates and shells subjected to static loading. The kinematic assumptions are extended by a jump function in dependence of a damage parameter. Additionally, an intermediate layer is arranged at any position of the laminate. This allows numerical simulation of onset and growth of delaminations. The equations of the boundary value problem include besides the equilibrium in terms of stress resultants, the local equilibrium in terms of stresses, the geometric field equations, the constitutive equations, and a constraint which enforces the correct shape of a superposed displacement field through the thickness as well as boundary conditions. The weak form of the boundary value problem and the associated finite element formulation for quadrilaterals is derived. The developed shell element possesses the usual 5 or 6 degrees of freedom at the nodes. This is an essential feature since standard geometrical boundary conditions can be applied and the elements are applicable to shell intersection problems. With the developed model, residual load-carrying capacities of layered shells due to delamination failure are computed. KEYWORDSdamage model, layered plates and shells, progressive delaminations, standard nodal degrees of freedom, thin intermediate layers INTRODUCTIONDelamination, or interfacial cracking between layers, is one of the most common types of damage in laminated fibre-reinforced composite structures. The reason is the relative weak interlaminar strength. Delamination as result of impact or manufacturing defect can cause a significant reduction of the load-carrying capacity of a structure. In general, the fracture process in high performance composite laminates is quite complex, involving not only delamination but also occurrence of transverse matrix cracking or fibre fracture in the layers. Stress gradients that occur near geometric discontinuities such as ply drop-offs, stiffener terminations, bonded and bolted joints, and access holes promote delamination initiation, trigger intraply damage mechanisms, and may cause a significant loss of structural integrity. Thus, a reliable prediction of different failure modes is essential. The delamination failure mode is particularly important for the structural integrity of composite structures because it is difficult to detect during inspection.The simulation of delamination using the finite element method is performed by means of the virtual crack closure technique, eg, in the works of Rybicki and Kanninen 1 and Krueger, 2 or using cohesive finite elements, eg, in other works. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] Another approach is to use continuum damage models within the layers, eg, in the works of Simon et al, [18][19][20] or to introduce thin intermediate layers along with a damage model or an inelastic material model with softening, eg, in the works 132 of Allix and Ladevèze, 21 Wagner et al, 22 and Groh et al. 23 In the works of Remmers et al, 24,25 the kinematics of solid-like shell elements is enhanced to allow for...