PAPERmaking! Vol7 Nr3 2021

Energies 2021 , 14 , 3203

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region is in span, which clearly would evolve into the plastic joint (region B) for larger crushing loads. The elements, in which the material was identified to be plasticized, i.e., regions A and B, were obtained from FE computations, see Figure 9. Since 50% of the deformation was assumed to be elastic, new geometries for further computations with 50% less crushing were generated by f function, see Equation (4), but in A and B regions the material properties were deteriorated. Table2. Geometrical parameters of w and s for fluting to determine analytically the crushed geome- tries of corrugated cardboard used in the numerical part of this study.

w (-)

s (-) 1.06 0.98 0.92 0.86 0.80 0.75

Crushing (%)

0 (intact)

3.5 4.0 4.8 6.2 9.0

10 20 30 40 50

15.5

( a ) ( b ) Figure 8. Half-waves of fluting due to crushing obtained from the analytical formula (4) and parameters presented in Table 2: ( a ) shapes of the flute corresponding to different levels of crushing and ( b ) the comparison for 40% of crushing: FEM (magenta circles) vs analytical formula (solid line).

Figure 9. A and B regions for all geometries of corrugated cardboard considered, i.e., with crushing of ( a ) 10%, ( b ) 20%, ( c ) 30%, ( d ) 40%and ( e ) 50%. The local material deterioration was defined independently for two regions: A and B. Acquired material stiffness matrix of RVE with embedded orthotropic and locally

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