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I'm looking for an elastic material (e.g., a rubber), whose tangential elastic modulus E is lower than 1 MPa (0.5 MPa would be enough). Anyone has an idea of which kind of rubber could fit this specification? I need a tube (16-25 mm diameter, and 1-4 mm wall thickness) of this material to simulate an artery (e.g., aorta) in a biomedical engineering application at room temperature. Unfortunately, arteries have a very low Young Modulus and it is very difficult to find a material with characteristics as close as possible to the ones of an artery. Thank you for any helpful information.

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Silicone gels can be this soft.

Your requirement is quite extreme, so you are unlikely to find a ready tube. But you can find a solution, that will harden in a required shape.

So, I suggest to look for liquid silicone gels, that harden when mixed with hardener, like epoxy. An example, that is probably too soft, 0.2 MPa, but gives an idea: https://www.wacker.com/h/de-se/medias/6982-EN.pdf

It seems tupical silicone is too tough for your use, as it is about 5 MPa, and tupical silicone gel is too soft for your use, it is about 0.01 MPa. So look for tough silicone gel. I think it is easier to make silicone gel harder, than silicone softer.