| 1. |
- Alzweighi, Mossab, et al.
(författare)
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Anisotropic damage behavior in fiber-based materials : Modeling and experimental validation
- 2023
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Ingår i: Journal of the mechanics and physics of solids. - : Elsevier BV. - 0022-5096 .- 1873-4782. ; 181
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Tidskriftsartikel (refereegranskat)abstract
- This study presents a thermodynamically consistent continuum damage model for fiber-based materials that combines elastoplasticity and damage mechanisms to simulate the nonlinear mechanical behavior under in-plane loading. The anisotropic plastic response is characterized by a non-quadratic yield surface composed of six sub-surfaces, providing flexibility in defining plastic properties and accuracy in reproducing material response. The damage response is modeled based on detailed uniaxial monotonic and cyclic tension-loaded experiments conducted on specimens extracted from a paper sheet in various directions. To account for anisotropic damage, we propose a criterion consisting of three sub-surfaces representing tension damage in the in-plane material principal directions and shear direction, where the damage onset is determined through cyclic loading tests. The damage evolution employs a normalized fracture energy concept based on experimental observation, which accommodates an arbitrary uniaxial loading direction. To obtain a mesh-independent numerical solution, the model is regularized using the implicit gradient enhancement by utilizing the linear heat equation solver available in commercial finite-element software. The study provides insights into the damage behavior of fiber-based materials, which can exhibit a range of failure modes from brittle-like to ductile, and establishes relationships between different length measurements.
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| 3. |
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| 4. |
- Borgqvist, Eric, et al.
(författare)
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An anisotropic in-plane and out-of-plane elasto-plastic model for paperboar
- 2015
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Ingår i: Composite Structures. - : Elsevier BV. - 1879-1085 .- 0263-8223. ; 126, s. 184-195
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Tidskriftsartikel (refereegranskat)abstract
- A continuum model of paperboard material possessing a high degree of anisotropy is established. To handle the anisotropy, three vectors are introduced which phenomenologically represent the preferred directions of the material. The in-plane director vectors deform as line segments and the out-of-plane direction deforms as a normal vector. This allows for a decoupling of the in-plane and the out-of-plane responses in shearing. The model is developed for large plastic strains and consequently an expression for the plastic spin has been proposed. The choice of plastic spin allows for a control of the direction in which permanent deformations will occur. To show the predictive capabilities of the model, the important industrial process of creasing is simulated. Both the simplified line crease setup, as well as the actual rotation crease setup used in industrial applications are studied.
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| 5. |
- Borgqvist, Eric
(författare)
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Continuum modeling of the mechanical properties of paperboard
- 2014
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Continuum based elasto-plastic models for paperboard have been established in the work herein. The thesis begins with an introductory section that describes some of the background of the problem and gives some more motivation for the modeling choices made in the appended papers. Some preliminary simulation results on the folding operation is also provided. The main part of the thesis consists of the two papers, A and B. The thermodynamical framework is established in Paper A and a model for the in-plane response is developed. The anisotropy is handled by introducing a set of director vectors directed in-plane and evolves together with the continuum. A yield surface with several internal variables is introduced, which hardens distortionally in the stress space. The effects of pre-straining a sample in e.g. first MD and then subsequently load the sample in CD is studied. The model is compared to measurements obtained with Digital Image Correlation. In Paper B, the weak out-of-plane properties is included in the model. A normal vector is utilized for the preferred direction in ZD. An expression for the plastic spin is determined, which is used to control the direction of the plastic flow. Simulations are performed on the line crease setup and compared to experimental measurments and the industrial rotation crease setup is studied in detail using the developed model.
