An original mechanical formulation to treat nonlinear orthotropic behavior of composite materials is presented in this book. It also examines different formulations that allow us to evaluate the behavior of composite materials through the composition of its components, obtaining a new composite material. Also two multiple scale homogenization methods are given, one based on the analytical study of the cells (Ad-hoc homogenization) and other one, more general based on the finite element procedure applied on the macro scale (upper-scale) and in the micro scale (sub-scale).
A very general formulation to simulate the mechanical behavior for traditional composite structures (plywood, reinforced concrete, masonry, etc.), as well as the new composite materials reinforced with long and short fibers, nanotubes, etc., are also shown in this work.
Typical phenomena occurring in composite materials are also described in this work, including fiber-matrix debonding, local buckling of fibers and its coupling with the overall buckling of the structure. Finally, several numerical examples that evaluates the qualities and capabilities of the general model formulated are offered in this book.
This book is intended for graduate engineering students who want to expand their knowledge of composite structures behavior.
This book presents an original mechanical formulation for treating nonlinear orthotropic behavior of composite materials. The coverage includes several numerical models that evaluate the qualities and capabilities of the general model formulated here.
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
fibermatrix 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.
Sergio Oller was appointed Full Professor at the School of Civil Engineering of the Technical University of Catalonia, Barcelona, Spain in 1988 and has worked there, as well as at the International Center for Numerical Methods in Engineering (CIMNE), up to the present.
He has also been Visiting Professor at the Civil Engineering Laboratory of the National University of Tucumán, Argentina and at the Department of Civil and Environmental Engineering of the University of California at Berkeley, USA.
Oller teaches Strength of Materials and Structures, a course in Civil Engineering, Geologic Engineering and Aeronautical Engineering; Fracture Mechanics, a course in Numerical Methods in Engineering and Composite Materials and Non-linear Dynamics courses in the Doctoral Program in Structural Engineering.
His research fields include: New Structural Materials, Industrial Casting Processes, Parallel Computing, Constitutive Models, Composites Materials, Fatigue, Earthquake Engineering and Dynamic of Structures.
His research fields include: New Structural Materials, Industrial Casting Processes, Parallel Computing, Constitutive Models, Composites Materials, Fatigue, Earthquake Engineering and Dynamic of Structures.
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