Meso-scale modelling of 3D woven composite T-joints with weave variations

A meso-scale modelling framework is proposed to simulate the 3D woven fibre architectures and the mechanical performance of the composite T-joints, subjected to quasi-static tensile pull-off loading. The proposed method starts with building the realistic reinforcement geometries of the 3D woven T-joints at the mesoscale, of which the modelling strategy is applicable for other types of geometries with weave variations at the T-joint junction. Damage modelling incorporates both interface and constituent material damage, in conjunction with a continuum damage mechanics approach to account for the progressive failure behaviour. With a voxel based cohesive zone model, the proposed method is able to model mode I delamination based on the voxel mesh technique, which has advantages in meshing. Predicted results are in good agreement with experimental data beyond initial failure, in terms of load-displacement responses, failure events, damage initiation and propagation. The significant effect of fibre architecture variations on mechanical behaviour is successfully predicted through this modelling method without any further correlation of input parameters in damage model. This predictive method will facilitate the design and optimisation of 3D woven T-joint preforms

A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part II: the optimisation strategy

This work deals with the problem of the optimum design of a sandwich panel. The design strategy that we propose is a numerical optimisation procedure that does not make any simplifying assumption to obtain a true global optimum configuration of the system. To face the design of the sandwich structure at both meso and macro scales, we use a two-level optimisation strategy: at the first level we determine the optimal geometry of the unit cell of the core together with the material and geometric parameters of the laminated skins, while at the second level we determine the optimal skins lay-up giving the geometrical and material parameters issued from the first level. The two-level strategy relies both on the use of the polar formalism for the description of the anisotropic behaviour of the laminates and on the use of a genetic algorithm as optimisation tool to perform the solution search. To prove its effectiveness, we apply our strategy to the least-weight design of a sandwich plate, satisfying several constraints: on the first buckling load, on the positive-definiteness of the stiffness tensor of the core, on the ratio between skins and core thickness and on the admissible moduli for the laminated skins

Virtual Delamination Testing through Non-Linear Multi-Scale Computational Methods: Some Recent Progress

This paper deals with the parallel simulation of delamination problems at the meso-scale by means of multi-scale methods, the aim being the Virtual Delamination Testing of Composite parts. In the non-linear context, Domain Decomposition Methods are mainly used as a solver for the tangent problem to be solved at each iteration of a Newton-Raphson algorithm. In case of strongly nonlinear and heterogeneous problems, this procedure may lead to severe difficulties. The paper focuses on methods to circumvent these problems, which can now be expressed using a relatively general framework, even though the different ingredients of the strategy have emerged separately. We rely here on the micro-macro framework proposed in (Ladev\`eze, Loiseau, and Dureisseix, 2001). The method proposed in this paper introduces three additional features: (i) the adaptation of the macro-basis to situations where classical homogenization does not provide a good preconditioner, (ii) the use of non-linear relocalization to decrease the number of global problems to be solved in the case of unevenly distributed non-linearities, (iii) the adaptation of the approximation of the local Schur complement which governs the convergence of the proposed iterative technique. Computations of delamination and delamination-buckling interaction with contact on potentially large delaminated areas are used to illustrate those aspects

Optimal design of sandwich plates with honeycomb core

This work deals with the problem of the optimum design of a sandwich structure composed of two laminated skins and a honeycomb core. The goal is to propose a numerical optimisation procedure that does not make any simplifying hypothesis in order to obtain a true global optimal solution for the considered problem. In order to face the design of the sandwich structure at both meso and macro scales, we use a two-level optimisation strategy. At the first level, we determine the optimum geometry of the unit cell together with the material and geometric parameters of the laminated skins, while at the second level we determine the optimal skins lay-up giving the geometrical and material parameters issued from the first level. We will illustrate the application of our strategy to the least-weight design of a sandwich plate submitted to several constraints: on the first buckling load, on the positive-definiteness of the stiffness tensor of the core, on the ratio between skins and core thickness and on the admissible moduli for the laminated skins

Statistical Physics of Rupture in Heterogeneous Media

The damage and fracture of materials are technologically of enormous interest due to their economic and human cost. They cover a wide range of phenomena like e.g. cracking of glass, aging of concrete, the failure of fiber networks in the formation of paper and the breaking of a metal bar subject to an external load. Failure of composite systems is of utmost importance in naval, aeronautics and space industry. By the term composite, we refer to materials with heterogeneous microscopic structures and also to assemblages of macroscopic elements forming a super-structure. Chemical and nuclear plants suffer from cracking due to corrosion either of chemical or radioactive origin, aided by thermal and/or mechanical stress. Despite the large amount of experimental data and the considerable effort that has been undertaken by material scientists, many questions about fracture have not been answered yet. There is no comprehensive understanding of rupture phenomena but only a partial classification in restricted and relatively simple situations. This lack of fundamental understanding is indeed reflected in the absence of reliable prediction methods for rupture, based on a suitable monitoring of the stressed system. Not only is there a lack of non-empirical understanding of the reliability of a system, but also the empirical laws themselves have often limited value. The difficulties stem from the complex interplay between heterogeneities and modes of damage and the possible existence of a hierarchy of characteristic scales (static and dynamic). The paper presents a review of recent efforts from the statistical physics community to address these points.Comment: Enlarged review and updated references, 21 pages with 2 figure

Homogenization of plain weave composites with imperfect microstructure: Part II--Analysis of real-world materials

A two-layer statistically equivalent periodic unit cell is offered to predict a macroscopic response of plain weave multilayer carbon-carbon textile composites. Falling-short in describing the most typical geometrical imperfections of these material systems the original formulation presented in (Zeman and \v{S}ejnoha, International Journal of Solids and Structures, 41 (2004), pp. 6549--6571) is substantially modified, now allowing for nesting and mutual shift of individual layers of textile fabric in all three directions. Yet, the most valuable asset of the present formulation is seen in the possibility of reflecting the influence of negligible meso-scale porosity through a system of oblate spheroidal voids introduced in between the two layers of the unit cell. Numerical predictions of both the effective thermal conductivities and elastic stiffnesses and their comparison with available laboratory data and the results derived using the Mori-Tanaka averaging scheme support credibility of the present approach, about as much as the reliability of local mechanical properties found from nanoindentation tests performed directly on the analyzed composite samples.Comment: 28 pages, 14 figure