\[Mu] = 0.25;
\[CapitalEpsilon] = 25.34*10^9;
\[CurlyPhi] = 25.732 \[Degree];
\[ScriptC] = 23.915*10^6;
\[CapitalRho] = 65*10^6;
\[Alpha] = 180 \[Degree]/2 + \[CurlyPhi]/2;
\[CapitalTheta] = 0;
\[Beta] = Sin[\[CurlyPhi]]/(3 Sqrt[3 + Sin[\[CurlyPhi]]^2]);
\[ScriptF] = 906.88 + 17.3314*\[CapitalTheta];
\[ScriptM] =
0.6198 - 0.0036*\[CapitalTheta] + 2.5334*10^-5*\[CapitalTheta]^2;
rule = {\[ScriptK] -> ((((1 + \[Mu])*\[CapitalRho]^2*Sin[\[Alpha]])/(
3*\[CapitalEpsilon]*\[Epsilon]) - \[ScriptC])*
Cot[\[CurlyPhi]] - 2*\[ScriptC]*Sin[\[Alpha]])/(
Sin[\[Alpha]]*(1 +
Tan[\[Alpha]])), \[ScriptCapitalR] -> (\[Sigma] -
2*\[Mu]*\[CapitalTheta] - \[CapitalEpsilon]*\[Epsilon])/(
Tan[\[Alpha]]^2*\[ScriptK] + 2*\[ScriptC]*Tan[\[Alpha]] -
2*\[Mu]*\[ScriptK] - \[CapitalEpsilon]*\[Epsilon]),
ò -> (\[Sigma] - \[ScriptCapitalR]*(Tan[\[Alpha]]^2*\[ScriptK] +
2*\[ScriptC]*Tan[\[Alpha]]))/(1 - \[ScriptCapitalR]),
ó -> (\[CapitalTheta] - \[ScriptCapitalR]*\[ScriptK])/(
1 - \[ScriptCapitalR]), \[GothicCapitalI] ->
ò + 2*ó, \[GothicCapitalJ] ->
1/3 (ò - ó)^2, \[ScriptCapitalF] -> \[GothicCapitalI] +
Sin[\[CurlyPhi]]/(3 Sqrt[3 + Sin[\[CurlyPhi]]^2])
Sqrt[\[GothicCapitalJ]],
è -> Tan[\[Alpha]]^2*\[ScriptK] + 2*\[ScriptC]*Tan[\[Alpha]],
é -> \[ScriptK]};
Plot[\[Sigma] /.
FindRoot[\[Sigma] == \[CapitalEpsilon]*\[Epsilon]*
Exp[-(\[ScriptCapitalF]/\[ScriptF])^\[ScriptM]] +
2*\[Mu]*\[CapitalTheta] + (è - 2*\[Mu]*\[ScriptK])*(1 -
Exp[-(\[ScriptCapitalF]/\[ScriptF])^\[ScriptM]]) /.
rule, {\[Sigma], 0}], {\[Epsilon], 0, 0.012}, PlotRange -> All]
\[CapitalEpsilon] = 25.34*10^9;
\[CurlyPhi] = 25.732 \[Degree];
\[ScriptC] = 23.915*10^6;
\[CapitalRho] = 65*10^6;
\[Alpha] = 180 \[Degree]/2 + \[CurlyPhi]/2;
\[CapitalTheta] = 0;
\[Beta] = Sin[\[CurlyPhi]]/(3 Sqrt[3 + Sin[\[CurlyPhi]]^2]);
\[ScriptF] = 906.88 + 17.3314*\[CapitalTheta];
\[ScriptM] =
0.6198 - 0.0036*\[CapitalTheta] + 2.5334*10^-5*\[CapitalTheta]^2;
rule = {\[ScriptK] -> ((((1 + \[Mu])*\[CapitalRho]^2*Sin[\[Alpha]])/(
3*\[CapitalEpsilon]*\[Epsilon]) - \[ScriptC])*
Cot[\[CurlyPhi]] - 2*\[ScriptC]*Sin[\[Alpha]])/(
Sin[\[Alpha]]*(1 +
Tan[\[Alpha]])), \[ScriptCapitalR] -> (\[Sigma] -
2*\[Mu]*\[CapitalTheta] - \[CapitalEpsilon]*\[Epsilon])/(
Tan[\[Alpha]]^2*\[ScriptK] + 2*\[ScriptC]*Tan[\[Alpha]] -
2*\[Mu]*\[ScriptK] - \[CapitalEpsilon]*\[Epsilon]),
ò -> (\[Sigma] - \[ScriptCapitalR]*(Tan[\[Alpha]]^2*\[ScriptK] +
2*\[ScriptC]*Tan[\[Alpha]]))/(1 - \[ScriptCapitalR]),
ó -> (\[CapitalTheta] - \[ScriptCapitalR]*\[ScriptK])/(
1 - \[ScriptCapitalR]), \[GothicCapitalI] ->
ò + 2*ó, \[GothicCapitalJ] ->
1/3 (ò - ó)^2, \[ScriptCapitalF] -> \[GothicCapitalI] +
Sin[\[CurlyPhi]]/(3 Sqrt[3 + Sin[\[CurlyPhi]]^2])
Sqrt[\[GothicCapitalJ]],
è -> Tan[\[Alpha]]^2*\[ScriptK] + 2*\[ScriptC]*Tan[\[Alpha]],
é -> \[ScriptK]};
Plot[\[Sigma] /.
FindRoot[\[Sigma] == \[CapitalEpsilon]*\[Epsilon]*
Exp[-(\[ScriptCapitalF]/\[ScriptF])^\[ScriptM]] +
2*\[Mu]*\[CapitalTheta] + (è - 2*\[Mu]*\[ScriptK])*(1 -
Exp[-(\[ScriptCapitalF]/\[ScriptF])^\[ScriptM]]) /.
rule, {\[Sigma], 0}], {\[Epsilon], 0, 0.012}, PlotRange -> All]