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It is observed from fFrequentrequency experimentation has 1 shown that drawing pulling the identical bars from of steel and rubber having the same initial lengths by the same axial force, and consequentlythus the same axial stress, results of stress in different elongations from of these two bars. This material In mechanics, the difference the two bars in mechanical the materials of the two bars is represented by the therelationship between the components of stress and the strain. By The writingexpressing 2 each of these likeas a column matrix of column, i.e. , 3

(1)

(2)

 

have us

we obtain

(3)

whereHere, X is a 5 x× 4 5 matrix that characterizes the material of the body, and is generally. It is generally calledknown as the matrix of elasticity andmatrix ;5 its components elasticity’sare called elasticities or elastic constants of elasticity for the material of the body. Note that The shear strains have been multiplied by 2 in eqn.Eq. (2); the definitions (1) and (2) make ensure that. The stress–strainequation (3), in other words the relation shown in between the stresses and strains, areEq. (3) is called known as the relation constitutive relation for the material of the body. It is assumed in Eq. (3) that the body is stress- free 6 in the reference configuration of reference from which the strain d is measured.

Explanations

 

It is observed from frequency frequent experimentation has 1   shown that drawing pulling 2   identical bars from of steel and rubber by the same axial force, and consequentlythus the same axial stress, results of stress in different elongations from of 3   these two bars. This material In mechanics, the difference the two bars in mechanical the materials of the two bars is represented by the therelationship between the components of stress and the strain. By The writingexpressing each of these likeas a column matrix of column, i.e.,

(1)

(2)

 

have us

we obtain

(3)

where X is a 5 x× 4   5 matrix that characterizes the material of the body, and is generally calledknown as the matrix of elasticity andmatrix ; 5 [A5]  its components elasticity’sare called elasticities or elastic constants of elasticity for the material of the body. Note that The shear strains have been multiplied by 2 in eqn.Eq. (2); the definitions (1) and (2) make ensure that. The equation (3), in other words the relation between the stresses and strains shown in , areEq. (3) is called known as the relation constitutive relation for the material of the body. It is assumed in Eq. (3) that the body is stress- free 6  in the reference configuration of reference from which the strain d is measured.

Explanations

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