Dissertation was finished

bibliography.bib

@@ -1,6 +1,7 @@
 @ARTICLE{bib:surovikin,
   Author   = {Суровикин~В.~Ф. and Суровикин~Ю.~В. and Цеханович~М.~С.},
-  Title    = {Новые направления в технологии получения углерод-углеродных материалов. Применение углерод-углеродных материалов.},
+  Title    = {Новые направления в технологии получения углерод-углеродных
+материалов. Применение углерод-углеродных материалов.},
   Journal  = {Рос. хим. ж-л. (Ж-л Рос. хим. об-ва им. Д.~И.~Менделеева},
   Volume   = {4},
   Pages    = {111--118},
@@ -64,7 +65,8 @@
 
 @ARTICLE{bib:dedkov1,
   Author   = {Дедков~Д.~В. and Зайцев~А.~В. and Ташкинов~А.~А. },
-  Title    = {Концентрация напряжений в слое тканого композита с закрытыми внутренними технологическими порами},
+  Title    = {Концентрация напряжений в слое тканого композита с закрытыми
+внутренними технологическими порами},
   Journal  = {Вестник ПНИПУ. Механика},
   Volume   = {4},
   Pages    = {29--36},

c1.tex

@@ -1,15 +1,7 @@
 \chapter{Зависимость деформационных и прочностных свойств тканых композитов с
 поликристаллической матрицей от наличия локальных концентраторов напряжений}
 
-В главе рассматриваются технологические операции изготовления конструкций из
-тканых композиционных материалов с поликристаллической матрицей. Описывается
-процесс изготовления волокон, рассматриваются типы тканей и способы их
-производства, а так же совмещение тканого каркаса с поликристаллической
-матрицей.
-
-Также описаны методы контроля качества конструкций их тканых материалов с
-поликристаллической матрицей и типы дефектов, возникающие во время
-технологических процессов, выявляемых с их помощью.
+В главе\infirsttext
 
 \section{Технологические операции изготовления конструкций из тканых
 композиционных материалов, приводящие к появлению локальных концентраторов
@@ -363,7 +355,7 @@ $6\dots100$~МПа при температуре $550\dots 650^\circ\mathrm{C}$.
 матрицей}
 
 Особенностью тканых композитов с поликристаллической матрицей является то, что
-наряду сдефектами, присущими традиционным материалам, такими как трещины, поры,
+наряду с дефектами, присущими традиционным материалам, такими как трещины, поры,
 посторонние включения, могут образовываться дефекты, характерные только для
 данного вида материала, связанные с особенностями структуры ткани и методом
 формирования матрицы. Такие дефекты могут быть различными для каждого этапа
@@ -371,7 +363,7 @@ $6\dots100$~МПа при температуре $550\dots 650^\circ\mathrm{C}$.
 
 Дефекты связанные с отклонениями от расчетных параметров структуры возникают на
 этапе изготовления ткани. К числу таких дефектов можно отнести отклонения в
-напралении армирующих нитей, пропуски нитей в направлении армирования (рис.
+направлении армирующих нитей, пропуски нитей в направлении армирования (рис.
 \ref{fig:c1:no_fiber}).
 
 На этапе формирования матрицы могут возникнуть дефекты связанные с отклонением
@@ -381,7 +373,7 @@ $6\dots100$~МПа при температуре $550\dots 650^\circ\mathrm{C}$.
 трещины и внутренние поры (рис. \ref{fig:c1:pore}).
 
 Разрывы волокон утка или основы (рис. \ref{fig:c1:break}) могут возникать на
-каждом из этапов: на этапе формирования ткани --- вследствии очень тесного
+каждом из этапов: на этапе формирования ткани --- вследствие очень тесного
 размещения нитей, в процессе сшивки слоев ткани при формировании конструкции, на
 этапе формирования матрицы --- из-за внутренний напряжений, возникающих в
 материале во время его изготовления.

c2.tex

@@ -1,10 +1,13 @@
 \chapter{Локальные поля напряжений и деформаций в представительных объемах
 тканого композита с поликристаллической матрицей}
 
+В главе\insecondtext
+
 \section{Математическая модель упруго-хрупкого поведения тканого композита с
 поликристаллической матрицей}
 
 \subsection{Геометрическая модель слоя тканого композита}
+\label{c1:geometry}
 
 Будем моделировать слой тканого композита с армирующим каркасом полотняного
 переплетения образованного волокнами круглого поперечного сечения
@@ -36,7 +39,7 @@ NUclear REactor SIMulations), предназначенного для полно
 рис.~\ref{fig:c2:geometry}, формируется сегмент волокна, из которого, в свою
 очередь, с помощью операций трансляции и зеркалирования формируется фрагмент
 ткани (рис.~\ref{fig:c2:regular}~а). Матрица моделируется с помощью операции
-вычитания из твердотельного прямоугольного параллилепипеда фрагмента ткани,
+вычитания из твердотельного прямоугольного параллелепипеда фрагмента ткани,
 после чего матрица и фрагмент ткани совмещаются для получения твердотельной
 модели тканого композита с поликристаллической матрицей
 (рис.~\ref{fig:c2:regular}~б) \cite{bib:salome:geom,
@@ -174,7 +177,7 @@ C_{ijkl}^{m} \left[ 1-\lambda({\bf r}) \right ] \right\}
  \label{fig:c2:b_cond}
 \end{figure}
 
-Полости, вызванные наличием локальных дефектов и незаполенные матрицей имеют
+Полости, вызванные наличием локальных дефектов и незаполненные матрицей имеют
 внутреннюю поверхность $\Gamma_8$, на которой отсутствуют ограничения на
 перемещения, а сама поверхность свободна от напряжений:
 
@@ -217,17 +220,7 @@ C_{ijkl}^{m} \left[ 1-\lambda({\bf r}) \right ] \right\}
 матрицы слоя модельного тканого композита полотняного переплетения.
 Конечно-элементная сетка волокон представлена на рис.~\ref{fig:mesh:fibers}.
 
-Степень дискретизации выбиралась таким образом, чтобы чтобы полученные значения
-структурных перемещений, деформаций и напряжений в слое тканого композита без
-локальных дефектов и с несовершенствами ни качественно, ни количественно не
-изменялись при уменьшении характерных размеров конечных элементов.
-
-Из таблицы~{\ref{tab:convergence}}, в которой показана зависимость максимальных
-интенсивностей напяжений от количества конечных элементов, видно, что
-расхождение между двумя последними строками не превышает $1\%$. Это говорит о
-достаточной степени дискретизации модели.
-
-\begin{figure}[ht!]
+\begin{figure}[!ht]
  \centering
  \includegraphics[width=17cm]{mesh/v1/matrix}
  \caption{Пример дискретизации матрицы}
@@ -241,6 +234,16 @@ C_{ijkl}^{m} \left[ 1-\lambda({\bf r}) \right ] \right\}
  \label{fig:mesh:fibers}
 \end{figure}
 
