An anisotropic in-plane and out-of-plane elasto-plastic continuum model for paperboard

Borgqvist, Eric; Wallin, Mathias; Ristinmaa, Matti; Tryding, Johan

doi:10.1016/j.compstruct.2015.02.067

Cited by 62 publications

(64 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The potential governing the relationship between the stresses and the kinematical quantities is given by the free energy 0 D 0 ip C 0 op . A slightly different format of 0 compared with Borgqvist et al 7 is proposed, such that the Poisson's effect between the in-plane and out-of-plane directions initially is zero. This modification implies a zero initial Poisson's effect between the in-plane and out-of-plane directions, which provides a better experimental agreement.…”

Section: Materials Modelmentioning

confidence: 99%

“…The model has been implemented in the commercial software ABAQUS, 25 via the subroutine option UMAT. Details regarding the numerical implementation of the model is provided by Borgqvist et al 7 In the numerical model, the paperboard is homogeneous and therefore possess constant material parameters through the width and thickness. The geometry of the SCT is shown in Figure 8.…”

Section: Numerical Investigation Of Short-span Compression Testmentioning

confidence: 99%

See 1 more Smart Citation

Localized Deformation in Compression and Folding of Paperboard

Borgqvist

Wallin

Tryding

et al. 2016

Packag. Technol. Sci.

Self Cite

View full text Add to dashboard Cite

The localized deformation patterns developed during in-plane compression and folding of paperboard have been studied in this work. X-ray post-mortem images reveal that cellulose fibres have been reoriented along localized bands in both the compression and folding tests. In folding, the paperboard typically fails on the side where the compressive stresses exists and wrinkles are formed. The in-plane compression test is however difficult to perform because of the slender geometry of the paperboard. A common technique to determine the compression strength is to use the so-called short-span compression test (SCT). In the SCT, a paperboard with a free length of 0.7 mm is compressed. Another technique to measure the compression strength is the long edge test where the motion of the paperboard is constrained on the top and bottom to prevent buckling. A continuum model that previously has been proposed by the authors is further developed and utilized to predict the occurrence of the localized bands. It is shown that the in-plane strength in compression for paperboard can be correlated to the mechanical behaviour in folding. By tuning the in-plane yield parameters to the SCT response, it is shown that the global response in folding can be predicted. The simulations are able to predict the formation of wrinkles, and the deformation field is in agreement with the measured deformation pattern. The model predicts an unstable material response associated with localized deformation into bands in both the SCT and folding. the machine direction (MD), and the transverse direction to MD is known as the cross direction (CD). The failure stress in ZD is typically two orders of magnitude smaller than the failure stress in MD, while the failure stress in CD is about two to three times lower than MD. To obtain a low weight, paperboard is commonly produced as a sandwiched structure, with stronger mechanical properties in the outer-plies (top and bottom) and weaker properties in the middle. Measurements and simulations have been performed for a single-ply board in this work.Good foldability implies minimum spring back and absence of cracks along fold lines, cf. Cavlin. 1 Because of the bending state present during folding, in-plane compression strength has been attributed for being the dominant factor affecting the foldability of paperboard. The SCT value multiplied with the thickness is shown to be correlated to the maximum bending moment by, for example, Edholm. 4 However, later investigations have confirmed that the out-of-plane shear is an important mechanism to consider during converting procedures, cf. Nygårds et al., 5 Beex and Peerlings, 6 and Borgqvist et al. 7 The in-plane compression strength is difficult to measure because of that structural instabilities (buckling) easily are triggered as a result of the slender geometry of the paperboard. To overcome the difficulties associated with the structural stability in compression tests, short-span length can be used to prevent the buckling. An alternative experimental method is ba...

show abstract

Section: Materials Modelmentioning

confidence: 99%

Section: Numerical Investigation Of Short-span Compression Testmentioning

confidence: 99%

Localized Deformation in Compression and Folding of Paperboard

Borgqvist

Wallin

Tryding

et al. 2016

Packag. Technol. Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The out‐of‐plane material behaviour in the thickness direction, ZD, is described by a director vector

{bold-italicn}_{0}^{false(3 false)}

, which is defined to be orthogonal to MD and CD, ie,

{bold-italicn}_{0}^{false(3 false)} = {bold-italicv}_{0}^{false(1 false)} \times {bold-italicv}_{0}^{false(2 false)}

