1<TeXmacs|1.0.7.15>
2
3<style|<tuple|generic|maxima>>
4
5<\body>
6  Compute deformation tensors from the\ 
7
8  <\session|maxima|default>
9    <\output>
10      Maxima 5.27.0 http://maxima.sourceforge.net
11
12      using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (a.k.a. GCL)
13
14      Distributed under the GNU Public License. See the file COPYING.
15
16      Dedicated to the memory of William Schelter.
17
18      The function bug_report() provides bug reporting information.
19    </output>
20
21    <\unfolded-io>
22      <with|color|red|(<with|math-font-family|rm|%i>37) >
23    <|unfolded-io>
24      F:matrix([F0,F3,0],[F4,F1,0],[0,0,F2])
25    <|unfolded-io>
26      <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o37>)
27      >><matrix|<tformat|<table|<row|<cell|<with|math-font-family|rm|F0>>|<cell|<with|math-font-family|rm|F3>>|<cell|0>>|<row|<cell|<with|math-font-family|rm|F4>>|<cell|<with|math-font-family|rm|F1>>|<cell|0>>|<row|<cell|0>|<cell|0>|<cell|<with|math-font-family|rm|F2>>>>>>>>
28    </unfolded-io>
29
30    <\unfolded-io>
31      <with|color|red|(<with|math-font-family|rm|%i>38) >
32    <|unfolded-io>
33      transpose(F).F /* right cauchy green tensor */
34    <|unfolded-io>
35      <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o38>)
36      >><matrix|<tformat|<table|<row|<cell|<with|math-font-family|rm|F4><rsup|2>+<with|math-font-family|rm|F0><rsup|2>>|<cell|<with|math-font-family|rm|F1>*<with|math-font-family|rm|F4>+<with|math-font-family|rm|F0>*<with|math-font-family|rm|F3>>|<cell|0>>|<row|<cell|<with|math-font-family|rm|F1>*<with|math-font-family|rm|F4>+<with|math-font-family|rm|F0>*<with|math-font-family|rm|F3>>|<cell|<with|math-font-family|rm|F3><rsup|2>+<with|math-font-family|rm|F1><rsup|2>>|<cell|0>>|<row|<cell|0>|<cell|0>|<cell|<with|math-font-family|rm|F2><rsup|2>>>>>>>>
37    </unfolded-io>
38
39    <\unfolded-io>
40      <with|color|red|(<with|math-font-family|rm|%i>39) >
41    <|unfolded-io>
42      F.transpose(F) /* left cauchy green tensor */
43    <|unfolded-io>
44      <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o39>)
45      >><matrix|<tformat|<table|<row|<cell|<with|math-font-family|rm|F3><rsup|2>+<with|math-font-family|rm|F0><rsup|2>>|<cell|<with|math-font-family|rm|F0>*<with|math-font-family|rm|F4>+<with|math-font-family|rm|F1>*<with|math-font-family|rm|F3>>|<cell|0>>|<row|<cell|<with|math-font-family|rm|F0>*<with|math-font-family|rm|F4>+<with|math-font-family|rm|F1>*<with|math-font-family|rm|F3>>|<cell|<with|math-font-family|rm|F4><rsup|2>+<with|math-font-family|rm|F1><rsup|2>>|<cell|0>>|<row|<cell|0>|<cell|0>|<cell|<with|math-font-family|rm|F2><rsup|2>>>>>>>>
46    </unfolded-io>
47
48    <\unfolded-io>
49      <with|color|red|(<with|math-font-family|rm|%i>40) >
50    <|unfolded-io>
51      p:matrix([p0,p3/sqrt(2),0],[p3/sqrt(2),p1,0],[0,0,p2])
52    <|unfolded-io>
53      <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o40>)
54      >><matrix|<tformat|<table|<row|<cell|<with|math-font-family|rm|p0>>|<cell|<frac|<with|math-font-family|rm|p3>|<sqrt|2>>>|<cell|0>>|<row|<cell|<frac|<with|math-font-family|rm|p3>|<sqrt|2>>>|<cell|<with|math-font-family|rm|p1>>|<cell|0>>|<row|<cell|0>|<cell|0>|<cell|<with|math-font-family|rm|p2>>>>>>>>
55    </unfolded-io>
56
57    <\unfolded-io>
58      <with|color|red|(<with|math-font-family|rm|%i>41) >
59    <|unfolded-io>
60      s:F.p.transpose(F)
61    <|unfolded-io>
62      <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o41>)
