Finite Strain14

Finite Strain14 - 12.005 Lecture Notes 14 Finite Strain...

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12.005 Lecture Notes 14 Finite Strain The "paradox" of finite strain and preferred orientation – pure vs. simple shear Suppose: 1) Anisotropy develops as mineral grains grow such that they are preferentially oriented with the "easy slip" direction facilitating deformation. 2) New grain growth is determined by the state of stress. (What else would a mineral grain "know" about?) 3) The state of stress for pure shear and simple shear are identical – pure and simple shear stress differ only by a rotation of 45° in coordinate system. 4) In pure shear there is only one slip direction, whereas in pure shear, 2 systems could be active. Paradox : If the stress state is the same, how does the rock "know" to have 1 preferred orientation in simple shear, but not in pure shear? Figure 14.1 Up to now, we have considered infinitesimal strain, where e ij = ( u i / x j + u j / x i )/2 <<1. For the kinds of deformations common in structural geology, as well as for the deforming telephone book example shown in class, this condition of "infinitesimal" deformation no longer holds. Life becomes complicated. In particular, it's important to know whether one is coming or going:
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Reference frame : Consider a medium undergoing motion & deformation, with the displacement a (vector) function of position. x3
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This note was uploaded on 10/25/2010 for the course MIT Geodynamic taught by Professor Ywn during the Fall '10 term at MIT.

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Finite Strain14 - 12.005 Lecture Notes 14 Finite Strain...

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