Example 10 with linear elasticity

[Olymptopus]

Hi everyone,
I am new to MFEM and honestly to FEM in general.
I am trying to modify the example 10 to use a linear elasticity model instead of the hyperelastic one.
For this I consulted example 2 and tried to apply the ElasticityIntegrator instead of the HyperelasticNLFIntegrator.
This should be quite straightforward, but I seem to miss something fundamental, since the simulation results do not make any sense: The beam seems to collapse into itself in a very small period of time and is quickly deforming beyond recognition even if I set the initial velocity to zero everywhere.
These are the changes I made in ex10.cpp so far:

• Changed the type of H in HyperelasticOperator and ReducedSystemOperator to BilinearForm (including the constuctors etc.)
• Modified the HyperelasticOperator Constructor:

ConstantCoefficient lambda_((K - 2.0*mu/3.0));  
ConstantCoefficient mu_(mu);
H.AddDomainIntegrator(new ElasticityIntegrator(lambda_,mu_));
H.Assemble(skip_zero_entries);
H.FormSystemMatrix(ess_tdof_list, tmp);

instead of

model = new NeoHookeanModel(mu, K);  
H.AddDomainIntegrator(new HyperelasticNLFIntegrator(model));  
H.SetEssentialTrueDofs(ess_tdof_list);

• Modified one line in Operator &ReducedSystemOperator::GetGradient:

SparseMatrix *grad_H = &H->SpMat();

instead of

SparseMatrix *grad_H = dynamic_cast<SparseMatrix *>(&H->GetGradient(z));

I am happy to provide more information if needed, but I assume that I made some fundamental mistake in regards to the elasticity model that can be spotted in my changes. Thank you for your help!

[Olymptopus]

I am going to quickly answer my own question for future beginners like me:
The BilinearForm a in example 2 is applied to the relative displacements, while the NonlinearForm H in example 10 operates on the absolute positions x.
So, in addition to replacing the NonlinearForm with a bilinear one, I had to change the initial condition for x to be zero (thus representing relative displacements) and change the visualization to apply the relative deformation to the original node positions.