Mittuniversitetet

This work is concerned with the determination of the adhesion strength between a paper web and an adhesive surface. Edvardsson et al. [Edvardsson, S., Gradin, P., and Isaksson, P., "On Dissipative Effects of Paper Web Adhesion Strength," Int. J. Solids Struct., Vol. 48(1), 2011, pp. 24-30] suggested recently a model that takes into account the energy dissipation caused by elastic plastic deformation in the bent structure of a paper specimen. This model is further developed and investigated in the present work. A linear relation in plastic dissipation is discovered facilitating a novel analysis of the peeling tension and a more convenient determination of the proper adhesion strength. Industrial relevant examples are made with wet newsprint and kraft stock. A straightforward experimental procedure for determining the consistent adhesion strength is suggested. It is found that the agreement between the model and the experimental observations is good.

The present work is concerned with new ideas of potential value for solving differential equations. First, a brief introduction to particle methods in mechanics is made by revisiting the vibrating string. The full case of nonlinear motion is studied and the corresponding nonlinear differential equations are derived. It is suggested that the particle origin of these equations is of more general interest than usually considered. A novel possibility to develop particle methods for solving differential equations in a direct way is investigated. The dynamical functional particle method (DFPM) is developed as a solution method for boundary value problems. DFPM is based on the concept of an interaction functional as a dynamical force field acting on quasi particles. The approach is not limited to linear equations. We exemplify by applying DFPM to several linear Schrödinger type of problems as well as a nonlinear case. It is seen that DFPM performs very well in comparison with some standard numerical libraries. In all cases, the convergence rates are exponential in time. © 2012 American Society of Mechanical Engineers.

In order to be able to study the damage mechanisms and in general the mechanisms active when a wood chip is created during the wood chipping process, it is crucial to have access to an experimental equipment in which chips can be produced under realistic conditions. In this paper is presented a laboratory chipper, which has been developed to admit chipping at rates that can be varied in a large interval i.e. at rates ranging from zero to 50 m/s. The knife used to cut the chips is mounted in a knife holder, which is instrumented in such a way that forces in three orthogonal directions can be measured. Since the actual force and the measured force differs due to inertia effects, a simple mathematical model is developed and used to evaluate the force acting on the knife. Some results are shown from the force measurements and it is concluded that the laboratory chipper is a versatile tool in the process of increasing the understanding of the chipping process.

Theconditions under which force vectors and corresponding displacement vectors becomeco-linear are investigated under the assumption of a linear elasticstructure and for an arbitrary number of loading points. Itis shown that there exist an infinite number of directionsalong which the load and displacement vectors in each loadingpoint coincide. Moreover, the problem of co-linearity is analogous tothe problem of finding the extreme values of the workperformed on an elastic structure under the constraint that eachforce has a given magnitude. The result for a finitenumber of loading points is extended to a continuous loaddistribution on the boundary of an elastic structure, i.e., itis possible to find an infinite number of load distributionssuch that the displacement in a point on the boundaryis co-linear with the boundary stress vector in that samepoint.

In this paper, the Lame coefficients in the linear elasticity problem are estimated by using the measurements of displacement. Some a posteriori error estimators for the approximation error of the parameters are derived, and then adaptive finite element schemes are developed for the discretization of the parameter estimation problem, based on the error estimators. The Gauss-Newton method is employed to solve the discretized nonlinear least-squares problem. Some numerical results are presented.

Inverse simulations of musculoskeletal models computes the internal forces such as muscle and joint reaction forces, which are hard to measure, using the more easily measured motion and external forces as input data. Because of the difficulties of measuring muscle forces and joint reactions, simulations are hard to validate. One way of reducing errors for the simulations is to ensure that the mathematical problem is well-posed. This paper presents a study of regularity aspects for an inverse simulation method, often called forward dynamics or dynamical optimization, that takes into account both measurement errors and muscle dynamics. The simulation method is explained in detail. Regularity is examined for a test problem around the optimum using the approximated quadratic problem. The results shows improved rank by including a regularization term in the objective that handles the mechanical over-determinancy. Using the 3-element Hill muscle model the chosen regularization term is the norm of the activation. To make the problem full-rank only the excitation bounds should be included in the constraints. However, this results in small negative values of the activation which indicates that muscles are pushing and not pulling. Despite this unrealistic behavior the error maybe small enough to be accepted for specific applications. These results is a starting point start for achieving better results of inverse musculoskeletal simulations from a numerical point of view.

An analytical model has been applied to calculate the acquired strain energy density in order to achieve a certain damage state in a softwood fibre by uniaxial tension or shear load. The energy density was found to be dependent on the microfibril angle in the middle secondary wall, the loading case, the thicknesses of the fibre cell wall layers, and conditions such as moisture content and temperature. At conditions, prevailing at the entrance of the gap between the plates in a refiner and at relative high damage states, more energy is needed to create cracks at higher microfibril angles. The energy density was lower for earlywood compared to latewood fibres. For low microfibril angles, the energy density was lower for loading in shear compared to tension for both earlywood and latewood fibres. Material parameters, such as initial damage state and specific fracture energy, were determined by fitting of input parameters to experimental data.

A new class of Preisach operators based on play operators with an inverse in a closed form and allowing for saturation has recently been proposed. Its existence criteria and identification procedure were considered in earlier articles. The present paper analyses the identification procedure with respect to the sensitivity to underlying functions (i.e. intrinsic behaviour of the hysteretic system), to spline approximation, and to the least square error estimation procedure. The analysis shows that model errors are significantly influenced by large derivatives of the underlying functions. Spline approximations have generally little effect on model errors. In particular, an upper bound of for the relative parameter error due to measurement discrepancies has been derived for the least square error problem. The bound increases, the closer to saturation data are measured.