# For a plane strain problem, which strain value is correct if the problem is characterized by the displacement field ux=ux(x,y), uy=uy(x,y) and uz=0?

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For a plane strain problem, which strain value is correct if the problem is characterized by the displacement field ux=ux(x,y), uy=uy(x,y) and uz=0?

(a) εxy=0

(b) εxz=0

(c) εyz≠0

(d) εxz≠0

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I want to ask this question from Plane Elasticity topic in division Plane Elasticity of Finite Element Method

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Right choice is (b) εxz=0

For explanation: The plane strain problems are characterized by the displacement field ux=ux(x,y), uy=uy(x,y) and uz=0, where (ux, uy, uz) denote the components of this displacement vector u in the (x, y, z) coordinate system. The displacement field results in the following strain field:

$\epsilon_{xz}=\epsilon_{yz}=\epsilon_{zz}=0, \epsilon_{xx}=\frac{\partial u_x}{\partial x}, 2\epsilon_{xy}=\frac{\partial u_x}{\partial y}+\frac{\partial u_y}{\partial x}$ and $\epsilon_{yy}=\frac{\partial u_y}{\partial y}$.

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