+Степень дискретизации выбиралась таким образом, чтобы чтобы полученные значения
+структурных перемещений, деформаций и напряжений в слое тканого композита без
+локальных дефектов и с несовершенствами ни качественно, ни количественно не
+изменялись при уменьшении характерных размеров конечных элементов.
+
+Из таблицы~{\ref{tab:convergence}}, в которой показана зависимость максимальных
+интенсивностей напряжений от количества конечных элементов, видно, что
+расхождение между двумя последними строками не превышает $1\%$. Это говорит о
+достаточной степени дискретизации модели.
+
 \begin{table}[ht!]
  \caption{Зависимость максимальных интенсивностей напряжений от количества
 	  \newline конечных элементов}
@@ -278,21 +281,21 @@ C_{ijkl}^{m} \left[ 1-\lambda({\bf r}) \right ] \right\}
       & Тетраэдральные элементы & Гексаэдральные элементы \\
     \hline
     \hline
-     Идеальная периодическая структура & 298 255 & 77 760 \\
+     Идеальная периодическая структура & 298~255 & 77~760 \\
     \hline
-     Тунельная пора & 285 664 & 69 984 \\
+     Тунельная пора & 285~664 & 69~984 \\
     \hline
-     Туннельная пора с доуплотнением & 266 314 & 69 984 \\
+     Туннельная пора с доуплотнением & 266~314 & 69~984 \\
     \hline
-     Разрыв волокна основы & 285 466 & 75 168 \\
+     Разрыв волокна основы & 285~466 & 75~168 \\
     \hline
-     Разрыв волокна основы с доуплотнением & 296 499 & 75 168 \\
+     Разрыв волокна основы с доуплотнением & 296~499 & 75~168 \\
     \hline
-     Разрыв волокон основы и утка & 279 276 & 72 576 \\
+     Разрыв волокон основы и утка & 279~276 & 72~576 \\
     \hline
-     Разрыв волокон основы и утка с доуплотнением & 276 175 & 72 576 \\
+     Разрыв волокон основы и утка с доуплотнением & 276~175 & 72~576 \\
     \hline
-     Внутренняя технологическая пора & 287 934 & 77 760 \\
+     Внутренняя технологическая пора & 287~934 & 77~760 \\
     \hline
   \end{tabular}
  \label{tab:discr}
@@ -303,7 +306,7 @@ C_{ijkl}^{m} \left[ 1-\lambda({\bf r}) \right ] \right\}
 Упругие модули поликристаллической матрицы были выбраны следующими: $E_m
 = 0{,}28$~ГПа и коэффициент Пуассона $\nu_m = 0,40$. 
 
-Распределения интесивностей напряжений в слое тканого композита с идеальной
+Распределения интенсивностей напряжений в слое тканого композита с идеальной
 периодической структурой, полученные в ходе решения задачи показаны на
 рис.~\ref{fig:vmis_v1_s1}. 
 
@@ -317,7 +320,7 @@ C_{ijkl}^{m} \left[ 1-\lambda({\bf r}) \right ] \right\}
 Из рисунка видно, что распределение искомых полей в рассматриваемом случае
 удовлетворяют условиям симметрии и периодичности геометрической модели и
 приложенной внешней нагрузке, что говорит о корректно построенной
-геометрической модели и корректности полученного численного решенеия.
+геометрической модели и корректности полученного численного решения.
 Максимальных значений интенсивность напряжений достигает в местах наибольшей
 кривизны волокон.
 
@@ -333,7 +336,7 @@ C_{ijkl}^{m} \left[ 1-\lambda({\bf r}) \right ] \right\}
 простым и, в то же время, мощным интерпретируемым объектно-ориентированным
 языком программирования. Он предоставляет структуры данных высокого уровня,
 имеет изящный синтаксис и использует динамический контроль типов, что делает
-его деальным языком для быстрого написания различных приложений, работающих
+его идеальным языком для быстрого написания различных приложений, работающих
 на большинстве распространенных платформ \cite{bib:rossum}.
 
 Максимальные значения коэффициентов концентрации напряжений представлены в
@@ -391,7 +394,7 @@ C_{ijkl}^{m} \left[ 1-\lambda({\bf r}) \right ] \right\}
 
 На рис.~\ref{fig:k_d1d2_s1}~--~\ref{fig:k_d5_s1} показаны распределения
 коэффициентов концентрации интенсивностей напряжений в слое тканого композита с
-искривленными волокнами и поликристалической матрицей при наличии различных
+искривленными волокнами и поликристаллической матрицей при наличии различных
 типов технологических дефектов и с учётом дополнительной пропитки композита
 материалом матрицы. Расположение областей, в которых интенсивность напряжений
 достигает максимальных значений в местах, где искривленные волокна основы или
@@ -528,19 +531,9 @@ $\sigma_{12}$ и $\sigma_{23}$ и нормальная составляющая
 
 На рис.~\ref{fig:k_d1d2_s2}~--~\ref{fig:k_d5_s2} показаны распределения
 коэффициентов концентрации интенсивностей напряжений в слое тканого композита с
-искривленными волокнами и поликристалической матрицей при наличии различных
+искривленными волокнами и поликристаллической матрицей при наличии различных
 типов технологических дефектов и с учётом дополнительной пропитки композита
-материалом матрицы под воздействием сдвиговых нагрузок. Вблизи локальных
-дефектов интенсивности напряжений превышают соответствующие интенсивности
-напряжений определенное  для композита идеальной периодической структуры в
-$1{,}2$ раза при наличии внутренней технологической поры, в $1{,}3$  раза для
-слчая пропуска или разрыва волокна основы и в $1{,}6$ раз для одновременного
-разрыва волокон основы и утка. При этом, в случае разрыва волокна основы
-или волокон основы и утка, значение коэффициентов концентрации интенсивностей
-напряжений ожет быть снижено до $1{,}2$ и $1{,}5$ соответственно, с помощью
-дополнительных операций доуплотнения поликристаллической матрицы.
-
-\pagebreak
+материалом матрицы под воздействием сдвиговых нагрузок.
 
 \begin{figure}[ht!]
  \includegraphics[width=17cm]{concentrators/v1/scheme2/d1d2}
@@ -576,6 +569,16 @@ $1{,}2$ раза при наличии внутренней технологич
  \label{fig:k_d5_s2}
 \end{figure}
 
+Вблизи локальных дефектов интенсивности напряжений превышают соответствующие
+интенсивности напряжений определенное  для композита идеальной периодической
+структуры в $1{,}2$ раза при наличии внутренней технологической поры, в $1{,}3$ 
+раза для случая пропуска или разрыва волокна основы и в $1{,}6$ раз для
+одновременного разрыва волокон основы и утка. При этом, в случае разрыва волокна
+основы или волокон основы и утка, значение коэффициентов концентрации
+интенсивностей напряжений может быть снижено до $1{,}2$ и $1{,}5$
+соответственно, с помощью дополнительных операций доуплотнения
+поликристаллической матрицы.
+
 \subsection{Коэффициенты концентрации напряжений при одноосном растяжении}
 
 В случае, если граничные условия \ref{eq:b_cond} в краевой задаче
@@ -657,16 +660,14 @@ $1{,}2$ раза при наличии внутренней технологич
 $\sigma_{13}$ и $\sigma_{23}$ и нормальная составляющая $\sigma_{33}$.
 Исключение составляет случай, когда в слое тканого композита присутствует
 внутренняя технологическая пора. В этом случае значение касательной
-компоненты тензора напряжений превышает соответсвующее значение в и деальной
+компоненты тензора напряжений превышает соответствующее значение в и идеальной
 периодической структуре в $4{,}59$ раз.
 
