Mechanical stress & strain

Mechanical stress & strain of a book. Also see these illustration of strain with a book.

mechanics_stress_strain-001.pngmechanics_stress_strain-002.pngmechanics_stress_strain-003.png

Edit and compile if you like:

% Author: Izaak Neutelings (December 2020)
\documentclass[border=3pt,tikz]{standalone}
\usepackage{physics}
\usepackage{graphicx}
\usepackage{tikz}
\usetikzlibrary{angles,quotes} % for pic (angle labels)
\tikzset{>=latex}

\colorlet{mydarkblue}{blue!40!black}
\colorlet{myblue}{blue!70!black}
\colorlet{myred}{red!65!black}
\colorlet{vcol}{green!45!black}
\tikzstyle{book}=[brown!20!black,fill=brown!80!black!95]
\tikzstyle{vvec}=[->,very thick,vcol,line cap=round]
\tikzstyle{force}=[->,myred,very thick,line cap=round]
\def\tick#1#2{\draw[thick] (#1)++(#2:0.12) --++ (#2-180:0.24)}

\begin{document}


% BOOK straight
\def\W{2.0}  % total width
\def\H{1.5}  % total height
\def\N{30}   % number of layers
\def\t{0.04} % thickness
\begin{tikzpicture}
  \foreach \i [evaluate={\ya=(\i-1)*\H/\N; \yb=\i*\H/\N;}] in {1,...,\N}{
    \draw[line width=0.05] (0,\ya) |- (\W,\yb) to[out=-110,in=110] (\W,\ya) -- cycle;
  }
  \draw[fill=white,rounded corners=0.4,line width=0.05]
    (0,0) rectangle (\t/2,\H);
  \draw[brown!20!black,fill=brown!70!black,rounded corners=0.2,line width=0.2]
    (0,0) -| (1.01*\W,-\t) -| (-\t,\H+\t) -| (1.01*\W,\H) -| cycle;
\end{tikzpicture}

% BOOK sheared
\begin{tikzpicture}
  \def\Dw{0.8} % sheared
  \coordinate (O) at (-\t/2-\t*\Dw/\H/2,-\t/2);
  \coordinate (T) at (-\t/2-\t*\Dw/\H/2,\H+\t/2);
  \coordinate (T') at (\Dw,\H+\t/2);
  
  % BOOK
  \foreach \i [evaluate={
    \ya=(\i-1)*\H/\N;  \yb=\i*\H/\N;
    \xa=(\i-1)*\Dw/\N; \xb=\i*\Dw/\N;
                         }] in {1,...,\N}{
    \draw[line width=0.05] (\xa,\ya) -- (\xb,\yb) -- (\xb+\W,\yb) to[out=-110,in=110] (\xa+\W,\ya) -- cycle;
  }
  \draw[fill=white,rounded corners=0.4,line width=0.05]
    (0,0) -- (\Dw,\H) -- (\Dw+\t/2,\H) -- (\t/2,0) -- cycle;
  \draw[brown!20!black,fill=brown!70!black,rounded corners=0.2,line width=0.2]
    (0,0) -| (1.01*\W,-\t) -- (-\t-\t*\Dw/\H,-\t) --
    (\Dw-\t,\H+\t) -- (\Dw+1.01*\W,\H+\t) -- (\Dw+1.01*\W,\H) -- (\Dw,\H) -- cycle;
  
  % MEASURES
  \draw[dashed] (O) -- (T) --++ (-0.1*\W,0);
  \draw[dashed] (T') -- (T) --++ (0,0.1*\H);
  \draw[<->] (-0.1*\W,-\t/2) -- (-0.1*\W,\H+\t/2) node[midway,fill=white,inner sep=1] {$L$};
  \draw[->] (-\t/2,1.06*\H+\t) --++ (\Dw,0) node[midway,left=1,above=-1] {$\Delta x$};
  \draw pic[<-,"$\theta$"{above=-1},draw=black,angle radius=20,angle eccentricity=1] {angle = T'--O--T};
  \draw[force] (\Dw+0.2*\W,1.1*\H) --++ (0.5*\W,0) node[midway,above] {$\vb{F}_\mathrm{s}$};
  
\end{tikzpicture}


% PRESSURE
\begin{tikzpicture}[x={(1cm,0)},y={(0.35cm,0.23cm)},z={(0,1cm)}]
  \def\L{3.0}  % total length
  \def\Dw{0.8} % sheared
  \coordinate (O) at (-\t/2-\t*\Dw/\H/2,0,-\t/2);
  \coordinate (T) at (-\t/2-\t*\Dw/\H/2,0,\H+\t/2);
  \coordinate (T') at (\Dw,0,\H+\t/2);
  
