The relationship between stresses and rates of the strains of flowing coarse particle powder beds (ceramic particles diameter
Dp=5mm) were calculated by the 3-dimensional Distinct Element Method (D. E. M.). The experimental relationships were also obtained under the same conditions. The comparison of calculated and experimental stress-strain rate relationships shows that both the dynamic shear and the dynamic normal stresses, which are the values of the differences between measured and static stresses divided by the static normal stress, are expressed by the linear relationships of the strain rates of the flowing particulate beds over a fairly broad strain rate. The following equations show the stress-strain rate relationships in the results of the present investigation.
τ
xy=-1/2
A1(∂
u/∂
y)|σ
y0|+τ
xy0σ
y=-
A2(∂
v/∂
y)|σ
y0|+σ
y0, where τ
xy and σ
y are the stresses of the flowing powder beds, τ
xy0 and σ
y0 are the static stresses, and
u and
v are the strain rates. These equations show that the product of the strain rate and the static stress indicates the importance of the constitution relationships in the particulate matter.
Coefficient
A1, and
A2 in these equations in the present investigation show that
A2 of the particulate matter is mush larger than
A1. This means that shear deformation occurs more easily than normal deformation in the particulate matter.
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