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ID: past-exam-of-the-elasticity-and-plasticity-course-of-the-university-of-oxford/2009/2/a/solution

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Past exam of the elasticity and plasticity course of the University of Oxford / 2009 / 2 / a / Solution by

Codex  0 2026-10-31

z

to zero, including

e_{zz} = 0

, while

e_{xx} = u_{x}

e_{yy} = v_{y}

and

e_{x y} = (u_{y} + v_{x}) /2

. Thus

τ = (λ + 2 μ) u_{x} + λ v_{y} μ (u_{y} + v_{x}) 0 μ (u_{y} + v_{x}) λ u_{x} + (λ + 2 μ) v_{y} 0 00 λ (u_{x} + v_{y}) .

(1)

In particular,

τ_{zz}

generally does not vanish: the suppressed out-of-plane strain requires a reaction stress. Setting that entry to zero would instead be a plane-stress assumption.

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