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Solve PDEs that model plane stress and strain in solid
mechanics

In structural mechanics, the equations that relate stress and
strain arise from the balance of forces in the material medium. Plane
stress is a condition that prevails in a flat plate in the * x*-

* u* is the displacement in the

Plane strain is a deformation state where there are no displacements
in the * z*-direction, and the displacements in the

Shear modulus

*G*=*E*/(2(1 +*ν*))Poisson's ratio

*ν*(plane stress)*µ*= 2*G**ν*/(1 –*ν*))(plane strain)*µ*= 2*G**ν*/(1 – 2*ν*))von Mises effective stress $$\sqrt{{\sigma}_{1}^{2}+{\sigma}_{2}^{2}-{\sigma}_{1}{\sigma}_{2}}$$ (plane stress)

von Mises effective stress $$\sqrt{\left({\sigma}_{1}^{2}+{\sigma}_{2}^{2}\right)\left({\nu}^{2}-\nu +1\right)+{\sigma}_{1}{\sigma}_{2}\left(2{\nu}^{2}-2\nu -1\right)}$$ (plane strain)

For details, see Plane Stress and Plane Strain.

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