I am the author of the book ‘’Soft-Material Robotics" (ISBN 978-1680832648).
In chapter 3 of the book, I summarized three methods for modelling kinematics and dynamics of soft bodies for robots.
A simulator that could be useful for you is Voxcad. It used voxels to simulate soft bodies. For each voxel, you may choose material mechanical properties such as modulus.
Existing physics engines may have soft-body mechanics, but I have not used them for that purpose myself.
What about VoxCad, a voxel based approach that allows defining properties of soft volumetric elements. They can be controlled by varying environmental variables like temperature.