 Распределение коэффициентов концентрации интенсивностей напряжений в слое
-тканого композита с искривленными волокнами и поликристалической матрицей при
+тканого композита с искривленными волокнами и поликристаллической матрицей при
 наличии различных типов технологических дефектов и с учётом дополнительной
 пропитки композита материалом матрицы под воздействием сдвиговых нагрузок
-представлены на рис.~\ref{fig:k_d1d2_s3}~--~\ref{fig:k_d5_s3}. 
-
-\pagebreak
+представлены на рис.~\ref{fig:k_d1d2_s3}~--~\ref{fig:k_d5_s3}.
 
 \begin{figure}[ht!]
  \includegraphics[width=17cm]{concentrators/v1/scheme3/d1d2}
@@ -706,7 +707,7 @@ $\sigma_{13}$ и $\sigma_{23}$ и нормальная составляющая
 Из рисунков видно что вблизи локальных дефектов интенсивности напряжений
 превышают соответствующие интенсивности напряжений определенное  для композита
 идеальной периодической структуры в $1{,}2$ раза при наличии внутренней
-технологической поры или разрыва волокна основы, в $1{,}3$  раза для слчая
+технологической поры или разрыва волокна основы, в $1{,}3$  раза для случая
 пропуска или разрыва волокна основы и в $1{,}4$ раз для одновременного
 разрыва волокон основы и утка. При этом, в случае пропуска или разрыва волокна
 основы, значение коэффициентов концентрации интенсивностей напряжений может быть
@@ -718,15 +719,16 @@ $\sigma_{13}$ и $\sigma_{23}$ и нормальная составляющая
 
 \begin{enumerate}
  \item Построена твердотельная модель фрагмента слоя тканого композита с
-искривленными волокнами и поликристалической матрицей с идеальной
+искривленными волокнами и поликристаллической матрицей с идеальной
 периодической структурой и локальными технологическими дефектами, такими как
 пропуск волокна основы, разрыв волокна основы, разрыв волокон основы и утка и
 внутренняя технологическая пора.
  \item Получены численные решения краевых задач на двухосное растяжение в
 плоскости слоя, чистый сдвиг и одноосное растяжение в направлении утка.
  \item Вычислены безразмерные коэффициенты концентрации напряжений, вызванные
-наличием локальных технологическх дефектов в виде пропуска волокна основы,
+наличием локальных технологических дефектов в виде пропуска волокна основы,
 разрыва волокна основы, разрыва волокон основы и утка, а также внутренней
 технологической поры.
- \item Определены механизмы инициирующие разрушение матрицы.
+ \item Определены механизмы инициирующие разрушение матрицы в слое тканого
+композита с искривленными волокнами.
 \end{enumerate}

c3.tex

@@ -1,189 +1,469 @@
 \chapter{Влияние локальных полей напряжений на прочностные свойства тканых
 композитов с поикристаллической матрицей с учётом трения между волокнами}
 
+В главе\inthirdtext
+
 \section{Математическая модель упруго-хрупкого поведения слоят тканого
 композита с поликристаллической матрицей при наличии контакта с трением между
 волокнами}
 
-В случае, если в модельном материале не исключается возможность контакта
-нитей основы и утка, на соответствующих контактных поверхностях
-$\Gamma_9$ (положение и геометрия которых считается заданными и неизменными
-в процессе нагружения слоя) будем считать справедливыми условия контакта
-с кулоновским трением. На $\Gamma_9$ следует задать 2 условия: 
+\subsection{Геометрическая модель слоя тканого композита с контактом между
+волокнами}
+
+В процессе изготовления тканого композиционного материала с поликристаллической
+матрицей не всегда удается исключить соприкосновение нитей основы и утка,
+вследствие чего в конструкции могут возникать такие локальные дефекты как
+разрывы нитей основы, разрывы нитей основы и утка, а также внутренние
+технологические поры. Поэтому необходимо построение моделей, где волокна основы
+и утка не всегда окружены гарантированной прослойкой поликристаллической
+матрицы. 
+
+Геометрические параметры модели аналогичны указанным в
+разделе~\ref{c1:geometry}, за исключением того что расстояние между волокнами в
+точках максимальных кривизн равно нулю (рис.~\ref{fig:c3:fibers}), а в матрице,
+вблизи максимальных кривизн волокон всегда присутствуют внутренние
+технологические поры из-за невозможности заполнить это простаранство материалом
+матрицы (рис.~\ref{fig:c3:matrix}).
+
+\begin{figure}[ht]
+ \includegraphics[width=17cm]{geometry/v2/regular_slice}
+ \caption{Фрагмент слоя ткани с контактом между волокнами}
+ \label{fig:c3:fibers}
+\end{figure}
+
+\begin{figure}[ht!]
+ \centering
+ \includegraphics[width=10cm]{geometry/v2/matrix}
+ \caption{Фрагмент поликристаллической матрицы слоя тканого композита с
+внутренними технологическими порами}
+ \label{fig:c3:matrix}
+\end{figure}
+
+В качестве дефектов, вызывающих концентрации напряжений будем рассматривать
+типичные дефекты, возникающие вследствии очень плотного расположения волокон
+--- разрыв волокна основы (рис.~\ref{fig:c3:d1d3}~а) и разрывы волокон основы и
+утка (рис.~\ref{fig:c3:d2d4}~а). Кроме того рассмотрим случаи когда пора в
+матрице, образованная дефектом заполняется материалом матрицы в ходе
+дополнительных технологических операций (рис.~\ref{fig:c3:d1d3}~б и
+\ref{fig:c3:d2d4}~б).
+
+\begin{figure}
+ \includegraphics[width=17cm]{geometry/v2/d1d3}
+ \caption{Разрыв волокна основы в тканом композите с поликристаллической
+матрицей при наличии контакта между волокнами~(а) с дополнительной
+пропиткой~(б)}
+ \label{fig:c3:d1d3}
+\end{figure}
+
+\begin{figure}
+ \includegraphics[width=17cm]{geometry/v2/d2d4}
+ \caption{Разрыв волокон основы и утка в тканом композите с поликристаллической
+матрицей при наличии контакта между волокнами~(а) с дополнительной
+пропиткой~(б)}
+ \label{fig:c3:d2d4}
+\end{figure}
+
+
+\subsection{Постановка краевой задачи теории упругости при наличии контакта с
+трением}
+
+Краевая задача теории упругости для случая когда в материале возникает контакт
+с трением между волокнами основы и утка в местах наибольших кривизн
+волокон аналогична краевой задаче \ref{eq:Eqvilibrium}~--~\ref{eq:Guck} с
+граничными условиями \ref{eq:b_cond}~--~\ref{eq:b_cond_free}, за исключением
+того, что соответствующих контактных поверхностях $\Gamma_9$
+(рис.~\ref{fig:c3:bc}) необходимо задать дополнительные граничные условия.
+
+\begin{figure}[!ht]
+ \centering
+ \includegraphics[width=10cm]{geometry/v2/bc}
+ \caption{Граничные условия краевой задачи теории упругости при наличии контакта
+с трением между волокнами}
+ \label{fig:c3:bc}
+\end{figure}
 
