Any second order tensor, such as strain tensor, has three eigenvalues, which are more commonly known as principal values. Using the method described before, the three eigenvalues of strain may be found from its characteristic equation (2.48)ε3−Iεε2+IIεε−IIIε=0, with the following...
沪江词库精选strain-rate equation是什么意思、英语单词推荐 应变率方程 相似短语 strain rate equation 应变率方程 soil strain rate behaviour 土壤应变比特性 strain energy rate 应变能释放率 strain rate tensor 应变率张量 rate of strain 【化】 应变率 strain rate 应变速率,变形速度 rate of ...
Since the mixed partial derivatives must be independent of order, a consequence of the last equation is that ∂σij([ε], θ)/∂εkl = ∂σkl([ε], θ)/∂εij, which requires that Cijkl = Cklij, or equivalently that the matrix [c] be symmetric, [c] = [c]T, reducing ...
We use this equation to obtain a simplified identity for the growth of enstrophy for mild solutions that depends only on the strain tensor, not on the nonlocal interaction of the strain tensor with the vorticity. The resulting identity allows us to prove a new family of scale-critical, ...
4.8.5 Governing equation 4.8.5.1 Equilibrium equations The governing equation for equilibrium of the workpiece is given by (4.7)∂σij∂xj=0 where σij is the Cauchy stress tensor with i, j = 1, 2, and 3. 4.8.5.2 Constitutive equation The analysis of metal forming processes is based...
Equation (5) then reduces to $$\begin{array}{ll}\Delta\,=\,\frac{{\hslash }^{2}{k}_{0}^{2}}{2{m}_{l}}{e}^{-{({k}_{0}{l}_{z})}^{2}}+\frac{{V}_{0}}{2}{e}^{-{(2{k}_{0}-{G}_{\lambda })}^{2}{l}_{z}^{2}/4}\\\quad-i{\varepsilon }_{xy...
Equation (4) is a new expression for the total strain tensor consisting of thermal, elastic and plastic parts, and more details about the new decomposition of deformation Gradient and total strain were displayed in our early work25. Although the deformation gradient can be decomposed as \({\var...
The equality equation is established such that the sum of the moments generated by muscle forces and the moment of the knee load balance each other at the femoral head. Because the hip joint is a ball-and-socket joint, the moment from the acetabulum to the femoral head is ignored (Shahar...
Asghari, M., Naghdabadi, S., Sohrabpour, S.: Some basis-free expressions for stresses conjugate to Hill’s strains through solving the tensor equation AX+XA=C. Int. J. Solids Struct. 45, 3584–3595 (2008) Article MATH Google Scholar Atluri, S.N.: On constitutive relations at finit...
Any second order tensor, such as strain tensor, has three eigenvalues, which are more commonly known as principal values. Using the method described before, the three eigenvalues of strain may be found from its characteristic equation (2.48)ε3−Iεε2+IIεε−IIIε=0, with the following...