Sébastien Mercier

Micromechanical modelling of porous materials under dynamic loading

The behaviour of porous material under dynamic conditions is assessed by a micromechanical approach. By averaging, a general form for the dynamic macrostress is proposed which recovers the static definition when inertia effects are neglected. In this work, a representative volume element for the porous material is defined as a hollow sphere. Using an approximation of the velocity field and the principle of virtual work, an explicit relationship is found between the macroscopic stress and strain rate. The macrostress tensor is proved to be symmetric, in the present formulation proposed for porous materials. Illustrations are shown for hydrostatic tension or compression and also for axisymmetric loading. In the latter case, the effect of stress triaxiality is captured.

Predictions of bifurcation and instabilities during dynamic extension

Dynamic bifurcation and flow instabilities of cylindrical bars, made of an incompressible strain hardening plastic material, are investigated. A Lagrangian linear perturbation analysis is performed to obtain a fourth order partial differential equation which governs the evolution of the perturbation. The analysis shows that inertia slows down the growth of long wavelengths while bidimensional effects conjugated to strain hardening extinct short wavelengths. The present approach is applied successfully to the analysis of bifurcation and instabilities in (i) a rectangular block during plane strain extension, (ii) a circular bar during uniaxial extension. New results are obtained in the case of rate independent materials and a synthetical point of view is obtained for rate dependent behaviors.

Comparison of different homogenization approaches for elastic–viscoplastic materials

Homogenization of linear viscoelastic and non-linear viscoplastic composite materials is considered in this paper. First, we compare two homogenization schemes based on the Mori–Tanaka method coupled with the additive interaction (AI) law proposed by Molinari et al (1997 Mech. Mater. 26 43–62) or coupled with a concentration law based on translated fields (TF) originally proposed for the self-consistent scheme by Paquin et al (1999 Arch. Appl. Mech. 69 14–35). These methods are also evaluated against (i) full-field calculations of the literature based on the finite element method and on fast Fourier transform, (ii) available analytical exact solutions obtained in linear viscoelasticity and (iii) homogenization methods based on variational approaches. Developments of the AI model are obtained for linear and non-linear material responses while results for the TF method are shown for the linear case. Various configurations are considered: spherical inclusions, aligned fibers, hard and soft inclusions, large material contrasts between phases, volume-preserving versus dilatant anelastic flow, non-monotonic loading. The agreement between the AI and TF methods is excellent and the correlation with full field calculations is in general of quite good quality (with some exceptions for non-linear composites with a large volume fraction of very soft inclusions for which a discrepancy of about 15% was found for macroscopic stress). Description of the material behavior with internal variables can be accounted for with the AI and TF approaches and therefore complex loadings can be easily handled in contrast with most hereditary approaches.

Steady-State shear band propagation under dynamic conditions

Abstract The dynamic propagation of a shear band is assessed in mode II. A layer of finite thickness is subjected to simple shearing. The band propagates in the shear direction under steady state conditions. Three parameters are used to characterize the process : the shear band velocity, the length of the process zone and the width of the shear band. The process zone is the region at the vicinity of the shear band tip where the strain rate changes rapidly from a quasi-uniform profile to a localized distribution. The shear band velocity and the length of the process zone are calculated by use of a variational approach. We analyse the roles of inertia, of loading conditions and of material properties such as yield stress, strain (or thermal ) softening, strain hardening, strain rate sensitivity. The effect of elastic energy release is shown to be important in general. Comparisons with experimental results are made.

Void coalescence in a porous solid under dynamic loading conditions

Void coalescence in ductile voided solids subjected to dynamic loading is investigated numerically. Finite element simulations of an axisymmetric unit cell, taking inertia and finite strain effects into account, are used to describe the coalescence process in a porous material containing a periodic distribution of initially spherical voids. The numerical results suggest that inertia yields a stabilizing effect and slows down the necking of the ligaments between neighbouring voids. Besides, for sufficiently high stress triaxiality and loading rate, coalescence is found to occur by direct impingement, instead of ligament necking. This result correlates with experimental observations in spall fracture and dynamic crack propagation.

Thermo-mechanical simulation of PCB with embedded components

Abstract In recent years, in order to increase density and performance of electronic boards, components are embedded in internal layers of printed circuit boards (PCBs). The reliability of this new technology has to be investigated to ensure the working of the electronic boards submitted to harsh environment and long mission profiles. To study the thermo-mechanical behavior of these boards, finite element simulations have been performed. It is observed that embedded passive chips are subjected to complex loading during the lamination process, due mostly to shrinkage of the resin, differences in material properties and also because of temperature excursion. The effects of material parameters and of the geometrical configuration are investigated in details. It will be shown that the generated stresses are not critical for the passive chip size considered in the present work.

Homogeneization of Viscoplastic Materials

The approximate solution of the non-linear inclusion problem, Molinari, Canova, Ahzi (1987), Molinari (1997) is used to define various averaging schemes for viscoplastic heterogeneous materials, among which the tangent self-consistent model and the non-linear Mori-Tanaka model.