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NNSE618-L23-stress-strain

NNSE618-L23-stress-strain - 1 Lecture contents Stress and...

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NNSE 618 Lecture #23 1 Lecture contents Stress and strain Deformation potential
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NNSE 618 Lecture #23 2 Stress = force/area ( 3x3 symmetric tensor ! ) Stresses applied to a infinitely small volume: Strain = D displacement/ D coordinate ( 3x3 symmetric tensor ! ) Diagonal (axial) strain components: Explanation of shear strain components: Few concepts from linear elasticity theory : Stress and Strain i j j i ij x u x u 2 1 ji ij i i ii x u 6 independent components 6 independent components
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NNSE 618 Lecture #23 3 Few concepts from linear elasticity theory : Hooke’s law Stress- Strain relation: extension of Hooke’s law (linear regime): Due to symmetry of stress-strain tensors the matrix of elastic moduli (elastic stiffness constants) can be reduced to 6x6: Note: for non-diagonal strain components For cubic crystals, only 3 constants are independent: ij ij 2
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NNSE 618 Lecture #23 4 Effects of crystal symmetry on elastic constants
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NNSE 618 Lecture #23 5 For cubic crystal (3 constants are independent) : Anisotropy ratio For isotropic material, A=1,
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