-\noindent если $\left[\sigma_{n\tau} {\bf (r)}
-\right] |_{\Gamma_9^{+}} < \left[ {f | \sigma_{nn} {\bf (r)} |}
-\right] |_{\Gamma_9^{-}}$, то
+Положение и геометрия контактных поверхностей считается заданными и неизменными
+в процессе нагружения слоя, кроме того будем считать справедливыми условия
+контакта с кулоновским трением, тогда на $\Gamma_9$ следует задать 2 условия: 
+
+\noindent если $\left[\sigma_{n\tau} {\bf (r)} \right] |_{\Gamma_9^{+}} < \left[
+{f | \sigma_{nn} {\bf (r)} |} \right] |_{\Gamma_9^{-}}$, то
 
 \begin{equation}
 \left[\sigma_{n\tau} {\bf (r)} n_{n} \right] |_{\Gamma_9^{+}} =
 \left[\sigma_{n\tau} {\bf (r)} n_{n} \right] |_{\Gamma_9^{-}}, \quad
-\left[u_n {\bf (r)}\right]|_{\Gamma_9^{+}} = \left[u_n {\bf
-(r)}\right]|_{\Gamma_9^{-}} ,
+\left[u_n {\bf (r)}\right]|_{\Gamma_9^{+}} = 
+\left[u_n {\bf (r)}\right]|_{\Gamma_9^{-}} ,
 \label{eq:b_cond_Colomb_1}
 \end{equation}
 
-\noindent а, если $\left[\sigma_{n\tau} {\bf (r)} \right]
-|_{\Gamma_9^{+}} \geq \left[ {f | \sigma_{nn} {\bf (r)} |} \right ]
-|_{\Gamma_9^{-}}$, то
+\noindent а, если $\left[\sigma_{n\tau} {\bf (r)} \right]|_{\Gamma_9^{+}} \geq
+\left[ {f | \sigma_{nn} {\bf (r)} |} \right]|_{\Gamma_9^{-}}$, то
 
 \begin{equation}
-\left[\sigma_{n\tau} {\bf (r)} \right] |_{\Gamma_9^{+}} \geq \left[
-f | \sigma_{nn} {\bf (r)} | \right ] |_{\Gamma_9^{-}}, \quad
-\left[u_n {\bf (r)}\right]|_{\Gamma_9^{+}} = \left[u_n {\bf
-(r)}\right]|_{\Gamma_9^{-}} , \label{eq:b_cond_Colomb_2}
+\left[\sigma_{n\tau} {\bf (r)} \right] |_{\Gamma_9^{+}} \geq 
+\left[f|\sigma_{nn} {\bf (r)}| \right] |_{\Gamma_9^{-}},\quad
+\left[u_n {\bf (r)}\right]|_{\Gamma_9^{+}} = 
+\left[u_n {\bf (r)}\right]|_{\Gamma_9^{-}}, 
+\label{eq:b_cond_Colomb_2}
 \end{equation}
 
 \noindent где $f$ --- статический коэффициент трения, а индексы $n$ и $\tau$
 --- определяют направление внешней нормали и касательной к
 поверхности $\Gamma_9$.
 
-Внутренние поры имеют место в слое композита в случае, если не
-исключается соприкосновение волокон. Это герметичные полости, недоступные
-для материала матрицы, 
+В случае если в слое тканого композита с поликристаллической матрицей не
+исключено соприкосновение волокон, вблизи мест с максимальной
+кривизной волокон остаются герметичные полости, незаполненные материалом
+матрицы. На поверхностях этих пор отсутствуют ограничения на перемещения, а
+сама поверхность свободна от напряжений. Граничные условия на этих поверхностях
+аналогичны граничным условиям \ref{eq:b_cond_free}.
 
-\begin{figure}[!ht]
+\subsection{Численное решение краевой задачи упругости}
+
+Для численного решения задачи равнокомпонетного растяжения тканого композита с
+искривленными волокнами и поликристаллическкой матрицей в плоскости слоя
+необходимо задать свойства материала. Модуль Юнга $E_f
+= 280$~ГПа и коэффициент Пуассона $\nu_f = 0,20$ волокон зададим
+в соответствии с данными работы \cite{bib:tarnapolsky}, а упругие модули
+поликристаллической матрицы выберем следующими: $E_m = 0,28$~ГПа и
+коэффициент Пуассона $\nu_m = 0,40$. Так как между волокнами присутствует
+контакт с трением, необходимо задать статический коэффициент трения
+\cite{bib:code-aster:contact}: $f = 0,12$, который соответствует случаю
+скольжения волокна по поверхности поликристаллической матрицы. 
+
+Матрицу будем разбивать 14-узловыми тетраэдральными элементами
+(рис.~\ref{fig:c3:mesh:matrix}), а волокно --- 20-узловыми гексаэдральными
+элементами (рис.~\ref{fig:c3:mesh:fibers}). Степень дискретизации
+конечно-элементной сетки будем выбирать таким образом, чтобы дальнейшее
+ументшение характерных размеров элементов ни качественно ни количественно не
+влияло на значения структурных перемещений, деформаций и напряжений в слое
+тканого композита. Параметры сеток, удовлетворяющих этим условиям показаны в
+таблице~\ref{tab:c3:discr}.
+
+\begin{figure}[ht]
+ \includegraphics[width=17cm]{mesh/v2/matrix}
+ \caption{Пример дискретизации матрицы}
+ \label{fig:c3:mesh:matrix}
+\end{figure}
+
+\begin{figure}[ht!]
+ \includegraphics[width=15cm]{mesh/v2/fibers}
+ \caption{Пример дискретизации волокон}
+ \label{fig:c3:mesh:fibers}
+\end{figure}
+
+\begin{table}[ht]
+ \caption{Параметры конечно-элементной сетки}
+ \begin{tabular}{|p{8.25cm}||>{\centering}p{3.45cm}|p{3.45cm}<{\centering}|}
+    \hline
+      & Тетраэдральные элементы & Гексаэдральные элементы \\
+    \hline
+    \hline
+     Идеальная периодическая структура & 405~480 & 77~760 \\
+    \hline
+     Разрыв волокна основы & 405~480 & 75~168 \\
+    \hline
+     Разрыв волокна основы с доуплотнением & 355~341 & 75~168 \\
+    \hline
+     Разрыв волокон основы и утка & 405~480 & 72~576 \\
+    \hline
+     Разрыв волокон основы и утка с доуплотнением & 390~862 & 72~576 \\
+    \hline
+ \end{tabular}
+ \label{tab:c3:discr}
+\end{table}
+
+Решив задачу \ref{eq:Eqvilibrium}~--~\ref{eq:Koshi} с граничными условиями
+\ref{eq:b_cond}~--~\ref{eq:b_cond_Colomb_2} методом конечных элементов получим
+поля интенсивностей напряжений в искривленных нитях основы и утка слоя
+модельного тканого композита идеальной периодической структуры, показанных
+на рис.~\ref{fig:c3:vmis_v2_s1}. Как видим, распределение искомых полей в
+рассматриваемом случае удовлетворяет условиям симметрии и периодичности
+геометрической модели и приложенной внешней нагрузке. Это свидетельствует о
+корректно построенной модели и корректности полученного численного решения.
+Кроме того, обращает на себя внимание концентрация напряжений в местах, где
+искривленные нити основы и утка имеют наибольшую кривизну.
+
+В табл. \ref{tab:c3:max_k_s1} представлены максимальные безразмерные
+коэффициенты $K_{\sigma_{ij}} = \sigma_{ij}({\bf r}) /
+\sigma_{ij}^{per}({\bf r})$, определяемые отношением компонент тензора
+напряжений в слое модельного тканого композита с локальным дефектом к
+соответствующим компонентам в слое материала идеальной периодической
+структуры. Обратим внимание на то, что наибольший вклад в коэффициенты
+концентрации вносят касательные составляющие тензора напряжений $\sigma_{13}$.
+Напряжения для этих компонент, в 10--48 раз превышают соответствующие значения
+для модельного материала с идеальной периодической структурой.
+
+\begin{figure}[t!]
  \centering
-%  \includegraphics[width=0.83\linewidth]{img/matrix}
- \caption{Фрагмент тканого композита с искривленными волокнами}
- \label{fig:matrix}
-\end{figure}
-
-На рис.~\ref{fig:sigma} показаны распределения интенсивностей напряжений
-в искривленных нитях основы и утка при равнокомпонентном двухосном
-однородном деформировании слоя модельного тканого композита
-идеальной периодической структуры в собственной плоскости. Модуль Юнга $E_f
-= 280$~ГПа и коэффициент Пуассона $\nu_f = 0,20$ волокон соответствовали
-данным работы \cite{bib:tarnapolsky}. Упругие модули поликристаллической
-матрицы ыли выбраны следующими: $E_m = 0,28$~ГПа и коэффициент Пуассона $\nu_m
- = 0,40$. Статический коэффициент трения $f = 0,12$ соответствовал
-случаю скольжения волокна по поверхности поликристаллической матрицы. Как
-видим, распределение искомых полей в рассматриваемом случае
-удовлетворяет условиям симметрии и периодичности геометрической модели
-и приложенной внешней нагрузке. Это свидетельствует о корректно
-построенной модели и корректности полученного численного решения. Кроме
-того, обращает на себя внимание концентрация напряжений в местах,
-где искривленные нити основы и утка имеют наибольшую кривизну.
+ \includegraphics[width=17cm]{vmis_v2_s1}
+ \caption{Поля интенсивности напряжений в нитях основы и утка при
+равнокомпонентном двухосном растяжении}
+ \label{fig:c3:vmis_v2_s1}
+\end{figure}
 
