Rotational Constraint between Beams in 3-D Space

In this paper, we develop two alternative formulations for the rotational constraint between the tangents to connected beams with large deformations in 3-D space. Such a formulation is useful for modeling bonded/welded connections between beams. The first formulation is derived by consistently linearizing the variation of the strain energy and by assuming linear shape functions for the beam elements. This formulation can be used with both the Lagrange multiplier and the penalty stiffness method. The second non-consistent formulation assumes that the contact normal is independent of the nodal displacements at each iteration, and is updated consistently between iterations. In other words, we ignore the contribution due to the change of the contact normal in the linearization of the contact gap function. This assumption yields simpler equations and requires no specific assumption regarding the shape functions for the underlying beam elements. However, it is limited to the penalty method. We demonstrate the performance of the presented formulations in solving problems using implicit time integration. We also present a case showing the implications of ignoring this rotational constraint in modeling a network of beams.</p

Вплив попиту на процес ціноутворення

The creep behavior of nanocellulose films and aerogels are studied in a dynamic moisture environment, which is crucial to their performance in packaging applications. For these materials, the creep rate under cyclic humidity conditions exceeds any constant humidity creep rate within the cycling range, a phenomenon known as mechanosorptive creep. By varying the sample thickness and relative humidity ramp rate, it is shown that mechanosorptive creep is not significantly affected by the through-thickness moisture gradient. It is also shown that cellulose nanofibril aerogels with high porosity display the same accelerated creep as films. Microstructures larger than the fibril diameter thus appear to be of secondary importance to mechanosorptive creep in nanocellulose materials, suggesting that the governing mechanism is found between molecular scales and the length-scales of the fibril diameter.funding agencies|BiMaC Innovation|

Embedded Discontinuity Finite Element Method (ED-FEM) for Modeling Fiber Failures in Random Fiber Networks

Paper materials are natural composite materials where fibers are almost randomly distributed in a fiber network. Mechanical properties of fiber networks are known to be strongly controlled by fiber-fiber interactions and single fiber properties. A fiber network is often modeled as a beam network where beam-to-beam interactions are treated as cohesive zones and single beams stretch indefinitely without breaking. The latter assumption is not physically correct and leads to an overprediction of the mechanical response of the beam network. In this work, we present a computational modeling framework for simulating beam failures and thereby closing the gap to physically based micromechanical modeling of paper and packaging products. Modeling beam failure is a challenging engineering problem. At the onset of failure, the tangent stiffness tensor projected in a direction normal to the surface of discontinuity (commonly referred to as the localization tensor) is singular, i.e. we have a bifurcation point and the problem is ill-posed. Another implication of ill-posedness for the numerical simulation after a spatial discretization is a pathological mesh dependency of the computed result. We use the ED-FEM where a failure process zone (FPZ) is introduced into a multi-scale continuum mechanics formulation (i.e. the material is split into a small scale and a large scale defining the FPZ and the bulk material, respectively), making the computed result mesh independent. The multi-scale nature of the ED-FEM enables an operator splitting implementation method as opposed to carrying out the computations of the nodal displacement vector and the displacement discontinuity vector simultaneously with the global loop where the global stiffness matrix would be singular at the onset of failure. We show that fiber failures and fiber-fiber bond failures can contribute to the observed elastoplastic stress-strain response of paper

Estimation of the in-situ elastic constants of wood pulp fibers in freely dried paper via AFM experiments

Atomic force microscopy-based nanoindentation (AFM-NI) enables characterization of the basic mechanical properties of wood pulp fibers in conditions representative of the state inside a paper sheet. Determination of the mechanical properties under different loads is critical for the success of increasingly advanced computational models to understand, predict and improve the behavior of paper and paperboard. Here, AFM-NI was used to indent fibers transverse to and along the longitudinal axis of the fiber. Indentation moduli and hardness were obtained for relative humidity from 25 % to 75 %. The hardness and the indentation modulus exhibit moisture dependency, decreasing by 75 % and 50 %, respectively, over the range tested. The determined indentation moduli were combined with previous work to estimate the longitudinal and transverse elastic modulus of the fiber wall. Due to the relatively low indentation moduli, the elastic constants are also low compared to values obtained via single fiber testing

