Vôùi dydz z x y x 2 dxdz z x x x 2 dxdy y x x x 2 dz z x dy y x dx 1 x x dx dx

Vôùi dydz z x y x 2 dxdz z x x x 2 dxdy y x x x 2

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Vôùi: dydz z x y x 2 dxdz z x x x 2 dxdy y x x x 2 dz z x dy y x dx 1 x x dx dx ' ' ' ' ' ' 2 2 ' 2 2 ' 2 2 ' 2 2 ' (2.80) Töông töï: 2 2 ' 2 2 ' dz dz va ø dy dy Neáu ij laø kí hieäu kronecker: 3 1 k , j , i j i khi 0 j i khi 1 ij (2.81) Ñaïi löôïng trong ngoaëc laø 1 tensor haïng hai vaø goïi laø tensor bieán daïng, noù coù tính ñoái xöùng ñoái vôùi caùc chæ soá i & j. Ta duøng caùc kí hieäu ñeå chæ caùc thaønh phaàn tensor ñoù: ij j ' k i ' k ij x x x x e 2 (2.82) Neáu kí hieäu 3 2 1 u , u , u u thì: k ' k k ki i k i ' k k k ' k x x u x u x x x u x (2.83)
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Giaùo Trình CÔ CHÖÔNG 2: ÖÙNG SUAÁT VAØ BIEÁN DAÏNG 90 TS. Vuõ Coâng Hoøa Thay (2.83) vaøo (2.82): j k i k j k ki i k kj ij x u x u x u x u 2 1 e (2.84) j k i k j i i j ij x u x u x u x u 2 1 e (5.85) Neáu chuyeån qua kí hieäu thoâng thöôøng ta seõ coù 6 thaønh phaàn ñoäc laäp cuûa tensor bieán daïng: zy yz zx xz yx xy 2 2 2 zz 2 2 2 yy 2 2 2 xx e z w y w z v y v z u y u y w z v 2 1 e e z w x w x v x v z u x u x w z u 2 1 e e y w x w y v x v y v x u x v y u 2 1 e z w z v z u 2 1 z w e y w y v y u 2 1 y v e x w x v x u 2 1 x u e Vaø Tensor bieán daïng: zz zy zx yz yy yx xz xy xx e e e e e e e e e T (2.87) Treân ñaây laø caùch dieãn taû ñuùng ñaén cuûa bieán daïng baát chaáp caáp cuûa ñoä lôùn cuûa chuyeån vò.
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