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| 6. |
- Borgqvist, Eric
(författare)
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Continuum modelling of the mechanical response of paper-based materials
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Continuum based elasto-plastic-damage models for paperboard have been established in this work. The thesis begins with an introductory section that describes the mechanical properties of paperboard and some of the converting processes during forming of a package. A short review of modeling concepts that have been applied to paperboard is presented and then some key aspects and assumptions developed in this work are summarized. The main part of the thesis consists of the five papers, A, B, C, D and E. In addition to these works, a possible concept to reduce a pathological mesh-dependency is reviewed. The thermodynamical framework is established in Paper A and a model for the in-plane response is developed. The anisotropy is handled by introducing a set of director vectors that change direction along with the continuum. A distortion hardening yield surface coupled to several scalar internal variables is introduced. The effects of pre-straining a sample in one direction and then subsequently load the sample in the perpendicular direction is studied. The model is compared to measurements obtained with Digital Image Correlation. In Paper B, the model is further developed to model out-of-plane deformations. A normal vector is introduced to model the out-of-plane direction. Key ingredients in the model includes the specific format for the elastic part of the free energy and an expression for the plastic spin. The spin is used to control the direction of the plastic flow. Simulations are performed on the line crease setup and compared to experimental measurements. Furthermore, the industrial rotation crease setup is studied in detail using the developed model. The Short-span Compression Test (SCT) and the line folding operation are investigated in Paper C and the deformation patterns extracted from x-ray images are studied. The model parameters are calibrated to uniaxial tests and the SCT, and then the folding of uncreased paperboard is simulated. The simulated global force-displacement/rotation curves matches the measurements and the simulated deformation patterns are similar to that observed experimentally. A numerical scheme is presented in Paper D, where the governing equations of the elasto-plastic boundary value problem are interpreted as a Differential-Algebraic Equation (DAE) system. In particular, two material models, which includes damage variables, are investigated using the Diagonally Implicit Runge-Kutta (DIRK) scheme. The error obtained using the DIRK-method is compared to the standard implicit Euler method. In Paper E, the continuum model that has been developed in paper A-C is further enhanced to include the effect of damage. Two damage variables are introduced in the elastic part of the free energy which is associated with out-of-plane deformations. The softening in the out-of-plane normal and shear deformations can then be recovered. The folding of creased paperboard is simulated and compared to measurements.
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| 7. |
- Borgqvist, Eric, et al.
(författare)
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Distortional hardening plasticity model for paperboard
- 2014
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 51:13, s. 2411-2423
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Tidskriftsartikel (refereegranskat)abstract
- A distortional hardening elasto-plastic model at finite strains suitable for modeling of orthotropic materials is presented. As a prototype material, paperboard is considered. An in-plane model is established. The model developed is motivated from non-proportional loading tests on paperboard where the paperboard is pre-strained in one direction and then loaded in the perpendicular direction. A softening effect is revealed in the pre-strained samples. The observed experimental findings cannot be accurately predicted by current models for paperboard. To be able to model the softening effects, a yield surface based on multiple hardening variables is introduced. It is shown that the model parameters can be obtained from simple uniaxial experiments. The model is implemented in a finite element framework which is used to illustrate the behavior of the model at some specific loading situations and is compared with strain fields obtained from Digital Image Correlation experiments.
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| 8. |
- Borgqvist, Eric, et al.
(författare)
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Localized Deformation in Compression and Folding of Paperboard
- 2016
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Ingår i: Packaging Technology & Science. - : Wiley. - 0894-3214. ; 29:7, s. 397-414
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 9. |
- Borgqvist, Eric, et al.
(författare)
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Numerical integration of elasto-plasticity coupled to damage using a diagonal implicit Runge-Kutta integration scheme
- 2013
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Ingår i: International Journal of Damage Mechanics. - : SAGE Publications. - 1056-7895 .- 1530-7921. ; 22:1, s. 68-94
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Tidskriftsartikel (refereegranskat)abstract
- Abstract in UndeterminedThis article is concerned with the numerical integration of finite strain continuum damage models. The numerical sensitivity of two damage evolution laws and two numerical integration schemes are investigated. The two damage models differ in that one of the models includes a threshold such that the damage evolution is suppressed until a certain effective plastic strain is reached. The classical integration scheme based on the implicit Euler scheme is found to suffer from a severe step-length dependence. An alternative integration scheme based on a diagonal implicit Runge--Kutta scheme originally proposed by Ellsiepen (1999) is investigated. The diagonal implicit Runge--Kutta scheme is applied to the balance of momentum as well as the constitutive evolution equations. When applied to finite strain multiplicative plasticity, the diagonal implicit Runge--Kutta scheme destroys the plastic incompressibility of the underlying continuum evolution laws. Here, the evolution laws are modified such that the incompressibility of the plastic deformation is preserved approximately. The presented numerical examples reveal that a significant increase in accuracy can be obtained at virtually no cost using the diagonal implicit Runge--Kutta scheme. It is also shown that for the model including a discontinuous evolution law, the superiority of the diagonal implicit Runge--Kutta scheme over the implicit Euler scheme is reduced.
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