Module d'Young

formules en 3D

${\displaystyle (\lambda ,G)}$

${\displaystyle (E,G)}$

${\displaystyle (K,\lambda )}$

${\displaystyle (K,G)}$

${\displaystyle (\lambda ,\nu )}$

${\displaystyle (G,\nu )}$

${\displaystyle (E,\nu )}$

${\displaystyle (K,\nu )}$

${\displaystyle (K,E)}$

${\displaystyle (M,G)}$

${\displaystyle K\,[\mathrm {Pa} ]=}$

${\displaystyle \lambda +{\tfrac {2G}{3}}}$

${\displaystyle {\tfrac {EG}{3(3G-E)}}}$

${\displaystyle {\tfrac {\lambda (1+\nu )}{3\nu }}}$

${\displaystyle {\tfrac {2G(1+\nu )}{3(1-2\nu )}}}$

${\displaystyle {\tfrac {E}{3(1-2\nu )}}}$

${\displaystyle M-{\tfrac {4G}{3}}}$

${\displaystyle E\,[\mathrm {Pa} ]=}$

${\displaystyle {\tfrac {G(3\lambda +2G)}{\lambda +G}}}$

${\displaystyle {\tfrac {9K(K-\lambda )}{3K-\lambda }}}$

${\displaystyle {\tfrac {9KG}{3K+G}}}$

${\displaystyle {\tfrac {\lambda (1+\nu )(1-2\nu )}{\nu }}}$

${\displaystyle 2G(1+\nu )\,}$

${\displaystyle 3K(1-2\nu )\,}$

${\displaystyle {\tfrac {G(3M-4G)}{M-G}}}$

${\displaystyle \lambda \,[\mathrm {Pa} ]=}$

${\displaystyle {\tfrac {G(E-2G)}{3G-E}}}$

${\displaystyle K-{\tfrac {2G}{3}}}$

${\displaystyle {\tfrac {2G\nu }{1-2\nu }}}$

${\displaystyle {\tfrac {E\nu }{(1+\nu )(1-2\nu )}}}$

${\displaystyle {\tfrac {3K\nu }{1+\nu }}}$

${\displaystyle {\tfrac {3K(3K-E)}{9K-E}}}$

${\displaystyle M-2G}$

${\displaystyle G\,[\mathrm {Pa} ]=}$

${\displaystyle {\tfrac {3(K-\lambda )}{2}}}$

${\displaystyle {\tfrac {\lambda (1-2\nu )}{2\nu }}}$

${\displaystyle {\tfrac {E}{2(1+\nu )}}}$

${\displaystyle {\tfrac {3K(1-2\nu )}{2(1+\nu )}}}$

${\displaystyle {\tfrac {3KE}{9K-E}}}$

${\displaystyle \nu \,[1]=}$

${\displaystyle {\tfrac {\lambda }{2(\lambda +G)}}}$

${\displaystyle {\tfrac {E}{2G}}-1}$

${\displaystyle {\tfrac {\lambda }{3K-\lambda }}}$

${\displaystyle {\tfrac {3K-2G}{2(3K+G)}}}$

${\displaystyle {\tfrac {3K-E}{6K}}}$

${\displaystyle {\tfrac {M-2G}{2M-2G}}}$

${\displaystyle M\,[\mathrm {Pa} ]=}$

${\displaystyle \lambda +2G}$

${\displaystyle {\tfrac {G(4G-E)}{3G-E}}}$

${\displaystyle 3K-2\lambda \,}$

${\displaystyle K+{\tfrac {4G}{3}}}$

${\displaystyle {\tfrac {\lambda (1-\nu )}{\nu }}}$

${\displaystyle {\tfrac {2G(1-\nu )}{1-2\nu }}}$

${\displaystyle {\tfrac {E(1-\nu )}{(1+\nu )(1-2\nu )}}}$

${\displaystyle {\tfrac {3K(1-\nu )}{1+\nu }}}$

${\displaystyle {\tfrac {3K(3K+E)}{9K-E}}}$

formules en 2D

${\displaystyle (\lambda _{\mathrm {2D} },G_{\mathrm {2D} })}$

${\displaystyle (E_{\mathrm {2D} },G_{\mathrm {2D} })}$

${\displaystyle (K_{\mathrm {2D} },\lambda _{\mathrm {2D} })}$

${\displaystyle (K_{\mathrm {2D} },G_{\mathrm {2D} })}$

${\displaystyle (\lambda _{\mathrm {2D} },\nu _{\mathrm {2D} })}$

${\displaystyle (G_{\mathrm {2D} },\nu _{\mathrm {2D} })}$

${\displaystyle (E_{\mathrm {2D} },\nu _{\mathrm {2D} })}$

${\displaystyle (K_{\mathrm {2D} },\nu _{\mathrm {2D} })}$

${\displaystyle (K_{\mathrm {2D} },E_{\mathrm {2D} })}$

${\displaystyle (M_{\mathrm {2D} },G_{\mathrm {2D} })}$

${\displaystyle K_{\mathrm {2D} }\,[\mathrm {N/m} ]=}$

${\displaystyle \lambda _{\mathrm {2D} }+G_{\mathrm {2D} }}$

${\displaystyle {\tfrac {G_{\mathrm {2D} }E_{\mathrm {2D} }}{4G_{\mathrm {2D} }-E_{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {\lambda _{\mathrm {2D} }(1+\nu _{\mathrm {2D} })}{2\nu _{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {G_{\mathrm {2D} }(1+\nu _{\mathrm {2D} })}{1-\nu _{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {E_{\mathrm {2D} }}{2(1-\nu _{\mathrm {2D} })}}}$

