Suppose a free sponge ball is being compressed, due to applying a known force in a specific direction.
The ball's shape will be distorted. Given are the direction of the applied force, as well as its magnitude.
Can I calculate the deformation that the ball experiences in any other direction?
Does it depend on some tensor?
There are soft body simulations using a spring mesh and pressure. The soft bodies are a closed mesh and the simplest is a spherical/circle (3D/2D). The shapes are then inflated to a certain pressure. Numerical methods are used to create the realistic simulation of elastic deformation as a result of collisions.
Let's suppose that you mean something similar to what @ChetMiller proposed in the comments. That is, a sphere between two place frictionless walls or, equivalently, a sphere with two diametrically opposing force.
If we express this problem in spherical coordinates the stress, strain and displacement are independent of the azimuth. That means that it can be expressed in axisymmetric solid spherical harmonics. The expressions are rather long, so if you are interested you could read reference 1.
Note: A foam is probably not well represented by this model since it will present non-linear behavior. Probably, a hyperelastic behavior comes into place.
Can I calculate the deformation that the ball experiences in any other direction?
If you are asking to calculate the lateral strain of an object that results from longitudinal stress and strain, the material property involved is Poisson’s ratio $\nu$, which is the ratio of latitudinal strain to longitudinal strain when the material is subjected to longitudinal stress. The latter is determined by Hooke’s law and Young’s modulus.
The problem is Hooke’s law requires linear elastic behavior, and that may not apply to the sponge ball.
Hope this helps.