-\begin{figure}
+\begin{table}[t!]
  \centering
-%   \includegraphics[width=0.75\linewidth]{img/vmis}
- \caption{Поля интенсивности напряжений в нитях основы и утка}
- \label{fig:sigma}
+ \caption{Максимальные коэффициенты концентрации напряжений в матрице слоя
+тканого композита}
+  \begin{tabular}{|p{8cm}||c|c|c|c|c|c|}
+   \hline
+     & $K_{\sigma_{11}}$ 
+     & $K_{\sigma_{22}}$ 
+     & $K_{\sigma_{33}}$ 
+     & $K_{\sigma_{12}}$ 
+     & $K_{\sigma_{13}}$ 
+     & $K_{\sigma_{23}}$ \\
+    \hline 
+    \hline
+     Разрыв нити основы 
+     & $4{,}57$ & $3{,}61$ & $4{,}37$ & $6{,}87$ & $\bf 10{,}87$ & $3{,}69$ \\
+    \hline
+     Разрыв нити основы (доуплотнение) 
+     & $4{,}07$ & $4{,}69$ & $3{,}75$ & $8{,}72$ & $\bf 16{,}46$ & $7{,}27$ \\
+    \hline
+    \hline
+     Разрыв нитей основы и утка 
+     & $4{,}01$ & $3{,}73$ & $5{,}92$ & $6{,}59$ & $\bf 48{,}08$ & $3{,}70$ \\
+    \hline
+     Разрыв нитей основы и утка (доуплотнение) 
+     & $3{,}93$ & $4{,}38$ & $3{,}57$ & $8{,}42$ & $\bf 16{,}06$ & $3{,}85$ \\
+    \hline
+  \end{tabular}
+\label{tab:c3:max_k_s1}
+\end{table}
+
+На рис.~\ref{fig:c3:k_d1d3_s1} и \ref{fig:c3:k_d2d4_s1} представлены
+распределения коэффициентов концентрации интенсивностей напряжений для
+слоя модельного тканого композита с разрывом волокна основы и разрывом волокон
+основы и утка. Расположение областей, в которых интенсивность напряжений
+достигает максимальных значений в местах, где искривленные волокна основы или
+утка имеют наибольшую кривизну, строго периодично. Исключение составляют
+области, расположенные вблизи локального разрыва утка или одновременного
+разрыва основы и утка, где интенсивность напряжений превышает соответствующее
+значение, определенное для композита идеальной периодической структуры в $2{,}1$
+раза. Стоит заметить, что заполнение поры, образовавшейся вследствие дефекта,
+материалом поликристаллической матрицы путем дополнительной пропитки или
+осаждения матрицы из газовой фазы приводит к увеличению коэффициентов
+концентрации интенсивностей напряжений до $2{,}8$, при разрыве волокна основы
+(рис.~\ref{fig:c3:k_d1d3_s1}~б) и $3{,}1$ при разрыве волокон основы и утка
+одновременно (рис.~\ref{fig:c3:k_d2d4_s1}~б).
+
+\begin{figure}[ht!]
+ \includegraphics[width=17cm]{concentrators/v2/scheme1/d1d3}
+ \caption{Распределение коэффициентов концентрации интенсивностей напряжений в
+слое тканого композита с разрывом волокна основы~(а) и с учётом
+доуплотнения~(б)}
+ \label{fig:c3:k_d1d3_s1}
+\end{figure}
+
+\begin{figure}[ht!]
+ \includegraphics[width=17cm]{concentrators/v2/scheme1/d2d4}
+ \caption{Распределение коэффициентов концентрации интенсивностей напряжений в
+слое тканого композита с разрывом волокон основы и утка~(а) и с учётом
+доуплотнения~(б)}
+ \label{fig:c3:k_d2d4_s1}
+\end{figure}
+
+\subsection{Коэффициенты концентрации напряжений в слое тканого композита с
+соприкасащимися волокнами при чистом сдвиге}
+
+Решим задачу \ref{eq:Eqvilibrium}~--~\ref{eq:Guck} с граничными условиями
+\ref{eq:b_cond_ideal}~--~\ref{eq:b_cond:s2},
+соответствующими чистому сдвигу, дополненными граничными условиями
+\ref{eq:b_cond_Colomb_1} и \ref{eq:b_cond_Colomb_2}, задающими трения между
+волокнами основы и утка тканого композита с поликристаллической матрицей.
+
+Поля интенсивностей напряжений, полученные в результате решения такой задачи,
+показанные на рис.~\ref{fig:c3:vmis_v2_s2}, строго периодичны, что говорит о
+корректности полученного решения.
+
+\begin{figure}[ht]
+ \includegraphics[width=15cm]{vmis_v2_s2}
+ \caption{Поля интенсивности напряжений в слое тканого композита с идеальной
+периодической структурой при чистом сдвиге и наличии контакта между волокнами
+основы и утка}
+ \label{fig:c3:vmis_v2_s2}
 \end{figure}
 
+Максимальные значения коэффициентов концентрации напряжений представлены в
+таблице~\ref{tab:c3:max_k_s2}. Как видно из таблицы, наибольший вклад в
+коэффициенты концентрации напряжений вносят касательная составляющая
+$\sigma_{13}$ и нормальная составляющая $\sigma_{33}$ тензора напряжений.
+Значения этих составляющих в материале с дефектом в $10$~--~$29$ раз превышают
+соответствующие значения в материале с идеальной периодической структуре.
 