${\displaystyle M_{\mathrm {2D} }-G_{\mathrm {2D} }}$

${\displaystyle E_{\mathrm {2D} }\,[\mathrm {N/m} ]=}$

${\displaystyle {\tfrac {4G_{\mathrm {2D} }(\lambda _{\mathrm {2D} }+G_{\mathrm {2D} })}{\lambda _{\mathrm {2D} }+2G_{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {4K_{\mathrm {2D} }(K_{\mathrm {2D} }-\lambda _{\mathrm {2D} })}{2K_{\mathrm {2D} }-\lambda _{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {4K_{\mathrm {2D} }G_{\mathrm {2D} }}{K_{\mathrm {2D} }+G_{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {\lambda _{\mathrm {2D} }(1+\nu _{\mathrm {2D} })(1-\nu _{\mathrm {2D} })}{\nu _{\mathrm {2D} }}}}$

${\displaystyle 2G_{\mathrm {2D} }(1+\nu _{\mathrm {2D} })\,}$

${\displaystyle 2K_{\mathrm {2D} }(1-\nu _{\mathrm {2D} })}$

${\displaystyle {\tfrac {4G_{\mathrm {2D} }(M_{\mathrm {2D} }-G_{\mathrm {2D} })}{M_{\mathrm {2D} }}}}$

${\displaystyle \lambda _{\mathrm {2D} }\,[\mathrm {N/m} ]=}$

${\displaystyle {\tfrac {2G_{\mathrm {2D} }(E_{\mathrm {2D} }-2G_{\mathrm {2D} })}{4G_{\mathrm {2D} }-E_{\mathrm {2D} }}}}$

${\displaystyle K_{\mathrm {2D} }-G_{\mathrm {2D} }}$

${\displaystyle {\tfrac {2G_{\mathrm {2D} }\nu _{\mathrm {2D} }}{1-\nu _{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {E_{\mathrm {2D} }\nu _{\mathrm {2D} }}{(1+\nu _{\mathrm {2D} })(1-\nu _{\mathrm {2D} })}}}$

${\displaystyle {\tfrac {2K_{\mathrm {2D} }\nu _{\mathrm {2D} }}{1+\nu _{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {2K_{\mathrm {2D} }(2K_{\mathrm {2D} }-E_{\mathrm {2D} })}{4K_{\mathrm {2D} }-E_{\mathrm {2D} }}}}$

${\displaystyle M_{\mathrm {2D} }-2G_{\mathrm {2D} }}$

${\displaystyle G_{\mathrm {2D} }\,[\mathrm {N/m} ]=}$

${\displaystyle K_{\mathrm {2D} }-\lambda _{\mathrm {2D} }}$

${\displaystyle {\tfrac {\lambda _{\mathrm {2D} }(1-\nu _{\mathrm {2D} })}{2\nu _{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {E_{\mathrm {2D} }}{2(1+\nu _{\mathrm {2D} })}}}$

${\displaystyle {\tfrac {K_{\mathrm {2D} }(1-\nu _{\mathrm {2D} })}{1+\nu _{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {K_{\mathrm {2D} }E_{\mathrm {2D} }}{4K_{\mathrm {2D} }-E_{\mathrm {2D} }}}}$

${\displaystyle \nu _{\mathrm {2D} }\,[1]=}$

${\displaystyle {\tfrac {\lambda _{\mathrm {2D} }}{\lambda _{\mathrm {2D} }+2G_{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {E_{\mathrm {2D} }}{2G_{\mathrm {2D} }}}-1}$

${\displaystyle {\tfrac {\lambda _{\mathrm {2D} }}{2K_{\mathrm {2D} }-\lambda _{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {K_{\mathrm {2D} }-G_{\mathrm {2D} }}{K_{\mathrm {2D} }+G_{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {2K_{\mathrm {2D} }-E_{\mathrm {2D} }}{2K_{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {M_{\mathrm {2D} }-2G_{\mathrm {2D} }}{M_{\mathrm {2D} }}}}$

${\displaystyle M_{\mathrm {2D} }\,[\mathrm {N/m} ]=}$

${\displaystyle \lambda _{\mathrm {2D} }+2G_{\mathrm {2D} }}$

${\displaystyle {\tfrac {4G_{\mathrm {2D} }^{2}}{4G_{\mathrm {2D} }-E_{\mathrm {2D} }}}}$

${\displaystyle 2K_{\mathrm {2D} }-\lambda _{\mathrm {2D} }}$

${\displaystyle K_{\mathrm {2D} }+G_{\mathrm {2D} }}$

${\displaystyle {\tfrac {\lambda _{\mathrm {2D} }}{\nu _{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {2G_{\mathrm {2D} }}{1-\nu _{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {E_{\mathrm {2D} }}{(1-\nu _{\mathrm {2D} })(1+\nu _{\mathrm {2D} })}}}$

${\displaystyle {\tfrac {2K_{\mathrm {2D} }}{1+\nu _{\mathrm {2D} }}}}$

${\displaystyle {\tfrac {4K_{\mathrm {2D} }^{2}}{4K_{\mathrm {2D} }-E_{\mathrm {2D} }}}}$