https://en.wikipedia.org/wiki/Birefringence

When a material is birefringent, it will exhibit different indicies of refraction $n$ for light polarized along different axes. Light with polarization parallel to the optical axis (need definiton) will experience an index of refraction $n_o$, while light with perpendicular polarization will experience a larger index of refraction $n_e$. The difference between these two indices then characterizes the birefringence of a material ($\Delta n = n_e - n_o$).

In the case of acrylic, under ambient conditions it typically does not exhibit birefringence. When a force is applied, the material may distort and exhibit stress birefringence. This is known as Photoelasticity, and can be used to characterize materials and find otherwise invisible defects and weak points in objects. It can also be used to analyze stress in structures (such as bridges) by building a scale model from stress birefringent materials.

Mathematically, the observed fringes can be modeled with Breweter's Stress-Optic Law. The induced phase shift $\Delta$ is equal to the material thickness $t$ over the incident light's wavelength $\lambda$ times $2\pi$ times a stress-optic coefficient $C$ and the differences in stresses $\sigma_1 - sigma_2$.