 Solution

ID: past-exam-of-the-elasticity-and-plasticity-course-of-the-university-of-oxford/2009/1/a/solution

e_{ij} = \frac{1}{2} (\frac{\partial u _{i}}{\partial x _{j}} + \frac{\partial u _{j}}{\partial x _{i}}) .

Its diagonal entries are infinitesimal normal extensions; twice an off-diagonal entry is the corresponding engineering shear strain. An infinitesimal rigid rotation has an antisymmetric displacement gradient tensor and therefore contributes no linearized strain.

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