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I am looking for any software, or scientific works, or search phrase in the field of simulating graphic modeling of squeezing objects. I would like to simulate packing very oddly shaped soft elastic objects in a larger rectangular 2-D container. I am not interested in finding optimal packing solution. I am interested in modeling the squeezing of the shapes which depends on material properties and applied force. The objects are made of rubber or clay substances. Object shapes may be distorted depending on the properties of the substance and applied force.

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COMSOL Multiphysics

The COMSOL Multiphysics software has a Structural Mechanic module that can help you.

It has a good interface to design your system (with CAD tools) and add the possibility to add the type of physics you need to solve. One of the main feature is that you can connect one type of physics, for example, mechanical study, with thermal study.

Here you can find all the specifications.

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Rhinocerous-3d

I agree with the COMSOL Multiphysics answer.

In addition to that, you can use Rhinocerous-3d if simulating the scenario is the idea behind your question. But if you are just looking forward to visualize the effects, you can use Blender.

Both of them have a lot of tutorials online.

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