  % BOOK
  \draw[book,line width=0.2] % bottom front side
    (1.03*\W,-0.0415*\L,0) -- (1.03*\W,-0.0415*\L,-\t+0.004) --
    (1.03*\W,1.043*\L,-\t+0.004) -- (1.03*\W,1.043*\L,0.0012);
  \draw[book,line width=0.2] % back inside
    (0,-0.04*\L,0) -- (0,1.04*\L,0) -- (\Dw,1.04*\L,\H) -- (\Dw,-0.04*\L,\H) -- cycle;
  \draw[book,line width=0.2] % top cover
    (0,-0.042*\L,0) -- (0,1.04*\L,0) --
    (1.03*\W-0.0045,1.04*\L,0) -- (1.03*\W-0.0045,-0.042*\L,0);
  \foreach \i [evaluate={
    \za=(\i-1)*\H/\N;  \zb=\i*\H/\N;
    \xa=(\i-1)*\Dw/\N; \xb=\i*\Dw/\N;
                         }] in {1,...,\N}{
    \draw[line width=0.05,fill=white] (\xb+\W,0,\zb) -- (\xb+\W,\L,\zb) to[out=-110,in=110]
      (\xa+\W,\L,\za) -- (\xa+\W,0,\za) to[out=110,in=-110] cycle;
    \draw[line width=0.05,fill=white] (\xa,0,\za) -- (\xb,0,\zb) --
      (\xb+\W,0,\zb) to[out=-110,in=110] (\xa+\W,0,\za) -- cycle;
  }
  \draw[book,line width=0.2] % top front side
    (\Dw+1.03*\W,-0.042*\L,\H+\t) -- (\Dw+1.03*\W,-0.042*\L,\H+0.0048) --
    (\Dw+1.03*\W,1.043*\L,\H+0.0048) -- (\Dw+1.03*\W,1.043*\L,\H+\t+0.0012);
  \draw[book,line width=0.2] % top cover
    (\Dw-\t+0.0045,-0.042*\L,\H+\t) -- (\Dw-\t+0.0045,1.04*\L,\H+\t) --
    (\Dw+1.03*\W-0.0045,1.04*\L,\H+\t) -- (\Dw+1.03*\W-0.0045,-0.042*\L,\H+\t);
  \draw[book,rounded corners=0.2,line width=0.2] % side
    (0,-0.04*\L,0) -| (1.03*\W,-0.04*\L,-\t) -- (-\t-\t*\Dw/\H,-0.04*\L,-\t) --
    (\Dw-\t,-0.04*\L,\H+\t) -- (\Dw+1.03*\W,-0.04*\L,\H+\t) --
    (\Dw+1.03*\W,-0.04*\L,\H) -- (\Dw,-0.04*\L,\H) -- cycle;
  
  % MEASURES
  \draw[dashed] (O) -- (T) --++ (-0.1*\W,0,0);
  \draw[dashed] (T') -- (T) --++ (0,0,0.1*\H);
  \draw[<->] (-0.1*\W,0,-\t/2) -- (-0.1*\W,0,\H+\t/2) node[midway,fill=white,inner sep=1] {$L$};
  \draw[->] (-\t/2,0,1.06*\H+\t) --++ (\Dw,0,0) node[midway,left=1,above=-1] {$\Delta x$};
  \draw pic[<-,"$\theta$"{above=-1},draw=black,angle radius=20,angle eccentricity=1] {angle = T'--O--T};
  \draw[force] (\Dw+0.9*\W,0.5*\L,1.05*\H) --++ (0.6*\W,0,0) node[right] {$\vb{F}_\mathrm{s}$};
  
  % TEXT
  \node[below right,sloped,xslant=1.5,scale=0.2,align=left] at (\Dw+0.1*\W,1.04*\L,\H) {
    {\bfseries PHY111}\\
    Physics I for Physics Majors\\[2]
    \includegraphics[width=50pt]{logo_physik.pdf}\\[2]
    {\small\textsc{Prof. Ben Kilminster}}
  };
  
\end{tikzpicture}


%% TURBULENCE - REYNOLDS
%\begin{tikzpicture}
%  \def\xmax{4.8}
%  \def\ymax{3.0}
%  \def\xa{0.40*0.7*\xmax}
%  \def\xb{0.55*0.7*\xmax}
%  \fill[myblue!8] (0,0) rectangle (\xa,\ymax);
%  \fill[myorange!10] (\xa,0) rectangle (\xb,\ymax);
%  \fill[myred!8] (\xb,0) rectangle (\xmax,\ymax);
%  \draw[->,thick] (-0.05*\xmax,0) -- (1.05*\xmax,0) node[below left=0] {Pressure difference $\Delta P$};
%  \draw[->,thick] (0,-0.05*\xmax) -- (0,1.10*\ymax) node[above left=0,rotate=90] {Flow};
%  \draw[thick] ({(\xa+\xb)/2},0.035*\ymax) --++ (0,-0.07*\ymax);
%  \draw[thick,myblue,dashed] (0,0) -- (0.7*\xmax,\ymax);
%  \draw[very thick,myblue] (0,0) -- (\xa,0.40*\ymax) coordinate (T1);
%  \draw[very thick,myorange] (T1) to[out=40,in=-155] (\xb,0.51*\ymax) coordinate (T2);
%  \draw[very thick,myred] (T2) to[out=25,in=180] (\xmax,0.67*\ymax);
%  \node[right,myblue] at (0,0.54*\ymax) {laminar};
%  \node[right,myred] at (0.53*\xmax,0.50*\ymax) {turbulent};
%  %\draw[dashed] ({(\xa+\xb)/2},0) --++ (0,\ymax) node[above] {$\mathrm{Re}\sim2300$};
%\end{tikzpicture}


\end{document}

Click to download: mechanics_stress_strain.texmechanics_stress_strain.pdf
Open in Overleaf: mechanics_stress_strain.tex

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