Solving solid mechanics problems with material plasticity

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kevinarden
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Re: Solving solid mechanics problems with material plasticity

Post by kevinarden »

The solid mechanics solver in Elmer, and in most FEA tools is solving the equation F=Kx Hooke's law. K is the stiffness matrix, F force, x displacement. F is supplied by the user as boundary condition loads. K is supplied by the user with a material model, then X is solved for. The standard material model in solid mechanics is E, and Poisson ratio. In linear solution E is constant. In plastic solution E is a function of strain. However to calculate strain you must first have an E to develop K and solve F=Kx. In plastic material analysis this is referred to as a material model. A linear material model E is constant, a non-linear material model E is a function of strain.

However in FEA the user is supplying Force and the geometric properties of the model, so for example an tensile test model, user supplies force and area. Therefore stress is equal to Force/Area, displacement is equal to x=F/K, and K=Area*E/L.

In plastic material model there are too many unknowns to solve F=Kx unless you have the stress-strain curve.

One could write another solver that solves the solid mechanics problem a different way than F=Kx, but I don't know of any.
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