Theory and numerics of layered shells with variationally embedded interlaminar stresses

Gruttmann, Friedrich; Knust, Gregor; Wagner, Werner

doi:10.1016/j.cma.2017.08.038

Cited by 15 publications

(8 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Displacement control is applied to compute the load deflection curves. The elastic solution corresponds to the results in the work of Gruttmann et al 39 First, the influence of the parameters and h I using the mode I fracture parameters are investigated. Figure 21 shows the influence of on the load deflection behavior.…”

Section: Stiffened Cylindrical Shellmentioning

confidence: 97%

“…It has been treated in the work of Gruttmann et al 39 considering geometrical nonlinearity and elastic material behavior. Figure 20 shows a cross-section of the structure and a coarse finite The elastic material properties for carbon fibre reinforced polymers assuming transversal isotropy are taken from the work of Gruttmann et al 39 The fracture parameters for mode I and mode II are taken from the work of Lu et al 52 E 1 = 125 000 N/mm 2 cI = 45 N/mm 2 E 2 = 7400 N/mm 2 cII = 100 N/mm 2 G 12 = 4800 N/mm 2 g cI = 0.158 N/mm G 23 = 2700 N/mm 2 g cII = 0.315 N/mm. 12…”

Section: Stiffened Cylindrical Shellmentioning

confidence: 99%

“…2. In the work of Gruttmann et al, 39 an ansatz for the transverse shear stiffness is made, which is continuous in thickness direction. It suffers from a singularity problem due to vanishing shear strains at particular points of the structures.…”

mentioning

confidence: 99%

See 2 more Smart Citations

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

Gruttmann

Knust

2019

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

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...

show abstract

Section: Stiffened Cylindrical Shellmentioning

confidence: 97%

Section: Stiffened Cylindrical Shellmentioning

confidence: 99%

See 1 more Smart Citation

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

Gruttmann

Knust

2019

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Concerning the predefinition = 100 h we refer to the investigations in Ref. [20]. The FE approximation of the external virtual work ofp,m andt leads to…”

Section: Finite Element Formulationmentioning

confidence: 99%

An advanced shell model for the analysis of geometrical and material nonlinear shells

Gruttmann

Wagner

2020

Comput Mech

Self Cite

View full text Add to dashboard Cite

In this paper layered shells subjected to static loading are considered. The displacements of the Reissner–Mindlin theory are enriched by a an additional part. These so-called fluctuation displacements include warping displacements and thickness changes. They lead to additional terms for the material deformation gradient and the Green–Lagrangian strain tensor. Within a nonlinear multi-field variational formulation the weak form of the boundary value problem accounts for the equilibrium of stress resultants and couple resultants, the local equilibrium of stresses, the geometrical field equations and the constitutive equations. For the independent shell strains an ansatz with quadratic shape functions is chosen. This leads to a significant improved convergence behaviour especially for distorted meshes. Elimination of a set of parameters on element level by static condensation yields an element stiffness matrix and residual vector of a quadrilateral shell element with the usual 5 or 6 nodal degrees of freedom. The developed model yields the complicated three-dimensional stress state in layered shells for elasticity and elasto-plasticity considering geometrical nonlinearity. In comparison with fully 3D solutions present 2D shell model requires only a fractional amount of computing time.

show abstract

“…Over the last decades, the research activity has focused on the development of shell and plate models incorporating the effects mentioned above [9,10]. Most recent efforts describe well the open research topics and refinement techniques related to shells, such as, improvements of classical models [11] and higher-order models [12][13][14]; asymptotic approaches [15]; improvement of FE performances regarding membrane and shear locking [16][17][18][19][20][21], mesh accuracy [22], and distortion [23]; improved modeling of the interlaminar shear stresses [24]; Layer-Wise (LW) models [25,26]; Zig-Zag models [27,28]; mixed formulations [29][30][31]; variable kinematics finite elements with multifield effects [32]; extensions to non-linear problems [33,34] and peridynamics [35]; innovative solution schemes such as the numerical manifold method [36].…”

Section: Introductionmentioning

confidence: 99%

Best theory diagrams for multilayered structures via shell finite elements

Petrolo

Carrera

2019

Adv. Model. and Simul. in Eng. Sci.

View full text Add to dashboard Cite

Composite structures are convenient structural solutions for many engineering fields, but their design is challenging and may lead to oversizing due to the significant amount of uncertainties concerning the current modeling capabilities. From a structural analysis standpoint, the finite element method is the most used approach and shell elements are of primary importance in the case of thin structures. Current research efforts aim at improving the accuracy of such elements with limited computational overheads to improve the predictive capabilities and widen the applicability to complex structures and nonlinear cases. The present paper presents shell elements with the minimum number of nodal degrees of freedom and maximum accuracy. Such elements compose the best theory diagram stemming from the combined use of the Carrera Unified Formulation and the Axiomatic/Asymptotic Method. Moreover, this paper provides guidelines on the choice of the proper higher-order terms via the introduction of relevance factor diagrams. The numerical cases consider various sets of design parameters such as the thickness, curvature, stacking sequence, and boundary conditions. The results show that the most relevant set of higher-order terms are third-order and that the thickness plays the primary role in their choice. Moreover, certain terms have very high influence, and their neglect may affect the accuracy of the model significantly.

show abstract

Theory and numerics of layered shells with variationally embedded interlaminar stresses

Cited by 15 publications

References 36 publications

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

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

An advanced shell model for the analysis of geometrical and material nonlinear shells

Best theory diagrams for multilayered structures via shell finite elements

Contact Info

Product

Resources

About