Tekraren yapılan deneyler, özdeş çelik ve lastik çubukların aynı eksenel kuvvetle çekilmesinin, yani aynı eksenel gerilmenin, bu iki çubukta farklı uzamalara neden olduğunu göstermiştir. Mechanicste iki çubuğun malzemelerindeki farklılık gerilme ve gerinim arasındaki bağıntı ile temsil edilir. Her ikisi;
(1)
(2)
Şeklinde sütun matrisleri olarak ifade edildiğinde:
(3)
elde edelir. Burada X cismin malzemesini karakterize eden 5 × 5 matristir ve genellikle elastisite matrisi olarak adlandırılır; bu matrisin bileşenlerine ise cismin malzemesinin elastisiteleri veya elastik sabitleri denir. Denklem (2)’deki kayma gerinimleri 2 ile çarpılır; (1) ve (2) tanımlamaları 
olduğunu göstermektedir. Denklem (3)’te gösterilen gerilme ve gerinim arasındaki bağıntı, cismin malzemesinin bünye denklemi olarak bilinir. Denklem (3)’te, d geriniminin ölçüldüğü referans durumda gerilme olmadığı kabul edilir.
It is observedfrom frequent experimentation that drawing pulling 1identicalbars from steeland rubber by the same axial force,and consequentlythe sameaxial stress, results of stress indifferent elongations from the two bars. In mechanics, the differences difference inthe materials 2of the two bars is represented by the relationship betweenthe components of stress and the strain. TheBywriting each ofthese likeasa matrix of column matrix,i.e.,3
(1)
(2)
we have
(3)
where X is a 5 x 5 matrix that characterizes thematerial of the body, and is generallycalled the matrix of elasticityand itscomponents are called elasticity’s elasticities 4or elastic constantsof elasticity 5for the material of the body.Note that shear strains have been multiplied by 2 in eqn. (2); the definitions (1) and(2) make ensure6 that. Theequation (3), in other words the relation between the stresses and strains, areiscalled the relationconstitutive relation for the material of the body.It is assumed in Eq. (3) that the body is stress free in the reference configuration of reference from which the strain d is measured.
It is observed from fFrequent1experimentation has shown that drawing pulling 2the identical barsof from steel and rubber having the same initial lengths by the sameaxial force, and consequently thus thesame axial stress, results ofstress in different elongations from of these two bars. In mechanics, the differences difference in the materials 3of the two bars is represented by the relationship betweenthe components of stress and the strain.TheBywritingexpressing 4each of these likeasa matrix of column matrix5,i.e.,6
(1)
(2)
we haveobtain
(3)
whereHere,X is a 57 x× 5 matrix that characterizes thematerial of the body,and is generally. It is generally calledknown asthe matrix of elasticity andmatrix;8 itscomponents are called elasticity’s elasticities 9or elastic constants10of elasticity forthe material of the body. Note thatThe shear strains have been multiplied by 2 in eqn.Eq. (2); the definitions (1)and (2) makeensure11 that. Thestress-strainequation (3), in other words the relation shown inbetween the stresses and strains, are Eq. (3) is called known as therelation constitutiverelationfor the material of the body. 12It is assumed in Eq. (3) that thebody is stress-13free in the reference configuration of reference fromwhich the strain d is measured.
Frequent experimentation has shown that pulling the bars of steel and rubber having the same initial lengths by the same axial force, and thus the same axial stress, results in different elongations of these two bars. In mechanics, the difference in the materials of the two bars is represented by the relation between the components of stress and strain. By expressing each of these as a column matrix, i.e.,
(1)
(2)
we have
(3)
Here, X is a 5 × 5 matrix that characterizes the material of the body. It is generally known as the elasticity matrix; its components are called elasticities or elastic constants for the material of the body. The shear strains have been multiplied by 2 in Eq. (2); definitions (1) and (2) ensure that . The stress–strain relation shown in Eq. (3) is known as the constitutive relation for the material of the body. It is assumed in Eq. (3) that the body is stress-free in the reference configuration from which the strain d is measured.
