Pierre Ladevèze

Damage analysis of interlaminar fracture specimens

Abstract Interlaminar fracture specimens are widely used for studying the interlaminar toughness of composite laminates. The goal of this paper is to analyse delamination specimens within the framework of a damage meso-modelling of composite laminates. In this type of modelling a laminate is described as a stacking sequence of homogeneous layers and interlaminar interfaces. The interface is assumed to be damageable in order to model the delamination phenomena. In the case of the propagation of a pre-existing crack, the main parameters for the interface model identification are the critical energy release rates. Delamination specimens are here modelled as two beams connected by a damageable interface. By means of a Finite Element Scheme used in connection with a Riks-like algorithm, comparisons between numerical simulation and experiments have been performed for a wide class of specimens (D.C.B., E.N.F., E.L.S.). The results show the interest of the proposed modelling, which allows a complete simulation of delamination using of relatively little experimental data.

On a Multiscale Computational Strategy with Time and Space Homogenization for Structural Mechanics

A new multiscale computational strategy was recently proposed for the analysis of structures described both on a fine space scale and a fine time scale. This strategy, which involves homogenization in space as well as in time, could replace in several domains of application the standard homogenization techniques, which are generally limited to the space domain. It is an iterative strategy which calls for the resolution of problems on both a micro (fine) scale and a macro (homogenized) scale. In this paper, we review the bases of this approach and present improved approximation techniques to solve the micro- and macro-problems.

A mesomodel for localisation and damage computation in laminates

The basic aspects of a material mesomodel dedicated to composite laminates and capable of simulating complete fracture phenomena are discussed. Attention is focused herein on damage computation and, in particular, on the description of localisation phenomena. Both quasi-static and dynamic loadings are considered.

An enhanced mesomodel for laminates based on micromechanics

Abstract An enhanced version of the damage mesomodel for laminates (DML), which has been developed over the last 15 years at Cachan, is introduced in the light of the extensive work— both theoretical and experimental— in micromechanics. The new mesomodel is fully compatible with classical micromechanics models.

Delamination analysis by damage mechanics: Some applications

Delamination is a phenomenon which involves complex degradation of both layers and inter-laminar connections. To take into account these degradations, the composite laminate is modeled at a meso scale as a stacking of homogeneous layers connected by interfaces. Layers and interfaces may be damaged. Both onset of delamination and its propagation on a short distance are predicted. Two applications are presented, the numerical simulations are compared with experimental results: (i) delamination in the vicinity of a straight edge of a specimen under tension or compression, (ii) delamination near the hole of a perforated plate under tension.

The variational theory of complex rays for the calculation of medium‐frequency vibrations

A new approach called the “variational theory of complex rays” (VTCR) is developed for calculating the vibrations of weakly damped elastic structures in the medium‐frequency range. Here, the emphasis is put on the most fundamental aspects. The effective quantities (elastic energy, vibration intensity, etc.) are evaluated after solving a small system of equations which does not derive from a finite element discretization of the structure. Numerical examples related to plates show the appeal and the possibilities of the VTCR.

New concepts for linear beam theory with arbitrary geometry and loading

Abstract A new approach is introduced for the analysis and calculation of straight prismatic beams of piecewise constant cross-section under arbitrary loads. This theory can be called “exact” because it determines exact static and kinematic generalized quantities. Moreover, contrary to classical theories, it is not limited to high-aspect ratio (i.e. relatively slender) beams.

A Multiscale Computational Approach for Contact Problems

We introduce a two-scale computational strategy for the resolution of contact problems with friction, possibly with numerous contact surfaces; the structure studied may also be highly heterogeneous. The description of “micro” and “macro” quantities is performed on the interfaces arising from the decomposition of the structure studied into an assembly of substructures and interfaces. The efficiency and robustness of the method are illustrated on several examples. This iterative computational strategy is suitable for parallel computing; it can be interpreted as a mixed multilevel domain decomposition method. Its scalability has been demonstrated and comparisons with other domain decomposition methods are also given.

New advances on a posteriori error on constitutive relation in f.e. analysis

This paper deals with error estimators based on residuals on the constitutive relation which have been developed for the past 20 years at Cachan. Especially in the case of elasticity, these error estimators can become poor in situations where the material and the mesh are strongly anisotropic. The crucial point herein is the construction of equilibrated stress fields from the computed finite element solution. Therefore, in this paper, the approach and in particular this last point are re-examined. Several important modifications are introduced in the concepts and basic techniques. Hence, a new generation of error estimators which seem to be extremely robust upon initial applications has been generated.

Local error estimators for finite element linear analysis

Local error estimators on stresses, displacements, etc. are derived from constitutive relation error estimators. Examples show that they can be considered as an upper bound.