Strain Driven Analysis

4 months ago by
Hello everyone,

Is it possible to perform annonlinear analysis by strain driven ? I mean, I do not want to use any traction or body force but I want to define incremental strain as a boundary condition. How can I define such a input ?

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What exactly do you mean? You can prescribe Dirichlet or Neumann boundary conditions. For the balance of linear momentum this means either  $\mathbf{u}=\mathbf{u}_0\left(\mathbf{x},t\right)$u=u0(x,t)   or   $\mathbf{\sigma}\cdot\mathbf{n}=\mathbf{t}_0\left(\mathbf{x},t\right)$σ·n=t0(x,t)   on the boundary. You could reformulate this in terms of strain using a constitutive equation for the stress I guess...
written 4 months ago by klunkean  
I do not want to apply  $u=u_0\left(x,t\right)$u=u0(x,t) but I want to apply   $\varepsilon=\varepsilon_0\left(x,t\right)$ε=ε0(x,t) where
Eps = 0.5*(nabla_grad(u) + nabla_grad(u).T)​
written 4 months ago by Christian  
Can you derive a displacement from your desired strain? For instance, if you wanted a 0.01 strain in a bar with length L, you can fix one end an impose a displacement of 0.01*L at the other end. If you cannot do it, I believe you need to use FEM that solve for the strain or stress (mixed methods).
written 4 months ago by Miguel  
For a nonlinear problem that approach will not work. Do you have any example about that problem with mixed methods ?
written 4 months ago by Christian  
Nope, sorry. Do a literature search for mixed methods in elasticity. If you have large deformations and your stress is not symmetric, that will be something to take into account in your search.
written 4 months ago by Miguel  
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