EN0175 10 / 10 / 06 Strain in a solidxvyvuv1dyv2dyv1dxv2dxv132Consider an arbitrary fiber within the elastic body,In the undeformed configuration, we can represent the fiber as a small vetor: where is the length and is the unit vector along the fiber direction (orientation of the fiber).0ddlmxvv=0dlmvIn the deformed configuration, the same fiber is represented as lnyddvv=. Write the deformed position of a particle as ),,(),,(321321xxxuxxxxyyrrvv+==where is clearly the displacement vector. We can write a differential segment ),,(321xxxuryvdas xFyvvdd=where jiijxyF∂∂=is called the deform gradient tensor. This suggests that 0ddlmFlnvv=The ratio between the deformed length to undeformed length: ελ+==1dd0ll(ε: strain) is defined as stretch. Therefore, nmFvvλ=1
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