The development of new materials has been linked to the development of a new
theoretical field within the mechanics of solids. This branch of the mechanical,
known as Continuum Micromechanics, introduces a series of new concepts that are
key to the definition of the macroscopic properties of composite materials on the
basis of the definition of the characteristics of its components. Starting from the
premise of separation of scales and the concept of Representative Volume Element,
defined the so-called homogenization methods, whose number has been increasing
as the Micromechanics is gone extend over the years. Such methods are many and
varied, although especially there have been two that have been used and developed
by the majority of authors: the so-called Mean-Homogenization techniques and the
multi-scale based on Finite Element Approaches.

Mean-fifieeld homogenization schemes are an efficient way to predict the behavior
of heterogeneous materials. They range from the simplest hypotheses of the stress
or strain sharing among the phases which do not require analytical solution on the
associated boundary-value problem to more involved geometric models based on
the solution of a boundary-value problem involving a single or composite inclusion
embedded in an equivalent homogenized medium whose elastic module become part
of the solution procedure. In general, they are based on analytical solutions of the
boundary value problem defined in the microstructure level of the inhomogeneous
material and provide good predictions for the mean values over the RVE. Although
originally designed for elastic materials, some approaches to deal with elastoplastic
materials and even with viscoplastic materials have been developed over the years
and compared with the results obtained using Finite Element Approaches. The comparison between different methods of homogenization allows the definition of
a range of validity between the different methods, which helps to discover the
limitations of the various methods and aspects to take into account for future
developments and research.

The main goal of this work is, firstly, to present a general overview of the
different techniques that have been developed in the last years in order to obtain
a prediction of the behavior of elastoplastic composites by taking into account
geometrical and mechanical aspects. Secondly, a comparison between the different
approaches is carried out through a numerical implementation of such techniques.
Both objectives will be carried out through eight different chapters. The first
chapter serves as an introduction and historical review of the advances that have
been made in the field of micromechanics. On the other hand, the second chapter
deals with some important theoretical background that is important in the field
of Continuum Micromechanics, as well as a short introduction of the different
approaches that traditionally have been considered to solve the problem. One group
of methods, based on analytical solutions { the so-called Mean Field Analysis {
will be commented in chapter 3. Chapter 4 is devoted to the implementation
and validation of a numerical tool that solves the mean-field homogenization using
analytical schemes for elastoplastic materials. Subsequent chapters are devoted to
the comparison of the results with the results given by the Finite Element Method.
The general formulation of such method { applied to multi-scale problems { is
presented in chapter 5 from a theoretical point of view, as well as the corresponding
numerical examples. Finally, last chapter will be dedicated to enumerate some
conclusions extracted from the present work, including some aspects that can be
object of future works or improvements.

The current work presents some important aspects about the theoretical concepts
and the numerical implementation of some key approaches for solving the
mechanical problem regarding composite materials. There exist a large number
of possibilities to approximate the response of such complex materials, based in
different assumptions. This document shows the general efficiency of the so-called
mean-field homogenization schemes to capture correctly the macroscopic behavior
of composites. Although these techniques show some limitations, like the incapability
to provide results for the distribution of the different variables over the
microgeometry or the low accuracy in the case of complex microgeometries (like
porous materials), they represent an efficient way to predict the main general behavior
of a composite material spending low computational effort. They are specially
indicated to be used in the previous steps of an analysis or as a tool to validate the
results with more involved approaches.

La función de esta protección es evitar que se produzcan deslizamientos en masa cuando una
cantidad de agua anormalmente elevada circula accidentalmente por el espaldón de aguas abajo
de la presa por distintos motivos como pueden ser el vertido por coronación de la presa o la
pérdida de estanqueidad del elemento impermeable o del cimiento. Según los datos de la
International Commission on Large Dams (ICOLD 1995) el 70% de las causas de rotura o avería
grave en presas de materiales sueltos en el mundo están dentro de las que se han indicado con
anterioridad.

Esta circulación accidental de agua a través del espaldón de escollera, típicamente turbulenta, se
ha denominado en este trabajo percolación (“through flow”, en inglés) para diferenciarla del
término filtración, habitualmente utilizada para el flujo laminar a través de un material fino. El
fenómeno físico que origina la rotura de presas de materiales sueltos sometidas a percolación
accidental es complejo, entrando en juego diversidad de parámetros, muchas veces no
deterministas, y con acoplamiento entre procesos, tanto de filtración como de arrastre y
deslizamiento.

