A CAS Approach to Handle the Anisotropic Hooke’s Law for Cancellous Bone and Wood

Table 4

The stress, strain, elasticity, and compliance tensors components in Voigt’s, Kelvin’s, and MCN patterns.

	Voigt's notations	Kelvin's notations	MCN
Stress	𝜎11	𝜎1	𝜎1
	𝜎22	𝜎2	𝜎2
	𝜎33	𝜎3	𝜎3
	𝜎23	𝜎4	𝜎4
	𝜎13	𝜎5	𝜎5
	𝜎12	𝜎5	𝜎6
Strain	𝜖11	𝜖1	𝜖̂1
	𝜖22	𝜖2	𝜖̂2
	𝜖33	𝜖3	𝜖̂3
	𝜖23	𝜖4	𝜖̂4
	𝜖13	𝜖15	𝜖̂5
	𝜖12	𝜖6	𝜖̂6
Elasticity	𝐶1111	𝐶11	𝐶11
	𝐶2222	𝐶22	𝐶22
	𝐶3333	𝐶33	𝐶33
	𝐶1122	𝐶12	𝐶12
	𝐶1133	𝐶13	𝐶13
	𝐶2233	𝐶23	𝐶23
	𝐶2323	𝐶44	12𝐶44
	𝐶1313	𝐶55	12𝐶55
	𝐶1212	𝐶66	12𝐶66
	𝐶1323	𝐶54	12𝐶54
	𝐶1312	𝐶56	12𝐶56
	𝐶1223	𝐶64	14𝐶64
	𝐶2311	𝐶41	1√2𝐶41
	𝐶1311	𝐶51	1√2𝐶51
	𝐶1211	𝐶61	1√2𝐶61
	𝐶2322	𝐶42	1√2𝐶42
	𝐶1322	𝐶52	1√2𝐶52
	𝐶1222	𝐶62	1√2𝐶62
	𝐶2333	𝐶43	1√2𝐶43
	𝐶1333	𝐶53	1√2𝐶53
	𝐶1233	𝐶63	1√2𝐶63
Compliance	𝐾1111	𝑆11	𝑆11
	𝐾2222	𝑆22	𝑆22
	𝐾3333	𝑆33	𝑆33
	𝐾1122	𝑆12	𝑆12
	𝐾1133	𝑆13	𝑆13
	𝐾2233	𝑆23	𝑆23
	𝐾2323	14𝑆44	12𝑆44
	𝐾1313	14𝑆55	12𝑆55
	𝐾1212	14𝑆66	12𝑆66
	𝐾1323	14𝑆54	12𝑆54
	𝐾1312	14𝑆56	12𝑆56
	𝐾1223	14𝑆64	12𝑆64
	𝐾2311	12𝑆41	1√2𝑆41
	𝐾1311	12𝑆51	1√2𝑆51
	𝐾1211	12𝑆61	1√2𝑆61
	𝐾2322	12𝑆42	1√2𝑆42
	𝐾1322	12𝑆52	1√2𝑆52
	𝐾1222	12𝑆62	1√2𝑆62
	𝐾2333	12𝑆43	1√2𝑆43
	𝐾1333	12𝑆53	1√2𝑆53
	𝐾1233	12𝑆63	1√2𝑆63