. This choice for the out‐of‐plane director vector follows from the assumption that paperboard can be considered as an idealized layered structure; details regarding this assumption are presented in Borgqvist et al The in‐plane director vectors are assumed to follow the elastic part of the deformation gradient, while the out‐of‐plane director vector is constructed to be orthogonal to the updated in‐plane directors, ie,

v^{false(1 false)} = F^{e} {bold-italicv}_{0}^{false(1 false)}, v^{false(2 false)} = F^{e} {bold-italicv}_{0}^{false(2 false)} and n^{false(3 false)} = J^{e} F^{e - T} {bold-italicn}_{0}^{false(3 false)},

with J e being the determinant of the elastic deformation gradient. The Helmholtz free energy is assumed to be a function of the elastic Finger tensor b e = F e ( F e ) T and the structural tensors m (1) = v (1) ⊗ v (1) , m (2) = v (2) ⊗ v (2) , m (3) = n (3) ⊗ n (3) using the following invariants:

\begin{matrix} right & left I_{11} = \sqrt{{bold-italicm}^{(1)} : I}, I_{12} = \sqrt{{bold-italicm}^{(2)} : I}, I_{13} = \frac{1}{J^{e}} \sqrt{{bold-italicm}^{(3)} : {bold-italicb}^{e} {bold-italicb}^{e}}, & right \\ right & left I_{23} = \end{matrix}

…”

Section: Materials Model For Paperboardmentioning

confidence: 99%

“…The paperboard model has previously been used to study a number of industrial applications. In Borgqvist et al, a numerical study of the creasing process was considered using a simplified line‐creasing operation as well as a more realistic, 3D rotational setup. Furthermore, it was shown in Borgqvist et al that the paperboard model was able to capture the formation of wrinkles for both the line‐folding process of uncreased paperboard and for the short‐span compression test.…”

Section: Introductionmentioning

confidence: 99%

Efficient and accurate simulation of the packaging forming process

et al. 2018

Self Cite

View full text Add to dashboard Cite

To allow for large‐scale forming applications, such as converting paperboard into package containers, efficient and reliable numerical tools are needed. In finite element simulations of thin structures, elements including structural features are required to reduce the computational cost. Solid‐shell elements based on reduced integration with hourglass stabilization is an attractive choice. One advantage of this choice is the natural inclusion of the thickness, not present in standard degenerated shells, which is especially important for many problems involving contact. Furthermore, no restrictions are imposed on the constitutive models since the solid‐shell element does not require the plane stress condition to be enforced. In this work, a recently proposed efficient solid‐shell element is implemented together with a state‐of‐the‐art continuum model for paperboard. This approach is validated by comparing the obtained numerical results with experimental results for paperboard as well as with those found by using 3D continuum elements. To show the potential of this approach, a large‐scale forming simulation of paperboard is used as a proof of concept.

show abstract

“…For paperboard and paperboard products, finite element simulations have previously successfully been used to study creasing and folding, brim forming, point loading of packages, delamination during printing, and 3D forming . Test methods such as the short compression test have been modelled.…”

Section: Introductionmentioning

confidence: 99%

Simulation and experimental verification of a drop test and compression test of a gable top package

et al. 2019

View full text Add to dashboard Cite

A finite element framework has been proposed that can be used to simulate both empty paperboard packages and package filled with plastic granulates. A gable top package was made of a commercial paperboard, and material properties needed in the material model were determined. Two simulations were performed, a drop test and a compression test. By comparison between experimental and numerical results, the deformation mechanisms at impact could be identified and correlated to material properties. When the package was filled with granulates, different mechanisms was activated compared with an empty package. The granulates contribute to bulging of the panels, such that the edges became more load bearing compared with the panels. When the edges carried the loads, the importance of the out‐of‐plane properties also increased, and local failure initiation related to delamination was observed. Comparison between experimental and numerical impact forces shows that there are still important things to consider in the model generation, eg, variation of properties within the package, which originate both from material property variations, and the loading history, eg, during manufacturing and handling.

show abstract

An anisotropic in-plane and out-of-plane elasto-plastic continuum model for paperboard

Cited by 62 publications

References 31 publications

Localized Deformation in Compression and Folding of Paperboard

Localized Deformation in Compression and Folding of Paperboard

Efficient and accurate simulation of the packaging forming process

Simulation and experimental verification of a drop test and compression test of a gable top package

Contact Info

Product

Resources

About