A lo largo de la investigación se han realizado diferentes estudios experimentales y numéricos con
objeto de analizar el efecto sobre el nivel de protección frente al deslizamiento en masa que
producen los principales parámetros geométricos que definen el repié: la anchura de la berma, el
talud exterior y su altura máxima desde la base. También se han realizado estudios sobre factores
con gran influencia en el fenómeno de la percolación como son la anisotropía del material y el
incremento de los caudales unitarios en el pie de presa debidos a la forma de la cerrada.
A partir de los resultados obtenidos en las distintas campañas de modelación física y numérica se
han obtenido conclusiones respecto a la efectividad de este tipo de protección para evitar parcial
o totalmente los daños provocados por percolación accidental en presas de escollera. El resultado
final del trabajo es un procedimiento de diseño para este tipo de protecciones.

Con objeto de completar los criterios de dimensionamiento, teniendo en cuenta los mecanismos
de rotura por erosión interna y arrastre, se han incluido dentro del procedimiento
recomendaciones adicionales basadas en investigaciones existentes en la bibliografía técnica.
Finalmente, se han sugerido posibles líneas de investigación futuras para ampliar el conocimiento
de fenómenos complejos que influyen en el comportamiento de este tipo de protección como son
el efecto de escala, la anisotropía de la escollera, las leyes de resistencia que rigen la filtración
turbulenta a través de medios granulares, los efectos de cimentaciones poco competentes o la
propia caracterización de las propiedades de la escollera de presas.

On the other hand, the multifield theory is a mathematical tool able to describe materials
which contain a complex substructure (Mariano & Stazi 2005). This substructure is endowed
with its own properties and it interacts with the macrostructure and influences drastically its
behavior. Under this mathematical framework, materials such as cement composites can be
seen as a continuum with a microstructure. Therefore, the whole continuum damage mechanics
theory, incorporating a new microstructure, is still applicable.

A formulation, initially based on the theory of continua with microstructure Capriz
(Capriz 1989), has been developed to model the mechanical behavior of the high performance
fiber cement composites with arbitrarily oriented fibers. This formulation approaches
a continuum with microstructure, in which the microstructure takes into account the fibermatrix
interface bond/slip processes, which have been recognized for several authors (Li
2003, Naaman 2007b) as the principal mechanism increasing the ductility of the quasi-brittle
cement response. In fact, the interfaces between the fiber and the matrix become a limiting
factor in improving mechanical properties such as the tensile strength. Particularly, in short
fiber composites is desired to have a strong interface to transfer effectively load from the
matrix to the fiber. However, a strong interface will make difficult to relieve fiber stress
concentration in front of the approaching crack. According to Naaman (Naaman 2003), in
order to develop a better mechanical bond between the fiber and the matrix, the fiber should
be modified along its length by roughening its surface or by inducing mechanical deformations.
Thus, the premise of the model is to take into account this process considering a microfield that represents the slipping fiber-cement displacement. The conjugate generalized stress
to the gradient of this micro-field verifies a balance equation and has a physical meaning.

This contribution includes the computational modeling aspects of the high fiber reinforced
cement composites (HFRCC) model. To simulate the composite material, a finite
element discretization is used to solve the set of equations given by the multifield approach
for this particular case. A two field discretization: the standard macroscopic and the microscopic
displacements, is proposed through a mixed finite element methodology. Furthermore,
a splitting procedure for uncoupling both fields is proposed, which provides a more convenient
numerical treatment of the discrete equation system.

The initiation of failure in HPFRCC at the constitutive level identified as the onset of
strain localization depends on the mechanical properties of the all compounds and not only
on the matrix ones. As localization criteria is considered the bifurcation analysis in combination
with the localized strain injection technique presented by Oliver et al. (Oliver et al.
2010a). It consists of injecting a specific localization mode during the localization stage, via
mixed finite element formulations, to the path of elements that are going to capture the
cracks, and, in this way, the spurious mesh orientation dependence is removed.

Model validation was performed using a selected set of experiments that proves the viability
of this approach. The numerical examples of the proposed formulation illustrated two
relevant aspects, namely: 1) the role of the bonding mechanism in the strain hardening behavior
after cracking in the HPFRCC and 2) the role that plays the finite element formulation in
capturing the displacement localization in the localization stage.