63      >><matrix|<tformat|<table|<row|<cell|<with|math-font-family|rm|F0>*<around*|(|<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F3>|<sqrt|2>>+<with|math-font-family|rm|p0>*<with|math-font-family|rm|F0>|)>+<with|math-font-family|rm|F3>*<around*|(|<with|math-font-family|rm|p1>*<with|math-font-family|rm|F3>+<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F0>|<sqrt|2>>|)>>|<cell|<with|math-font-family|rm|F3>*<around*|(|<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F4>|<sqrt|2>>+<with|math-font-family|rm|p1>*<with|math-font-family|rm|F1>|)>+<with|math-font-family|rm|F0>*<around*|(|<with|math-font-family|rm|p0>*<with|math-font-family|rm|F4>+<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F1>|<sqrt|2>>|)>>|<cell|0>>|<row|<cell|<around*|(|<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F3>|<sqrt|2>>+<with|math-font-family|rm|p0>*<with|math-font-family|rm|F0>|)>*<with|math-font-family|rm|F4>+<with|math-font-family|rm|F1>*<around*|(|<with|math-font-family|rm|p1>*<with|math-font-family|rm|F3>+<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F0>|<sqrt|2>>|)>>|<cell|<with|math-font-family|rm|F1>*<around*|(|<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F4>|<sqrt|2>>+<with|math-font-family|rm|p1>*<with|math-font-family|rm|F1>|)>+<with|math-font-family|rm|F4>*<around*|(|<with|math-font-family|rm|p0>*<with|math-font-family|rm|F4>+<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F1>|<sqrt|2>>|)>>|<cell|0>>|<row|<cell|0>|<cell|0>|<cell|<with|math-font-family|rm|p2>*<with|math-font-family|rm|F2><rsup|2>>>>>>>>
64    </unfolded-io>
65
66    <\unfolded-io>
67      <with|color|red|(<with|math-font-family|rm|%i>42) >
68    <|unfolded-io>
69      fullratsimp(s[1,1])
70    <|unfolded-io>
71      <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o42>)
72      >><with|math-font-family|rm|p1>*<with|math-font-family|rm|F3><rsup|2>+<sqrt|2>*<with|math-font-family|rm|p3>*<with|math-font-family|rm|F0>*<with|math-font-family|rm|F3>+<with|math-font-family|rm|p0>*<with|math-font-family|rm|F0><rsup|2>>>
73    </unfolded-io>
74
75    <\unfolded-io>
76      <with|color|red|(<with|math-font-family|rm|%i>43) >
77    <|unfolded-io>
78      fullratsimp(s[2,2])
79    <|unfolded-io>
80      <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o43>)
81      >><with|math-font-family|rm|p0>*<with|math-font-family|rm|F4><rsup|2>+<sqrt|2>*<with|math-font-family|rm|p3>*<with|math-font-family|rm|F1>*<with|math-font-family|rm|F4>+<with|math-font-family|rm|p1>*<with|math-font-family|rm|F1><rsup|2>>>
82    </unfolded-io>
83
84    <\unfolded-io>
85      <with|color|red|(<with|math-font-family|rm|%i>44) >
86    <|unfolded-io>
87      fullratsimp(s[3,3])
88    <|unfolded-io>
89      <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o44>)
90      >><with|math-font-family|rm|p2>*<with|math-font-family|rm|F2><rsup|2>>>
91    </unfolded-io>
92
93    <\unfolded-io>
94      <with|color|red|(<with|math-font-family|rm|%i>45) >
95    <|unfolded-io>
96      fullratsimp(s[1,2]*sqrt(2))
97    <|unfolded-io>
98      <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o45>)
99      >><around*|(|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F3>+<sqrt|2>*<with|math-font-family|rm|p0>*<with|math-font-family|rm|F0>|)>*<with|math-font-family|rm|F4>+<sqrt|2>*<with|math-font-family|rm|p1>*<with|math-font-family|rm|F1>*<with|math-font-family|rm|F3>+<with|math-font-family|rm|p3>*<with|math-font-family|rm|F0>*<with|math-font-family|rm|F1>>>
100    </unfolded-io>
101
102    <\input>
103      <with|color|red|(<with|math-font-family|rm|%i>46) >
104    <|input>
105      \;
106    </input>
107  </session>
108</body>
109
110<\initial>
111  <\collection>
112    <associate|language|french>
113    <associate|page-type|a3>
114  </collection>
115</initial>