-\begin{table}
+\begin{table}[t!]
  \centering
  \caption{Максимальные коэффициенты концентрации напряжений в матрице слоя
-тканого композита}
-\begin{tabular}{p{6cm}||c|c|c|c|c|c}
-\hline
-     & $K_{\sigma_{11}}$ & $K_{\sigma_{22}}$ & $K_{\sigma_{33}}$ &
-$K_{\sigma_{12}}$ & $K_{\sigma_{13}}$ & $K_{\sigma_{23}}$ \\
-\hline \hline
-  Разрыв нити основы & $\frac{1{,}29} {4{,}57}$ & $\frac {1{,}63} {3{,}61}$ &
-$\frac {1{,}30} {4{,}37}$ & $\frac {1{,}25}
-  {6{,}87}$ & $\frac {2{,}31} {10{,}87}$ & $\frac {1{,}44} {3{,}69}$ \\
-\hline
-  Разрыв нити основы (доуплотнение) & $\frac{1{,}26}{4{,}07}$ &
-$\frac{1{,}49}{4{,}69}$ & $\frac{1{,}27}{3{,}75}$ & $\frac{1{,}25}{8{,}72}$ 
-  & $\frac{2{,}20}{16{,}46}$ & $\frac{1{,}32}{7{,}27}$ \\
-\hline\hline
-  Разрыв нитей основы и утка & $\frac{1{,}50} {4{,}01}$ & $\frac{1{,}92}
-{3{,}73}$ & $\frac{1{,}56} {5{,}92}$ & $\frac{1{,}58} {6{,}59}$
-   & $\frac{2{,}53} {48{,}08}$ & $\frac{1{,}70} {3{,}70}$ \\
-\hline
-  Разрыв нитей основы и утка (доуплотнение) & $\frac{1{,}35}{3{,}93}$ &
-$\frac{1{,}68}{4{,}38}$ & $\frac{1{,}41}{3{,}57}$ 
-  & $\frac{1{,}41}{8{,}42}$ & $\frac{2{,}21}{16{,}06}$ & $\frac{1{,}50}{3{,}85}$
-\\
-\hline
-\end{tabular}
-\label{tab:k}
+тканого композита при чистом сдвиге}
+  \begin{tabular}{|p{7cm}||c|c|c|c|c|c|}
+   \hline
+     & $K_{\sigma_{11}}$ 
+     & $K_{\sigma_{22}}$ 
+     & $K_{\sigma_{33}}$ 
+     & $K_{\sigma_{12}}$ 
+     & $K_{\sigma_{13}}$ 
+     & $K_{\sigma_{23}}$ \\
+    \hline 
+    \hline
+     Разрыв нити основы 
+     & $3{,}66$ & $5{,}70$ & $9{,}64$ & $5{,}16$ & $\bf12{,}30$ & $\bf10{,}54$\\
+    \hline
+     Разрыв нити основы (доуплотнение) 
+     & $3{,}36$ & $4{,}87$ & $\bf15{,}83$ & $6{,}53$ &$\bf11{,}59$ & $10{,}97$\\
+    \hline
+    \hline
+     Разрыв нитей основы и утка 
+     & $3{,}76$ & $7{,}53$ & $\bf29{,}34$ & $5{,}82$ & $\bf28{,}39$ & $8{,}02$\\
+    \hline
+     Разрыв нитей основы и утка (доуплотнение) 
+     & $3{,}33$ & $6{,}95$ & $\bf15{,}03$ & $5{,}85$ & $\bf12{,}71$ & $7{,}31$\\
+    \hline
+  \end{tabular}
+\label{tab:c3:max_k_s2}
 \end{table}
 
-В табл. \ref{tab:k} представлены максимальные безразмерные
-коэффициенты $K_{\sigma _{ij} } = {\sigma _{ij} \left( {\rm {\bf r}}
-\right)} \mathord{\left/ {\vphantom {{\sigma _{ij} \left( {\rm {\bf r}}
-\right)} {\sigma _{ij}^{\mbox{per}} \left( {\rm {\bf r}} \right)}}}
-\right. \kern-\nulldelimiterspace} {\sigma_{ij}^{\mbox{per}} \left( {\rm {\bf
-r}} \right)}$, определяемые отношением компонент тензора напряжений в
-слое модельного тканого композита с локальным дефектом к
-соответствующим компонентам в слое материала идеальной периодической
-структуры. Значения в числителе были определены в случае, когда каждая
-нить армирующего каркаса окружена гарантированным слоем матрицы, а в
-знаменателе --- в случае, когда нити основы и утка имеют общую
-поверхность контакта с трением, а между участками с наибольшей
-кривизной располагается внутренняя пора. Обратим внимание на то, что
-наибольший вклад в коэффициенты концентрации вносят касательные
-составляющие тензора напряжений $\sigma_{13}$ и $\sigma_{23}$. Кроме
-того, коэффициенты концентрации для этих компонент, определенные для
-слоя композита, содержащего внутренние поры, в 5--16 раз
-превышают соответствующие значения для материала, в котором каждая нить
-окружена гарантированным слоем поликристаллической матрицы.
+На рис.~\ref{fig:c3:k_d1d3_s2} и \ref{fig:c3:k_d2d4_s2} представлены
+распределения коэффициентов концентрации интенсивностей напряжений, вызванных
+наличием дефекта в виде разрыва волокна основы и разрыва волокон основы и утка в
+слое тканого композита с поликристаллической матрицей при чистом сдвиге. 
 
-\begin{figure}
- \begin{minipage}[h]{0.47\linewidth}
-%   \center{\includegraphics[width=1\linewidth]{img/d3_k}} \\ а)
- \end{minipage}
- \hfill
- \begin{minipage}[h]{0.47\linewidth}
-%   \center{\includegraphics[width=1\linewidth]{img/d3_k_fric}} \\ б)
- \end{minipage}
- \caption{Распределение коэффициентов концентрации интенсивности напряжений
-  в поликристаллической матрице тканого композита с локальным разрывом нити
-утка}
- \label{fig:k_rasp_1}
+\begin{figure}[ht!]
+ \includegraphics[width=17cm]{concentrators/v2/scheme2/d1d3}
+ \caption{Распределение коэффициентов концентрации интенсивностей напряжений в
+слое тканого композита с разрывом волокна основы~(а) и с учётом
+доуплотнения~(б) при чистом сдвиге}
+ \label{fig:c3:k_d1d3_s2}
 \end{figure}
 
