परिवर्तन के सूत्र
होमोजिनस आइसोट्रॉपिक रैखिक प्रत्यास्थ पदार्थ के कोई भी दो मापांक दिये हों तो अन्य गुण निम्नलिखित सूत्रों द्वारा प्राप्त किये जा सकते हैं।
(
K
,
E
)
{\displaystyle (K,\,E)}
(
K
,
λ
)
{\displaystyle (K,\,\lambda )}
(
K
,
G
)
{\displaystyle (K,\,G)}
(
K
,
ν
)
{\displaystyle (K,\,\nu )}
(
E
,
G
)
{\displaystyle (E,\,G)}
(
E
,
ν
)
{\displaystyle (E,\,\nu )}
(
λ
,
G
)
{\displaystyle (\lambda ,\,G)}
(
λ
,
ν
)
{\displaystyle (\lambda ,\,\nu )}
(
G
,
ν
)
{\displaystyle (G,\,\nu )}
(
G
,
M
)
{\displaystyle (G,\,M)}
K
=
{\displaystyle K=\,}
K
{\displaystyle K}
K
{\displaystyle K}
K
{\displaystyle K}
K
{\displaystyle K}
E
G
3
(
3
G
−
E
)
{\displaystyle {\tfrac {EG}{3(3G-E)}}}
E
3
(
1
−
2
ν
)
{\displaystyle {\tfrac {E}{3(1-2\nu )}}}
λ
+
2
G
3
{\displaystyle \lambda +{\tfrac {2G}{3}}}
λ
(
1
+
ν
)
3
ν
{\displaystyle {\tfrac {\lambda (1+\nu )}{3\nu }}}
2
G
(
1
+
ν
)
3
(
1
−
2
ν
)
{\displaystyle {\tfrac {2G(1+\nu )}{3(1-2\nu )}}}
M
−
4
G
3
{\displaystyle M-{\tfrac {4G}{3}}}
E
=
{\displaystyle E=\,}
E
{\displaystyle E}
9
K
(
K
−
λ
)
3
K
−
λ
{\displaystyle {\tfrac {9K(K-\lambda )}{3K-\lambda }}}
9
K
G
3
K
+
G
{\displaystyle {\tfrac {9KG}{3K+G}}}
3
K
(
1
−
2
ν
)
{\displaystyle 3K(1-2\nu )\,}
E
{\displaystyle E}
E
{\displaystyle E}
G
(
3
λ
+
2
G
)
λ
+
G
{\displaystyle {\tfrac {G(3\lambda +2G)}{\lambda +G}}}
λ
(
1
+
ν
)
(
1
−
2
ν
)
ν
{\displaystyle {\tfrac {\lambda (1+\nu )(1-2\nu )}{\nu }}}
2
G
(
1
+
ν
)
{\displaystyle 2G(1+\nu )\,}
G
(
3
M
−
4
G
)
M
−
G
{\displaystyle {\tfrac {G(3M-4G)}{M-G}}}
λ
=
{\displaystyle \lambda =\,}
3
K
(
3
K
−
E
)
9
K
−
E
{\displaystyle {\tfrac {3K(3K-E)}{9K-E}}}
λ
{\displaystyle \lambda }
K
−
2
G
3
{\displaystyle K-{\tfrac {2G}{3}}}
3
K
ν
1
+
ν
{\displaystyle {\tfrac {3K\nu }{1+\nu }}}
G
(
E
−
2
G
)
3
G
−
E
{\displaystyle {\tfrac {G(E-2G)}{3G-E}}}
E
ν
(
1
+
ν
)
(
1
−
2
ν
)
{\displaystyle {\tfrac {E\nu }{(1+\nu )(1-2\nu )}}}
λ
{\displaystyle \lambda }
λ
{\displaystyle \lambda }
2
G
ν
1
−
2
ν
{\displaystyle {\tfrac {2G\nu }{1-2\nu }}}
M
−
2
G
{\displaystyle M-2G\,}
G
=
{\displaystyle G=\,}
3
K
E
9
K
−
E
{\displaystyle {\tfrac {3KE}{9K-E}}}
3
(
K
−
λ
)
2
{\displaystyle {\tfrac {3(K-\lambda )}{2}}}
G
{\displaystyle G}
3
K
(
1
−
2
ν
)
2
(
1
+
ν
)
{\displaystyle {\tfrac {3K(1-2\nu )}{2(1+\nu )}}}
G
{\displaystyle G}
E
2
(
1
+
ν
)
{\displaystyle {\tfrac {E}{2(1+\nu )}}}
G
{\displaystyle G}
λ
(
1
−
2
ν
)
2
ν
{\displaystyle {\tfrac {\lambda (1-2\nu )}{2\nu }}}
G
{\displaystyle G}
G
{\displaystyle G}
ν
=
{\displaystyle \nu =\,}
3
K
−
E
6
K
{\displaystyle {\tfrac {3K-E}{6K}}}
λ
3
K
−
λ
{\displaystyle {\tfrac {\lambda }{3K-\lambda }}}
3
K
−
2
G
2
(
3
K
+
G
)
{\displaystyle {\tfrac {3K-2G}{2(3K+G)}}}
ν
{\displaystyle \nu }
E
2
G
−
1
{\displaystyle {\tfrac {E}{2G}}-1}
ν
{\displaystyle \nu }
λ
2
(
λ
+
G
)
{\displaystyle {\tfrac {\lambda }{2(\lambda +G)}}}
ν
{\displaystyle \nu }
ν
{\displaystyle \nu }
M
−
2
G
2
M
−
2
G
{\displaystyle {\tfrac {M-2G}{2M-2G}}}
M
=
{\displaystyle M=\,}
3
K
(
3
K
+
E
)
9
K
−
E
{\displaystyle {\tfrac {3K(3K+E)}{9K-E}}}
3
K
−
2
λ
{\displaystyle 3K-2\lambda \,}
K
+
4
G
3
{\displaystyle K+{\tfrac {4G}{3}}}
3
K
(
1
−
ν
)
1
+
ν
{\displaystyle {\tfrac {3K(1-\nu )}{1+\nu }}}
G
(
4
G
−
E
)
3
G
−
E
{\displaystyle {\tfrac {G(4G-E)}{3G-E}}}
E
(
1
−
ν
)
(
1
+
ν
)
(
1
−
2
ν
)
{\displaystyle {\tfrac {E(1-\nu )}{(1+\nu )(1-2\nu )}}}
λ
+
2
G
{\displaystyle \lambda +2G\,}
λ
(
1
−
ν
)
ν
{\displaystyle {\tfrac {\lambda (1-\nu )}{\nu }}}
2
G
(
1
−
ν
)
1
−
2
ν
{\displaystyle {\tfrac {2G(1-\nu )}{1-2\nu }}}
M
{\displaystyle M}
