Tensor and Vector Calculus

If you really know calculus I think you will know why the symbols mean:)

3:44 . . . Topic 1 - Preliminary Mathema... . . . Fourth rank or order (e.g. elastic tensor ) 4th order is a mapping between two 2nd order tensors 27/31 Stress-strain relation like Hooke's law o=C: 8 or Off = CikiEk "= EE EE Chee, exe, = Cykee, exe, 3x3x3x3 =81 i=1 j=1 k=1 1=1 Stress and strain are symmetric 61 0 12 613 Ell 812 813 8 22 8 23 36 5 21 0 22 0 23 8 21 031 032 0 33 8 33 Most general elastic W =10ijEij = CijntEijEx Cijkl = Cklij 21 solids have 21 constants Review on vector analysis Two vectors (the angle between them is denoted by 0) X 3 u = ujetuze2tuze3 , v = vieltvze2tvze3 Dot product e3 e2 Geometric definition s = | u | | v|cose (0