-\begin{figure}
- \begin{minipage}[h]{0.47\linewidth}
-%   \center{\includegraphics[width=1\linewidth]{img/d4_k}} \\ а)
- \end{minipage}
- \hfill
- \begin{minipage}[h]{0.47\linewidth}
-%   \center{\includegraphics[width=1\linewidth]{img/d4_k_fric}} \\ б)
- \end{minipage}
- \caption{Распределение коэффициентов концентрации интенсивности напряжений
-  в поликристаллической матрице тканого композита с локальным разрывом нитей
-  основы и утка}
- \label{fig:k_rasp_2}
-\end{figure}
-
-На рис.~\ref{fig:k_rasp_1} и \ref{fig:k_rasp_2} представлены
-распределения коэффициентов концентрации интенсивностей напряжений для
-слоя модельного тканого композита с различными локальными дефектами.
-Расположение областей, в которых интенсивность напряжений достигает
-максимальных значений в местах, где искривленные волокна основы или утка
-имеют наибольшую кривизну, строго периодично. Исключение составляют
-области, расположенные вблизи локального разрыва утка или одновременного
-разрыва основы и утка, где интенсивность напряжений превышает
-соответствующее значение, определенное для композита идеальной
-периодической структуры в $1,4$ и $1,6$ раз в случае, если нить
-армирующего каркаса окружена гарантированным слоем
-матрицы (рис.~\ref{fig:k_rasp_1},~б и \ref{fig:k_rasp_2}~б). Если в слое
-тканого композита не исключена возможность контакта с кулоновским
-трением искривленных нитей, а также присутствуют локальные поры в
-местах наибольших кривизн волокон, то коэффициенты концентрации
-для рассматриваемых случаев увеличиваются до $2,5$.
-
-\section{Выводы к третьей главе}
-
-На основе построенной модели слоя тканого композита с искривленными волокнами
-и поликристаллической матрицей определены коэффициенты концентрации
-напряжений, вызванные наличием локальных технологических дефектов в виде
-разрыва нити утка, одновременного разрыва нитей основы и утка, наличия
-закрытых пор при двухосном равнокомпонентном деформировании,
-определены механизмы, инициирующие разрушение матрицы.
-
-Полученные результаты позволяют сделать вывод о том, что для
-повышения способности тканым композитом сопротивляться внешнему
-силовому воздействию необходимо предусмотреть в технологическом
-процессе операции, обеспечивающие проникновение связующего в
-полости технологических локальных дефектов, а также дополнительную
-пропитку связующим, доуплотнение и карбонизацию, доосаждение
-поликристаллической матрицы из газовой фазы в случае, если в
-результате ультразвукового контроля готового изделия обнаруживаются
-закрытые внутренние поры. В противном случае возможно развитие дефектов
-и последующее разрушение материала матрицы по механизмам сдвигов.
+\begin{figure}[ht!]
+ \includegraphics[width=17cm]{concentrators/v2/scheme2/d2d4}
+ \caption{Распределение коэффициентов концентрации интенсивностей напряжений в
+слое тканого композита с разрывом волокон основы и утка~(а) и с учётом
+доуплотнения~(б) при чистом сдвиге}
+ \label{fig:c3:k_d2d4_s2}
+\end{figure}
+
+Распределение коэффициентов концентрации интенсивностей напряжений строго
+периодично и достигает максимальных значений в местах, расположенных вблизи
+локальных дефектов. При разрыве волокна основы максимальное значение
+коэффициентов концентрации интенсивностей напряжений равно $2{,}3$
+(рис.~\ref{fig:c3:k_d1d3_s2}~а), а при одновременном разрыве волокон основы и
+утка --- $3{,}0$ (рис.~\ref{fig:c3:k_d2d4_s2}~б). При этом, заполнение поры,
+образовавшейся в результате одновременного разрыва волокон основы и утка,
+материалом поликристаллической матрицы путем дополнительной пропитки или
+осаждения матрицы из газовой фазы позволяет снизить коэффициенты концентрации
+интенсивностей напряжений до $2{,}6$ (рис.~\ref{fig:c3:k_d2d4_s2}~б). 
+
+\subsection{Коэффициенты концентрации напряжений в слое тканого композита с
+соприкасащимися волокнами при одноосном растяжении}
+
+Решим задачу \ref{eq:Eqvilibrium}~--~\ref{eq:Guck} с граничными условиями
+\ref{eq:b_cond_ideal}, \ref{eq:b_cond_free} и \ref{eq:b_cond:s3},
+соответствующими одноосному растяжению в направлении утка, дополненными
+граничными условиями \ref{eq:b_cond_Colomb_1} и \ref{eq:b_cond_Colomb_2},
+задающими трения между волокнами основы и утка тканого композита с
+поликристаллической матрицей.
+
+Поля интенсивностей напряжений, полученные в результате решения такой задачи,
+показанные на рис.~\ref{fig:c3:vmis_v2_s3}, строго периодичны, что говорит о
+корректности полученного решения.
+
+В таблице \ref{tab:c3:max_k_s3} показаны макисмальные безразмерные коэффициенты
+концентрации напряжений, вызванные наличием разрыва волокна основы и разрывов
+волокон основы и утка в слое тканого композита с поликристаллической матрицей
+при одноосном растяжении. Максимальный вклад в коэффициенты концентраций вносит
+касательная составляющая тензора напряжений $\sigma_{13}$, значения которой в
+материале с локальным дефектом превышают соответствующие значения в материале с
+идеальной периодической структурой в $11$~--~$16$ раз.
+
+\begin{figure}[ht!]
+ \includegraphics[width=15cm]{vmis_v2_s3}
+ \caption{Поля интенсивности напряжений в слое тканого композита с идеальной
+периодической структурой при чистом сдвиге и наличии контакта между волокнами
+основы и утка}
+ \label{fig:c3:vmis_v2_s3}
+\end{figure}
+
+\begin{table}[t!]
+ \centering
+ \caption{Максимальные коэффициенты концентрации напряжений в матрице слоя
+тканого композита при одноосном растяжении}
+  \begin{tabular}{|p{7cm}||c|c|c|c|c|c|}
+   \hline
+     & $K_{\sigma_{11}}$ 
+     & $K_{\sigma_{22}}$ 
+     & $K_{\sigma_{33}}$ 
+     & $K_{\sigma_{12}}$ 
+     & $K_{\sigma_{13}}$ 
+     & $K_{\sigma_{23}}$ \\
+    \hline 
+    \hline
+     Разрыв нити основы 
+     & $3{,}84$ & $10{,}08$ & $6{,}56$ & $4{,}31$ & $\bf14{,}00$ & $6{,}22$ \\
+    \hline
+     Разрыв нити основы (доуплотнение) 
+     & $3{,}59$ & $4{,}50$ & $6{,}32$ & $3{,}98$ & $\bf11{,}21$ & $7{,}12$ \\
+    \hline
+    \hline
+     Разрыв нитей основы и утка 
+     & $3{,}82$ & $9{,}27$ & $6{,}96$ & $4{,}50$ & $\bf16{,}02$ &$\bf16{,}89$\\
+    \hline
+     Разрыв нитей основы и утка (доуплотнение) 
+     & $3{,}42$ & $4{,}22$ & $6{,}37$ & $3{,}87$ & $\bf11{,}47$ & $6{,}89$ \\
+    \hline
+  \end{tabular}
+\label{tab:c3:max_k_s3}
+\end{table}
+
+Распределение коэффициентов концентрации интенсивностей напряжений, вызванные
+наличием разрыва волокна основы и разрывов волокон основы и утка, показаны на
+рис.~\ref{fig:c3:k_d1d3_s3} и \ref{fig:c3:k_d2d4_s3}. 
+
+\begin{figure}[ht!]
+ \includegraphics[width=17cm]{concentrators/v2/scheme3/d1d3}
+ \caption{Распределение коэффициентов концентрации интенсивностей напряжений в
+слое тканого композита с разрывом волокна основы~(а) и с учётом
+доуплотнения~(б) при одноосном растяжении}
+ \label{fig:c3:k_d1d3_s3}
+\end{figure}
+
+\begin{figure}[ht!]
+ \includegraphics[width=17cm]{concentrators/v2/scheme3/d2d4}
+ \caption{Распределение коэффициентов концентрации интенсивностей напряжений в
+слое тканого композита с разрывом волокон основы и утка~(а) и с учётом
+доуплотнения~(б) при одноосном растяжении}
+ \label{fig:c3:k_d2d4_s3}
+\end{figure}
+
+Максимальных значений коэффициенты концентрации достигают в местах наибольшей
+кривизны волокон. Для материала с локальным разрывом волокна основы значения
+коэффициентов концентрации интенсивностей напяжений достигают $2{,}3$, а при
+одновременном разрыве волокон основы и утка --- $2{,}5$, причем заполнение
+поры, образовавшейся вследствие наличия локального дефекта, материалом
+поликристаллической матрицы, путем дополнительной пропитки конструкции или
+осаждения матрицы из газовой фазы, приводит к увеличению коэффициентов
+концентрации до $2{,}6$ и $3{,}7$ для случаев разрыва волокна основы и
+одновременного разрыва волокон основы и утка соответственно.
+
+\section*{Выводы к третьей главе}
+\addcontentsline{toc}{section}{Выводы к третьей главе}
+
+\begin{enumerate}
+ \item Построена твердотельная модель фрагмента слоя тканого композита с
+искривленными волокнами и поликристалической матрицей с идеальной
+периодической структурой и локальными технологическими дефектами, такими как
+разрыв волокна основы и одновременный разрыв волокон основы и утка с учетом
+контакта с трением между волокнами.
+ \item Получены численные решения краевых задач на двухосное растяжение в
+плоскости слоя, чистый сдвиг и одноосное растяжение в направлении утка с учетом
+контакта с трением между волокнами.
+ \item Вычислены безразмерные коэффициенты концентрации напряжений, вызванные
+наличием локальных технологических дефектов в виде разрыва волокна основы и
+одновременного разрыва волокон основы и утка.
+ \item Определены механизмы, инициирующие разрушение матрицы в слое тканого
+композита с искривленными волокнами и наличием контакта с трением между
+волокнами.
+\end{enumerate}

