S. Sadaba’s research while affiliated with Universidad Politécnica de Madrid and other places

A novel methodology is presented to introduce Periodic Boundary Conditions (PBC) on periodic Representative Volume Elements (RVE) in Finite Element (FE) solvers based on dynamic explicit time integration. This implementation aims at overcoming the difficulties of the explicit FE method in dealing with standard PBC. The proposed approach is based on the implementation of a user-defined element, named a Periodic Boundary Condition Element (PBCE), that enforces the periodicity between periodic nodes through a spring-mass-dashpot system. The methodology is demonstrated in the multiscale simulation of composite materials. Two showcases are presented: one at the scale of computational micromechanics, and another one at the level of computational mesomechanics. The first case demonstrates that the proposed PBCE allows the homogenization of composite ply properties through the explicit FE integration approach with increased efficiency and similar reliability with respect to the equivalent implicit simulations with traditional PBC. The second case demonstrates that the PBCE can be applied to the computational technique of Periodic Laminate Elements (PLE) to homogenize elastic and strength properties of entire laminates. Both demonstrations strongly support the method for the application of multiscale virtual testing to the building-block certification of composite materials.

This chapter proposes a systematic simulation strategy to determine the mechanical behaviour of composite laminates under impact loading using a computational mesomechanics approach. The methodology includes modelization of the physical mechanisms of damage observed in laminates: intralaminar (ply failure) and interlaminar (delamination failure). The methodology was applied to analyse the impact behaviour of carbon–epoxy laminates subjected to low- and high-velocity impacts, and the results were compared with experimental data in terms of energy absorption capacity and failure mechanisms.

A high-fidelity virtual tool for the numerical simulation of low-velocity impact damage in unidirectional composite laminates is proposed. A continuum material model for the simulation of intraply damage phenomena is implemented in a numerical scheme as a user subroutine of the commercially available Abaqus finite element package. Delaminations are simulated using of cohesive surfaces. The use of structured meshes, aligned with fibre directions allows the physically-sound simulation of matrix cracks parallel to fibre directions, and their interaction with the development of delaminations. The implementation of element erosion criteria and the application of intraply and interlaminar friction allow for the simulation of fibre splits and their entanglement, which in turn results in permanent indentation in the impacted laminate. It is shown that this simulation strategy gives sound results for impact energies bellow and above the Barely Visible Impact Damage threshold, up to laminate perforation conditions.

Ignoring crack tip effects, the stability of the X-FEM discretizations is trivial for open cracks but remains a challenge if we constrain the crack to be closed (i.e., the bi-material problem). Here, we develop a formulation for general cohesive interactions between crack faces within the X-FEM framework. The stability of the new formulation is demonstrated for any cohesive crack stiffness (including the closed crack) and illustrated for a nonlinear cohesive softening law. A benchmark of the new model is carried out with simpler approaches for a closed crack (i.e., Lagrange multipliers) and for a cohesive crack (i.e., penalty approach). Due to the analogies between stable cohesive X-FEM and Nitsche's methods, the new method simplifies the implementation and is attractive in dynamic explicit codes. Copyright © 2014 John Wiley & Sons, Ltd.

Low-velocity impact events occur with some frequency on composite applications such as airplane components. From ground operations to unavoidable birds, there is a range of situations where an aircraft outer component may be subjected to unexpected impact loads. In most cases, such as tool dropping, the impactor has a relatively high mass but low velocity. The damage produced in such cases is mostly in the form of delaminations which are not easily noticeable through routine naked eye inspections. However, the spread of these delaminations over wide areas of the structure may severely compromise the residual compressive strength of the structure. Therefore, the ability to predict the impact damage resultant from impact events likely to happen is of utmost importance in the aeronautical industry. Traditionally, impact damage models rely on either analytical calculations or extensive experimental data. By one side, analytical predictions of the impact damage resistance and tolerance of composite laminates are overly simplified and unreliable. By the other side, testing each promising design is time consuming and costly. Low-cost virtual testing by means of nonlinear finite element analyses can replace most of the actual impact testing of laminates. This paper proposes a systematic strategy to determine the mechanical behaviour of composite materials under low-velocity impact using a multiscale numerical approach. A virtual design/testing strategy is implemented that takes into account the physical mechanisms of damage at different length scales from ply to laminate. At mesoscale level, a three-dimensional continuum damage model for the simulation of intraply damage phenomena is used. Delamination is simulated by means of cohesive surfaces. The use of meshes aligned with fibre directions allows the accurate capturing of matrix cracking and its interaction with delamination. Element erosion and the application of friction allow for the simulation of fibre splits and their entanglement which highly influences the permanent indentation of the impacted specimen.

