A variable kinematic doubly-curved MITC9 shell element for the analysis of laminated composites

The present article considers the linear static analysis of composite shell structures with double-curvature geometry by means of a shell finite element with variable through-the-thickness kinematic. The refined models used are grouped in the Unified Formulation by Carrera (CUF) and they permit the distribution of displacements and stresses along the thickness of the multilayered shell to be accurately described. The shell element has nine nodes and the mixed interpolation of tensorial components (MITC) method is used to contrast the membrane and shear locking phenomenon. The governing equations are derived from the principle of virtual displacement (PVD) and the finite element method (FEM) is employed to solve them. Cross-ply spherical shells with simply-supported edges and subjected to bi-sinusoidal pressure are analyzed. Various laminations, thickness ratios, and curvature ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in the literature and the analytical solutions obtained using the CUF and the Navier's method. From the analysis, one can conclude that the shell element based on the CUF is very efficient and its use is mandatory with respect to the classical models in the study of composite structures. Finally, shells with different lamination, boundary conditions, and loads are also analyzed using high-order layer-wise theories in order to provide FEM benchmark solution

Hierarchical Modeling of the Mechanical Behavior of High Speed Steels as Layer-Structured Particulate MMCs

High Speed Steels (HSS) produced by electro-slag remelting can be viewed as particle reinforced Metal Matrix Composites (MMCs) consisting of alternating layers of high and low inclusion volume fraction. These phase arrangements require specific models to be used in analytical and numerical studies of the elastoplastic response of HSS. In the present study, a hierarchical micro-meso-macro approach is discussed, which combines the Multi-Particle Effective Field Method (MEFM) for describing the matrix-inclusion topology at the microscale with an extended lamination theory for handling the layered geometry at the mesoscale. In addition, a Finite Element based two-dimensional method is presented, in which HSS is modeled as a material with a graded microstructure. The obtained results are discussed in terms of overall elastoplastic behavior and of damage relevant microscale fields

Multiscale modeling of highly heterogeneous particulate MMCs

A continuum mechanics based multiscale modeling concept incorporating different material descriptions at appropriate length scales is presented and applied to High Speed Steels (HSSs) in order to study their overall and local thermomechanical behavior. Such materials can be viewed as particulate Metal Matrix Composites (MMCs) with a strongly clustered arrangement of thermoelastic carbidic particles embedded in a thermoelastoplastic steel matrix. In the contribution a Mesophase Cell Hierarchical Model is presented, which combines a unit cell approach for handling the clustered topology at the mesoscale with mean field based constitutive material laws (a mean field based version of the Transformation Field Analysis and an incremental Mori-Tanaka approach) for describing the matrix-inclusion-type composite at the microscale. As an alternative approach, a Finite Element based 2/D micromechanical method is used, in which the HSS is modeled as a material with a graded microstructure. Results are discussed in terms of the overall thermoelastoplastic behavior and of microscale parameters relevant for local damage initiation and evolution

Adaptive smoothed FEM for forming simulations

FEMsimulation of large deformations as occur in metal forming processes is usually accompanied with highly distorted meshes. This leads first to a reduction of accuracy and later to loss of convergence when implicit solvers are used. Remeshing can be used to reduce element distortion, but repeated remeshing will result in smoothing of data like equivalent plastic strain, due to averaging and interpolation. A meshless method circumvents the problem of mesh distortion, but depending on the integration of the weak formulation of equilibrium mapping of data and hence smoothing of data still remains unless a nodal integration scheme is used. Starting with a LocalMaximum Entropy approach [1] with nodal integration, we end-up with a smoothed Finite Element formulation in the limit of local approximations [2]. It is straightforward to adapt the triangulation in every increment, yielding an Adaptive Smoothed Finite Element Method, in which large deformations can be modelled with a Lagrangian description without the necessity to map data from one step to the other. A cell based stabilized conforming nodal integration method (SCNI) [3] is used. Depending on the configuration of nodes, nodal integration can yield singular stiffness matrices, resulting in spurious displacement modes [4]. A stabilization is used, based on minimizing the difference between a ‘linear assumed’ and the consistent strain field. The cells are based on the Delaunay triangulation, connecting mid-sides and centres of gravity of the triangles (Figure 1). Especially at the outer boundary, this yields a simpler formulation than using the dual Voronoi tesselatio

Space-time discretization for Fluid-Structure Interaction

Accurate numerical prediction of aeroelastic instabilities requires correct representation of the transfer of energy between the fluid and the structure, particularly when determining the neutral-stability point. In the numerical model, energy transfer depends on the discretization methods used for the fluid and the structure as well as on their coupling. In this paper we consider a space-time Galerkin least-squares formulation of the fluid equations and use shape functions which are discontinuous in time. For the time integration of the structure we investigate two essentially different methods, namely the trapezoidal method and a time-discontinuous Galerkin method. In particular, we assess their ability to conserve energy in the presence of a forcing term. Further, we show that these methods are different in their ability to conserve momentum and energy at the interface when coupled to the fluid discretization, We compare monolithic and partitioned fluid-structure coupling. Partitioned schemes are typically unstable. Structural prediction can improve their accuracy and stability, but the admissible time step still remains restricted. Although monolithic schemes do not necessarily imply energy conservation at the interface, they appear to have better stability properties than partitioned schemes allowing for larger time steps. Moreover, we show that the efficiency of the iterative solver employed in a monolithic scheme can be improved by prediction techniques. We illustrate our results by numerical experiments for a one-dimensional model problem of a piston interacting with a fluid

The influence of a brittle Cr interlayer on the deformation behavior of thin Cu films on flexible substrates Experiment and model

AbstractThin metal films deposited on polymer substrates are used in flexible electronic devices such as flexible displays or printed memories. They are often fabricated as complicated multilayer structures. Understanding the mechanical behavior of the interface between the metal film and the substrate as well as the process of crack formation under global tension is important for producing reliable devices. In the present work, the deformation behavior of copper films (50–200nm thick), bonded to polyimide directly or via a 10nm chromium interlayer, is investigated by experimental analysis and computational simulations. The influence of the various copper film thicknesses and the usage of a brittle interlayer on the crack density as well as on the stress magnitude in the copper after saturation of the cracking process are studied with in situ tensile tests in a synchrotron and under an atomic force microscope. From the computational point of view, the evolution of the crack pattern is modeled as a stochastic process via finite element based cohesive zone simulations. Both, experiments and simulations show that the chromium interlayer dominates the deformation behavior. The interlayer forms cracks that induce a stress concentration in the overlying copper film. This behavior is more pronounced in the 50nm than in the 200nm copper films