Question

stress-strain curve if the density of the polymer is 0.1 gcm . nhít ielsen p 237) 3.[Non-Gaussian Chain] The non-Gaussian stress-strain curve can be changed/into 30 eRTvn Plot the left hand side vs. λ using n = 75 for range 0 < λ < 7. The inver se Langevin function has an approximation 3x-2.6x2+0.7x3 L(x)

please show work

Answer 1

The plot is created here using Matlab Software. Please refer to matlab library for more information or drop a comment below. Don't forget to give a positive rating if solution is helpful.

Solution :

The Matalb code to create the plot would be as follows,

%% Initialization of given parameters
y = 0:0.2:7; % Lambda from 0 to 7
n = 75;

%% Defining L inverse function
Linv = @(x)(3*x - 2.6*(x.^2) + 0.7*(x.^3)) ./ ((1- x).*(1 + 0.1.*x));

%% Calculating the Left Hand Side(LHs) for each value of Lambda(y)
LHS = Linv(y/sqrt(n)) - (1./(y.^1.5)).*Linv(1./sqrt(n*y));

%% Creating the Plot
plot(y,LHS)
title('LHS v/s Lambda(y)')
xlabel('Lambda(y)')
ylabel('Left Hand Side (LHS)')

And the above code would return the following plot. Note that the steps used to define y would affect the shape of the curve.

LHS ws Lambday) 6 -6 -8 10 Lambda(y)

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