In homogeneous and isotropic solids, there are two kinds of waves, pressure waves and shear waves.
Dalam benda padat homogene dan isotropik, ada dua jenis gelombang, gelombang tekanan dan gelombang geser.
Shear modulus models that have been used in plastic flow computations include: the Varshni-Chen-Gray model developed by and used in conjunction with the Mechanical Threshold Stress (MTS) plastic flow stress model.
Model-model modulus geser yang sudah digunakan dalam komputasi aliran plastik termasuk: Model modulus geser MTS yang dikembangkan oleh dan digunakan dalam hubungan dengan model tegangan aliran plastik "Mechanical Threshold Stress" (MTS).
μ 0 + ∂ μ ∂ p p η 1 3 + ∂ μ ∂ T ( T − 300 ) ; η :ρ ρ 0 +{\frac {\partial \mu }{\partial p}}{\frac {p}{\eta ^{\frac {1}{3}}}}+{\frac {\partial \mu }{\partial T}}(T-300);\quad \eta :={\frac {\rho }{\rho _{0}}}} where, μ0 is the shear modulus at the reference state (T300 K, p0, η1), p is the pressure, and T is the temperature.
[ ( μ 0 + ∂ μ ∂ p p η 1 / 3 ) ( 1 − T ^ ) + ρ C m k b T ] ; C :( 6 π 2 ) 2 / 3 3 f 2 {{\mathcal {J}}({\hat {T}})}}\left[\left(\mu _{0}+{\frac {\partial \mu }{\partial p}}{\cfrac {p}{\eta ^{1/3}}}\right)(1-{\hat {T}})+{\frac {\rho }{Cm}}~k_{b}~T\right];\quad C:={\cfrac {(6\pi ^{2})^{2/3}}{3}}f^{2}} di mana J ( T ^ ) :1 + exp ⁡ [ − 1 + 1 / ζ 1 + ζ / ( 1 − T ^ ) ] for T ^ :T T m ∈ [ 0 , 1 + ζ ] , }({\hat {T}}):=1+\exp \left[-{\cfrac {1+1/\zeta }{1+\zeta /(1-{\hat {T}})}}\right]\quad {\text{for}}\quad {\hat {T}}:={\frac {T}{T_{m}}}\in [0,1+\zeta ],} dan µ0 adalah modulus geser pada suhu 0
The Nadal-Le Poac (NP) shear modulus model is a modified version of the SCG model.
Model modulus geser Nadal-Le Poac (NP) adalah suatu versi modifikasi model SCG.
The empirical temperature dependence of the shear modulus in the SCG model is replaced with an equation based on Lindemann melting theory.
Ketergantungan modulus geser secara empiris terhadap suhu pada SCG model digantikan dengan suatu persamaan yang berdasarkan pada teori peleburan Lindemann.
[ ( μ 0 + ∂ μ ∂ p p η 1 3 ) ( 1 − T ^ ) + ρ C m T ] ; C :( 6 π 2 ) 2 3 3 f 2 {{\mathcal {J}}\left({\hat {T}}\right)}}\left[\left(\mu _{0}+{\frac {\partial \mu }{\partial p}}{\frac {p}{\eta ^{\frac {1}{3}}}}\right)\left(1-{\hat {T}}\right)+{\frac {\rho }{Cm}}~T\right];\quad C:={\frac {\left(6\pi ^{2}\right)^{\frac {2}{3}}}{3}}f^{2}} where J ( T ^ ) :1 + exp ⁡ [ − 1 + 1 / ζ 1 + ζ / ( 1 − T ^ ) ] for T ^ :T T m ∈ [ 0 , 6 + ζ ] , }({\hat {T}}):=1+\exp \left[-{\frac {1+1/\zeta }{1+\zeta /\left(1-{\hat {T}}\right)}}\right]\quad {\text{for}}\quad {\hat {T}}:={\frac {T}{T_{m}}}\in [0,6+\zeta ],} and μ0 is the shear modulus at absolute zero and ambient pressure, ζ is an area, m is the atomic mass, and f is the Lindemann constant.
[ ( μ 0 + ∂ μ ∂ p p η 1 / 3 ) ( 1 − T ^ ) + ρ C m k b T ] ; C :( 6 π 2 ) 2 / 3 3 f 2 {{\mathcal {J}}({\hat {T}})}}\left[\left(\mu _{0}+{\frac {\partial \mu }{\partial p}}{\cfrac {p}{\eta ^{1/3}}}\right)(1-{\hat {T}})+{\frac {\rho }{Cm}}~k_{b}~T\right];\quad C:={\cfrac {(6\pi ^{2})^{2/3}}{3}}f^{2}} di mana J ( T ^ ) :1 + exp ⁡ [ − 1 + 1 / ζ 1 + ζ / ( 1 − T ^ ) ] for T ^ :T T m ∈ [ 0 , 1 + ζ ] , }({\hat {T}}):=1+\exp \left[-{\cfrac {1+1/\zeta }{1+\zeta /(1-{\hat {T}})}}\right]\quad {\text{for}}\quad {\hat {T}}:={\frac {T}{T_{m}}}\in [0,1+\zeta ],} dan µ0 adalah modulus geser pada suhu 0