Elastic modulus - danseikeisuu (English spelling) elastic modulus; modulus of elasticity

Japanese: 弾性係数 - だんせいけいすう（英語表記）elastic modulus; modulus of elasticity

Within the proportional limit of an elastic body, stress and strain are proportional, and the proportionality constant between them takes a value specific to the material (it varies depending on temperature). In physics, this value is called the elastic modulus or elastic constant, and in engineering, it is called the coefficient of elasticity. In a general elastic body, there are 36 proportionality constants, but in the case of an isotropic or homogeneous body, there are only two, such as λ and μ, which are called Lame's constants. However, since λ has no physical meaning, the following elastic constants are used exclusively in engineering. (1) Modulus of longitudinal elasticity or Young's modulus E Also called the elongation modulus of elasticity, this is a constant that expresses the proportional relationship σ = E ε between uniaxial normal stress σ and longitudinal strain ε, as when pulling a rod. (2) Modulus of transverse elasticity, rigidity modulus or shear modulus of elasticity G A constant that expresses the proportional relationship τ = G γ between shear stress τ and shear strain γ, as when twisting a round bar. (3) Bulk modulus of elasticity K is a constant that expresses the proportional relationship between the average normal stress σ _m acting on each side and the volumetric strain ε _v (volume change per unit volume, also called the volumetric expansion coefficient), σ _m = K ε _v , like the volume change of a rectangular solid placed in water. Here, σ _m is also called the mean stress or hydrostatic stress, and if the normal stresses are σ ₁ , σ ₂ , and σ ₃ , then σ _m = (σ ₁ + σ ₂ + σ ₃ )/3. (4) Poisson's ratio ν When a round bar is stretched, it stretches in the axial direction and its diameter becomes thinner. Now, the strain in the axial direction is the longitudinal strain ε, and the strain in the diametric direction is the transverse strain -ε'. The negative value of this ratio, i.e. ν = -ε'/ε, is called the Poisson's ratio, and its reciprocal, 1/ν, is called the Poisson's number. The value of ν cannot be greater than 0.5. These coefficients are related by the equation E = 2G (1 + v) = 3K (1 - 2 v), so if any two measurements are known, the others can be calculated.

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:

弾性体の比例限度内では応力とひずみは比例し，その間の比例定数は物質特有の値をとる（温度によって変わる）。この値を物理学では弾性率，弾性定数などと呼び，工学では弾性係数という。一般の弾性体では 36個の比例定数が存在するが，等方・等質の場合には 2個となり，ラメの定数と呼ばれる λ，μがその例になる。しかし，λは物理的意味をもたないので，工学ではもっぱら次の弾性係数を用いる。(1) 縦弾性係数またはヤング率 E　伸び弾性率ともいい，棒材を引っ張るときのように，単軸の垂直応力 σと縦ひずみ εの比例関係 σ＝Eεを表す定数。(2) 横弾性係数，剛性率または剪断弾性係数 G　丸棒をねじるときのように，剪断応力 τと剪断ひずみ γの比例関係 τ＝Gγを表す定数。(3) 体積弾性係数 K　水中に置かれた直方体の体積変化のように，各側面に作用する垂直応力の平均値 σ_m と，体積ひずみ ε_v（単位体積あたりの体積変化。体積膨張率ともいう）の比例関係 σ_m＝Kε_v を表す定数。ここで，σ_m は平均応力または静水圧応力とも呼ばれ，各垂直応力を σ₁，σ₂，σ₃とすれば，σ_m＝（σ₁＋σ₂＋σ₃）/3で与えられる。(4) ポアソン比 ν　丸棒を伸長すれば，軸方向に伸びるとともに直径は細くなる。いま，軸方向のひずみを縦ひずみ ε，直径方向のひずみを横ひずみ－ε'とし，その比に負号をつけた値すなわち ν＝－ε'/εをポアソン比，その逆数 1/νをポアソン数という。νの値は 0.5より大きくはならない。これらの係数の間には関係式 E＝2G（1＋ν）＝3K（1－2ν）があるから，いずれか二つの測定値がわかれば，ほかは計算によって求められる。

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