Підвищення енергоефективності комплекту розрядна лампа-ЕПРА

The network geometries of rigidly cross-linked fibrin and collagen type I networks are imaged using confocal microscopy and characterized statistically. This statistical representation allows for the regeneration of large, three-dimensional biopolymer networks using an inverse method. Finite element analyses with beam networks are then used to investigate the large deformation, nonlinear elastic response of these artificial networks in isotropic stretching and simple shear. For simple shear, we investigate the differential bulk modulus, which displays three regimes: a linear elastic regime dominated by filament bending, a regime of strain-stiffening associated with a transition from filament bending to stretching, and a regime of weaker strain-stiffening at large deformations, governed by filament stretching convolved with the geometrical nonlinearity of the simple shear strain tensor. The differential bulk modulus exhibits a corresponding strain-stiffening, but reaches a distinct plateau at about 5% strain under isotropic stretch conditions. The small-strain moduli, the bulk modulus in particular, show a significant size-dependence up to a network size of about 100 mesh sizes. The large-strain differential shear modulus and bulk modulus show very little size-dependence.Funding Agencies|BiMaC Innovation||Alf de Ruvo Memorial Foundation of SCA AB||WoodWisdom-net research program||Harvard MRSEC|DMR-0820484|NSF|DMR-1006546|</p

Mechanics of paper webs in printing press applications

The mechanics of paper is a difficult subject because paper is a unique material. It is very thin, flexible at bending, unstable in compression and stiff at tension. Dealing with paper we have to account for orthotropy and heterogeneities created during the manufacturing process. This thesis addresses two topics in mechanics of paper webs in printing press applications. First is the dynamic behaviour of the travelling webs. Second is so-called “fluting” after heat-set web-fed offset printing. There are a number of challenges in simulating the dynamics of the paper web. It is necessary to include the influence of the paper web transport velocity. Due to initial sag or vibrations, gyroscopic forces affect the dynamics of the webs. Furthermore, the transport velocity reduces the stress stiffening of the web. A good theoretical model should account for large displacements and should be capable of simulating wrinkles, which is essentially a post-buckling phenomenon. Finally, the paper web is surrounded with air which reduces the natural frequencies substantially by “adding" mass to the paper. A non-linear finite element formulation has been developed in this study for simulation of travelling webs. The results of the studies shows that for the tension magnitudes used in the printing industry the critical web speed lies far above those used today. Speed limitations are rather caused by ink setting and tension control problems. If the web tension profile is skew, however, edge vibrations are inevitable even at small external excitations. Fluting is a permanent wavy distortion of the paper web after heat-set web offset printing. It is often seen in high quality printing products, especially in areas covered with ink. It is generally accepted that tension and heat are required to create fluting. However, there have been certain disputes as to the mechanism of fluting formation, retention and key factors affecting this phenomenon. Most of the existing studies related to fluting are based on linear buckling theories. A finite element model, capable of simulating a post-buckling behaviour has been developed and experimentally verified. Studies show that none of the existing theories can consistently explain fluting. A new basic mechanism of fluting formation has been proposed and numerically demonstrated. Fluting was explained as a post-buckling phenomenon due to small scale moisture variations developing during through-air drying. It was concluded that air permeability variation is the key factor affecting fluting tendency. Fluting is retained due to inelastic deformations promoted by high drying temperatures.QC 20100906</p

The effect of geometry changes on the mechanical stiffness of fibre-fibre bonds

In this work, we discuss the effect of geometry on the compliance of the fibre bond regions against normal and tangent loads. Since the fibre bonds play a key role in defining the paper strength, the compliance of the bond regions can affect the amount of elastic energy stored in the bonds and thus change not only the strength but also the stiffness of paper products under certain conditions. Using finite element simulation tools, we overcome the major difficulty of performing controlled mechanical testing of the isolated bond region and reveal the key geometrical factors affecting the compliance of the bond region. Specifically, we show that the compliance of the fiber-fiber bond is strongly governed by its geometric configuration after pressing. Among the strongest factors is the collapse of the lumen and the crossing angle. Using the range of obtained stiffness values, we demonstrated the effect the bond stiffness has on the stiffness of the network using fiber-level simulation tools. We show how the dependence of tangent bond stiffness on fiber-to-fiber angle further softens the more compliance cross-machine direction.QC 20191001</p