This research focused on the evaluation of damage formation on ±45° carbon fiber laminates subjected to tensile tests. The damage was evaluated by means of X-ray tomography. A high density of cracks developed during the plateau of the stress-strain curve and were qualitatively analyzed, showing that the inner plies eventually developed a higher crack concentration than the outer plies. Delamination started to occur in the outermost ply interface when the slope after the plateau of the stress-strain curve began to increase.

A bottom-up, multiscale modeling approach is presented to carry out high-fidelity virtual mechanical tests of composite materials and structures. The strategy begins with the in situ measurement of the matrix and interface mechanical properties at the nanometer-micrometer range to build up a ladder of the numerical simulations, which take into account the relevant deformation and failure mechanisms at different length scales relevant to individual plies, laminates and components. The main features of each simulation step and the information transferred between length scales are described in detail as well as the current limitations and the areas for further development. Finally, the roadmap for the extension of the current strategy to include functional properties and processing into the simulation scheme is delineated.

material specimens, along with tests of components and structures up to entire tails, wing boxes, and fuselages, to achieve safety certification. This cost has to date been unavoidable: while computational stress analyses provide good predictions in the elastic regime, they have not achieved predictive accuracy in the presence of damage and fracture. This limitation is starting to be overcome by new modeling strategies, and the increased power of digital computers, which are making possible the development of accurate and reliable simulation tools. This is shown in this paper, in which "virtual" tests C/epoxy laminate coupons subjected to different loading conditions (tension, compression, impact) are carried out and validated against experimental results. VIRTUAL TESTING STRATEGY The discretization of the composite coupons explicitly includes all the plies in the laminate and the corresponding interfaces between them. Each ply was meshed explicitly with one solid element and interface elements were inserted between adjacent plies to take into account the presence of an interfacial region between plies. This strategy is ideal to take into account the different physical failure mechanisms at the intralaminar and interlaminar level. A model for the simulation of the impact of a 1/2 inch diameter steel tup on a square laminate coupon is shown in Fig. 1. Intralaminar failure mechanisms were taken into account in the model by means of a continuum damage mechanics approximation, in which the elastic constants of the each ply were degraded progressively as a function of the damage variables. The damage variables at each material point remain constant if the stresses (or strains) lie inside of a region in the stress (strain) space whose boundary is defined by the failure criteria corresponding to the different failure mechanisms for the ply, and which depend on the fiber architecture within the ply (weave or unidirectional fiber reinforcement). In the case of woven fabrics, the failure mechanisms taken into account included fill and warp fiber tensile/shear failure, in-plane compressive failure, through-thickness compressive failure, and in-plane shear matrix failure (1). For unidirectional lamina, they followed the LaRC03 criteria, which consider that intralaminar failure may be due to matrix failure under transverse compression and tension, and fiber failure under longitudinal compression and tension (2). Regularization of the constitutive models to avoid the dependence of the numerical results with the mesh size was included through the crack band model (3). Interface decohesion between plies was also included through a simple cohesive crack model, which controlled the behaviour of the interface elements between plies. Fully damaged

The mechanical behavior of polymer reinforced composite materials until fracture was simulated under the general framework of computational micro and mesomechanics. Within this framework, a representative volume element RVE of the composite material is discretized using three dimensional finite elements at the scale of the microstructure - including fiber-matrix topology-or at the scale of the mesostructure-including the laminate stacking sequence. The simulation strategy takes into account the different failure modes experimentally observed in unidirectional composite laminas (tensile splitting, compressive kinking and shear failure). The numerical predictions showed the potential of computational micro and meso-mechanics to reproduce accurately the damage pattern and the failure strength of composite materials. These results demonstrate that virtual fracture testing of composite coupon specimens is nowadays possible and opens the possibility of replacing (at least partially) the costly and time consuming mechanical tests by "virtual tests".

In order to assess reliability of components made of composites which have responsibility on human lives, there is a burden of costly experimental programs for validation. With the current state of realistic damage models in fiber� reinforced composites, the development of virtual tests which can at least partially substitute the expensive experimental programs is at hand. The proposed methodology consists of a finite element implementation of the LARC03�04 criteria as mate rial constitutive equations in a finite element model. One of the advantages of using the LARC model is that the relevant parameters can be obtained either by physical testing (at lamina level) or by means of computational micromechanical models. The later models may be developed from known properties of the composite constituents: fiber, matrix and interface. The described model has been combined with an interlaminar failure model, which has been implemented by means of cohesive elements, in order to capture delamination. PALABRAS CLAVE: Composites, crack band, fracture, delamination.