Publications

2009

• Cyclic approximation of the heat equation in finite strains for the build-up problem of rubber
  
  • Le Chenadec Yohann
  • Raoult Ida
  • Stolz Claude
  • Nguyen Thi Mac Lan
  Journal of Mechanics of Materials and Structures, Mathematical Sciences Publishers, 2009, 4 (2), pp.309-318.
• The effective behavior of (heterogeneous) elastic bodies containing defects localized on a surface
  
  • Marigo Jean-Jacques
  • Pideri Catherine
  , 2009.
• Elastic-wave identification of penetrable obstacles using shape-material sensitivity framework
  
  • Bonnet Marc
  • Guzina B. B.
  Journal of Computational Physics, Elsevier, 2009, 228, pp.294-311. This study deals with elastic-wave identification of discrete heterogeneities (inclusions) in an otherwise homogeneous ``reference'' solid from limited-aperture waveform measurements taken on its surface. On adopting the boundary integral equation (BIE) framework for elastodynamic scattering, the inverse query is cast as a minimization problem involving experimental observations and their simulations for a trial inclusion that is defined through its boundary, elastic moduli, and mass density. For an optimal performance of the gradient-based search methods suited to solve the problem, explicit expressions for the shape (i.e. boundary) and material sensitivities of the misfit functional are obtained via the adjoint field approach and direct differentiation of the governing BIEs. Making use of the message-passing interface, the proposed sensitivity formulas are implemented in a data-parallel code and integrated into a nonlinear optimization framework based on the direct BIE method and an augmented Lagrangian whose inequality constraints are employed to avoid solving forward scattering problems for physically inadmissible (or overly distorted) trial inclusion configurations. Numerical results for the reconstruction of an ellipsoidal defect in a semi-infinite solid show the effectiveness of the proposed shape-material sensitivity formulation, which constitutes an essential computational component of the defect identification algorithm. (10.1016/j.jcp.2008.09.009)
  DOI : 10.1016/j.jcp.2008.09.009
• A finite-strain model for anisotropic viscoplastic porous media: II – Applications
  
  • Danas Kostas
  • Ponte Castañeda Pedro
  European Journal of Mechanics - A/Solids, Elsevier, 2009, 28, pp.402-416. In Part I of this work, we have proposed a new model based on the "second-order" nonlinear homogenization method for determining the effective response and microstructure evolution in viscoplastic porous media with aligned ellipsoidal voids subjected to general loading conditions. In this second part, the new model is used to analyze the instantaneous effective behavior and microstructure evolution in porous media for several representative loading conditions and microstructural configurations. First, we study the effect of the shape and orientation of the voids on the overall instantaneous response of a porous medium that is subjected to principal loading conditions. Secondly, we study the problem of microstructure evolution under axisymmetric and simple shear loading conditions for initially spherical voids in an attempt to validate the present model by comparison with existing numerical and approximate results in the literature. Finally, we study the possible development of macroscopic instabilities for the special case of ideally-plastic solids subjected to plane-strain loading conditions. The results, reported in this paper, suggest that the present model improves dramatically on the earlier "variational" estimates, in particular, because it generates much more accurate results for high triaxiality loading conditions. (10.1016/j.euromechsol.2008.11.003)
  DOI : 10.1016/j.euromechsol.2008.11.003