common.tex

@@ -129,8 +129,54 @@ $n_2$-ти тезисах докладов~\citemy{bib:dedkov1}.
 научного руководителя.
 }
 
-\mkcommonsect{struct}{Структура и объем диссертации}{%
+\mkcommonsect{struct}{Структура и объем диссертации.}{%
 Диссертационная работа состоит из введения, $n$-х частей, заключения, выводов и
 списка литературы. Полный объем составляет $n_1$ страниц. Библиография включает
 $n_2$ наименований.
 }
+
+\mkcommonsect{inintro}{Во введении}{
+приведен краткий обзор, отражающий современное
+состояние вопросов исследования, сделано заключение об актуальности
+темы диссертационной работы. Сформулирована цель данной работы, полученные 
+в ней новые научные результаты, применение и практическая ценность,
+приведена аннотация содержания глав диссертационной работы.
+}
+
+\mkcommonsect{infirst}{В первой главе}{
+рассматриваются технологические операции изготовления конструкций из
+тканых композиционных материалов с поликристаллической матрицей. Описывается
+процесс изготовления волокон, рассматриваются типы тканей и способы их
+производства, а так же совмещение тканого каркаса с поликристаллической
+матрицей, методы контроля качества конструкций их тканых материалов с
+поликристаллической матрицей и типы дефектов, возникающие во время
+технологических процессов, выявляемых с их помощью.
+}
+
+\mkcommonsect{insecond}{Во второй главе}{
+рассматриваются математические модели упруго-хрупкого поведения
+слоя тканого композита с искривленными волокнами и поликристаллической матрицей
+при двухосном растяжении в плоскости слоя, чистом сдвиге и одноосном растяжении
+слоя в направлении утка. Приведены значения безразмерных коэффициентов
+концентрации напряжений, вызванных наличием таких локальных дефектов как
+пропуск волокна основы, разрыв волокна основы, разрыв волокон основы и утка, а
+также наличием внутренней технологической поры. Определены механизмы,
+приводящие к разрушению поликристалллической матрицы.
+}
+
+\mkcommonsect{inthird}{В третьей главе}{
+рассматриваются математические модели упруго-хрупкого поведения слоя такного
+композита с искривленными волокнами и поликристаллической матрицей при
+двухосном растяжении в плоскости слоя, чистом сдиге и одноосном
+растяжении в направлении утка, с учетом наличия контакта с трением между
+волокнами. Приведены значения безразмерных коэффициентов концентрации
+напряжений, вызванных наличием таких локальных дефектов как разрыв волокна
+основы и разрыв волокон основы и утка, учитывая внутренние технологические
+поры, образовавшиеся в результате недостаточной пропитки ткани материалом
+матрицы в местах наибольшей кривизны волокон. Определены механизмы,
+приводящие к разрушению поликристалллической матрицы.
+}
+
+\mkcommonsect{inend}{В заключении}{
+изложены основные результаты диссертационной работы в целом.
+}

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+\chapter*{Заключение}
+\addcontentsline{toc}{chapter}{Заключение}
+
+Основные результаты, полученные в диссертации сводятся к следующему:
+
+\begin{enumerate}
+ \item Рассмотрены основные технологические процессы изготовления конструкций
+из тканых композиционных материалов с поликристаллической матрицей, приводящие
+к появлению локальных технологических дефектов, определены типы дефектов,
+возникающие на каждой из стадиях этих технологических процессов. Описаны методы
+контроля качества, выявляющие локальные дефекты.
+ \item Построены твердотельные модели слоя тканого композиционного материала с
+искривленными волокнами и поликристаллической матрицей с гарантированной
+прослойкой матрицы между волокнами, а также с наличием контакта с трением между
+волокнами.
+ \item Определены концентраторы напряжений в слое тканого композита с
+искривленными волокнами и поликристаллической матрицей, вызванные наличием
+таких локальных дефектов как пропуск волокна основы, разрыв волокна основы,
+разрыв волокон основы и утка, наличие внутренней технологической поры при
+двухосном растяжении в плоскости слоя, чистом сдвиге, а также одноосном
+растяжении в направлении волокон основы.
+ \item Определены механизмы, инициирующие разрушение матрицы в слое тканого
+композита при наличии гарантированной прослойки матрицы между волокнами, а
+также при наличии контакта с трением между волокнами.
+\end{enumerate}

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intro.tex

@@ -38,4 +38,24 @@
 
 % Структура и объем диссертации
 \structsection
-\structtext
+\structtext
+
+% Содержание введения
+\inintrosection
+\inintrotext
+
+% СОдержание первой главы
+\infirstsection
+\infirsttext
+
+% Содержание второй главы
+\insecondsection
+\insecondtext
+
+% Содержание третьей главы
+\inthirdsection
+\inthirdtext
+
+% Содержание заключения
+\inendsection
+\inendtext

stress_concentartors.tex

@@ -37,6 +37,7 @@
 \input{c1}
 \input{c2}
 \input{c3}
+\input{end}
 
 \bibliography{bibliography}
 \bibliographystyle{disser}