透過頻繁的試驗，可以觀察到，當使用相同的軸向力拉伸兩個大小、外形完全相同的鋼棒和橡膠棒（這意味著，將產生相同的軸向應力）時，兩種棒體產生了不同的伸長量。在力學中，兩種棒體材料的差異可由應力和應變分量之間的關係來表示。透過將這種關係表示為行矩陣，即
(1)
(2)
我們將得到
(3)
其中，X 為一個可表徵棒體材料的 5×5 矩陣，通常被稱為彈性矩陣；它的分量被稱為棒體材料之彈力或彈性常量。在方程式 (2) 中，剪切應變已乘以 2；定義 (1) 和 (2) 確保
。方程式 (3) 呈現的應力與應變之間的關係被稱為棒體材料的物性關係。在方程式 (3) 中，假定在測量應變 d 的參考組態中，棒體不受應力作用。
翻譯: 您學科領域的翻譯師翻譯您的原稿
It is observed from frequent experimentation that drawing identical bars from steel and rubber by same axial force and consequently the same axial stress, results in different elongations from the two bars. In mechanics, the differences of the two bars is represented by the relationship between the components of stress and strain. The writing of these like a matrix of column, i.e
(1)
(2)
we have
(3)
where X is a 5 x 5 matrix that characterizes the material of the body, and is generally called the matrix of elasticity and its components are called elasticity’s or constants of elasticity for the material of the body. Note that shear strains have been multiplied by 2 in eqn. (2); the definitions (1) and (2) make sure that . The equation (3), in other words the relation between the stresses and strains, are called the relation constitutive for the material of the body. It is assumed in Eq. (3) that the body is stress free in the configuration of reference from which the strain d is measured.
雙語核對：雙語核對師依照原文檢查譯文是否正確，並修正錯誤
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.
編修：英文母語編修師改善文章整體的流暢度與呈現方式
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.
完稿：翻譯完成品準時遞交給客戶
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.
