Numerical Simulation of Mechanical Behavior of Composite Materials

Introduction.- Composite materials uses.- The use of composite materials in the automobile industry.- The use of composite materials in the Aeronautic industry.- Composite materials in the naval industry.- The use of composite materials in Civil Engineering.- Composites properties.- Classification of composite materials.- Classification by the topology.- Classification by their components.- Structural Classification.- Mechanical Anisotropy.- Introduction.- Generalities on the anisotropic formulation.- Yield function and plastic potential for isotropic materials.- General explicit definition of the isotropic yield criterion in the referential configuration.- General explicit definition of the orthotropic yield criterion in the referential configuration.- General implicit definition of the orthotropic criterion in the referential configuration.- Stresses space transformation.- Strain space transformation.- General definition of the stress space transformation tensor.- Numerical calculation of the adjusting tensor matrix form.- Mises-Hill orthotropic criterion verification by the space mapping theory.- Anisotropy in the updated configuration.- Transformation of the stresses space.- Transformation of the strain space.- Plastic flow rule. Internal variables evolution law.- Referential Configuration.- Updated Configuration.- Definition of the dissipation in the isotropic fictitious space. Unicity of the dissipation.- Referential configuration.- Updated configuration.- Tangent constitutive equation.- Referential Configuration.- Spatial Configuration.- Mixing Theory.- Introduction.- Classic Mixing Theory.- Free energy expression.- Classical theory modification. Serial-Parallel Model.- The generalized mixing theory.- Large strains classic mixing theory.- Closure or compatibility equation.- Free energy function.- The constitutive equation.- Generalized mixing theory formulated in large strains.- Constitutive equation.- Mixing theory modification for short length reinforcement.- Fiber axial stress distribution.- Tangent stress distribution in the interface.- Short fibers constitutive model.- Composite constitutive equation.- Free energy for short reinforced composite materials.- Fiber mechanical properties in the Mixing Theory – Linear behavior in small strains.- Comparative example. “Micromodel” vs. “Mixing Theory” with anisotropy in large strains.- Behavior simulation of asphalt mixtures.- Introduction.- Problem motivation and description.- Materials parameterization. Simplified granulometry and properties correction by aspect relation.- Numerical Simulation.- Fiber-Matrix Displacement (FMD)-Debonding.- Introduction.- Stresses distribution along the reinforced fiber.- Cracks and fibers interaction.- Constitutive models for composite materials with "FMD".- A procedure proposed for “FMD”.- The constitutive model modification. Procedure for the fiber–matrix displacement phenomenon (FMD).- Expression of the elastoplastic constitutive model of the reinforcement.- Yield condition.- Plastic flow rule.- "Total" and "Updated" Lagrangian Formulation.- Implementation of the mixing and anisotropy theory in the FEM context.- "FMD" Phenomenon: Micro model and Mixing Theory with anisotropy.- Homogenization Theory.- Introduction and state of the art.- Average Methods.- The asymptotic expansion theory.- Extension of the “Average Method” and the “Asymptotic Expansion Method” to the nonlinear problem.- Other homogenization-related subjects.- Homogenization Theory based on “Local Periodicity”.- Introduction.- Periodic structure concepts.- Variables Local periodicity.- Strains tensor homogenization.- The homogenized stress and the equilibrium equation.- Elastic problem basis at micro-macro scales.- Basis of the inelastic problem at micro-macro scales.- The elastic constitutive tensor determination for composite materials.- Quasi-tangent inelastic constitutive tensor determination for the composite materials. Analytical determination.- Micro-Macro structural coupling.- Local effects influence.- Test examples of the “Homogenization Theory of Local Periodicity”.- Transversal behavior of a reinforced long fibers matrix –Simple tensile test.- Thick cylinder subjected to internal pressure.- Masonry homogenized, treated as a composite.- Masonry-Homogenized Composite.- Introduction and background.- Masonry properties.- Masonry behavior under uniaxial compression.- Masonry behavior under uniaxial tension.- Biaxial behavior.- Post-peak masonry behavior. Softening.- Different methods for masonry calculation.- Constitutive model based on a particular case of the homogenization concept.- Constitutive model.- Formulation checkout.- Non-Linear Buckling of Reinforced Composites.- Introduction.- Problem description and state-of-the-art.- Euler critical load.- Rosen model.- Micro-mechanical models.- Mechanical damage models.- Model of stiffness-loss due to buckling in long-fibers composites reinforced.- Introduction.- Fiber model general definition.- Definition of the stiffness-loss variable due to buckling.- Main characteristics of the model.- Energy dissipation.- Test example.