The problem is that the polyfit call returned NaN for both parameters. I substituted a simple nonlinear power relation and used fminsearch to solve it. The fit is not excellent, however the parameters are finite. I used those in the second plot. (The added first plot simply showed the regression result of the data and the fit.)
stress = [0;0.0464;0.1940;0.4962;0.5040;0.5566;0.6040;0.6260;0.6240;0.6100;0.5880;0.5720];
strain = [0;0.2220;0.3600;0.4980;0.5040;0.8820;2.6640;4.4400;5.9100;6.7380;7.1460;7.2900];
coeffL = polyfit(strain,stress,1);
mL = coeffL(1);
bL =coeffL(2);
yL = @(x) mL*x+bL;
objfcn = @(b,x) b(2).*x.^b(1);
B = fminsearch(@(b)norm(stress-objfcn(b,strain)), rand(2,1)*10)
figure
plot(strain, stress, 'p')
hold on
plot(strain, objfcn(B,strain), '-r')
hold off
grid
coeffP = polyfit(log10(strain),log10(stress),1)
% mP = coeffP(1);
mP = B(2);
bP = B(1);
yP = @(x) bP.*(x.^mP);
coeffE = polyfit(strain,log(stress),1);
mE = coeffE(1);
bE = exp(coeffE(2));
yE = @(x) bE.*exp(mE.*x);
figure(2)
fplot(yL,[0,4]);
hold on
fplot(yP,[4,8]);
fplot(yE,[8,12]);
Experiment to get different results.
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