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I am trying to simulate contact between a flat rigid plate and a sphere. I am applying a load on the flat rigid plate and the sphere is flexible. How can I avoid this flat from penetrating into the sphere?

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It's not possible to give a discrete answer only by knowing what the geometries are. There are many factors affecting penetration. You still need to give more data about your analysis to get a better answer.

You should first make sure of Geometries, that are well assembled and are input with a good format.

A good practice is adjust to touch and pinball radius. If not you should then check other contact parameters.

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If you are using a non-linear contact (like frictional/frictionless/rough) between these two geometries, then you can go for Normal Lagrange formulation in ANSYS which, by definition, has zero contact penetration between the contact and target faces.

If the contact is linear (like bonded/no-separation) then you can switch the formulation to MPC i.e. Multi Point Constraint, where again the contact penetration is zero.

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