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In this work, we suggest a modified phase-field model for simulating the evolution of mixed mode fractures and compressive driven fractures in porous artificial rocks and Neapolitan Fine Grained Tuff. The numerical model has been calibrated using experimental observations of rock samples with a single saw cut under uniaxial plane strain compression. For the purpose of validation, results from the numerical model are compared to Meuwissen samples with different angles of rock bridge inclination subjected to uni-axial compression. The simulated results are compared to experimental data, both qualitatively and quantitatively. It is shown that the proposed model is able to capture the emergence of shear cracks between the notches observed in the Neapolitan Fine Grained Tuff samples as well as the propagation pattern of cracks driven by compressive stresses observed in the artificial rock samples. Additionally, the typical types of complex crack patterns observed in experimental tests are successfully reproduced, as well as the critical loads.

In this work, we propose a modified phase-field model for simulating the evolution of mixed mode fractures and compressive driven fractures in porous artificial rocks. For the purpose of validation, the behaviour of artificial rock samples, with either a single or double saw cuts, under uniaxial plane strain compression has been numerically simulated. The simulated results are compared to experimental data, both qualitatively and quantitatively. It is shown that the proposed model is able to capture the commonly observed propagation pattern of wing cracks emergence followed by secondary cracks driven by compressive stresses. Additionally, the typical types of complex crack patterns observed in experimental tests are successfully reproduced, as well as the critical loads.

Textbook covers the fundamental theory of structural mechanics and the modelling and analysis of frame and truss structures * Deals with modelling and analysis of trusses and frames using a systematic matrix formulated displacement method with the language and flexibility of the finite element method * Element matrices are established from analytical solutions to the differential equations  * Provides a strong toolbox with elements and algorithms for computational modelling and numerical exploration of truss and frame structures * Discusses the concept of stiffness as a qualitative tool to explain structural behaviour * Includes numerous exercises, for some of which the computer software CALFEM is used. In order to support the learning process CALFEM gives the user full overview of the matrices and algorithms used in a finite element analysis

Lack of straightness in timber is the most frequent complaint regarding solid (and laminated) timber products worldwide. Nowadays, customers demand higher quality in the shape stability of wood products than they did earlier. The final distortion of timber boards is mostly caused by moisture-related stresses in wood (drying distortions) and growth-related stresses (distortions appearing when logs are split up to timber boards by sawing). To get more knowledge on how these distortions can be reduced in wooden products, there is a need for improved understanding of this material behaviour through good numerical tools developed from empirical data. A three-dimensional finite element board distortion model developed by Ormarsson (Doctoral thesis, Publ. 99:7, 1999) has been extended to include the influence of growth stresses by incorporating a one-dimensional finite element growth stress model developed here. The growth stress model is formulated as an axisymmetric general plane strain model where material for all new annual rings is progressively added to the tree during the analysis. The simulation results presented include how stresses are progressively generated during the tree growth, distortions related to the redistribution of growth stresses during log sawing, and distortions and stresses in drying reflecting the effects of growth stresses. The results show that growth stresses clearly vary during tree growth and also form a large stress gradient from pith to bark. This in itself can result in significant bow and crook deformations when logs are sawn into timber boards. The distortion results from the simulations match well with the results observed in reality. The parametric study also showed that the radial growth stress distribution is highly influenced by parameters such as modulus of elasticity, micro fibril angle and maturation strain.

It is not fully understood how much growth stresses affect the final quality of solid timber products in terms of, e.g. shape stability. It is, for example, difficult to predict the internal growth stress field within the tree stem. Growth stresses are progressively generated during the tree growth and they are highly influenced by climate, biologic and material-related factors. To increase the knowledge of the stress formation, a finite element model was created to study how the growth stresses develop during the tree growth. The model is an axisymmetric general plane strain model where material for all new annual rings is progressively added to the tree during the analysis. The material model used is based on the theory of small strains (where strains refer to the undeformed configuration which is good approximation for strains less than 4%) where so-called biological maturation strains (growth-related strains that form in the wood fibres during their maturation) are used as a driver for the stress generation. It is formulated as an incremental material model that takes into account elastic strain, maturation strain, viscoelastic strain and progressive stiffening of the wood material. The results clearly show how the growth stresses are progressively generated during the tree growth. The inner core becomes more and more compressed, whereas the outer sapwood is subjected to slightly increased tension. The parametric study shows that the growth stresses are highly influenced by the creep behaviour and evolution of parameters such as modulus of elasticity, micro-fibril angle and maturation strain.

It is not fully understood how much growth stresses affect the final quality of solid timber products in terms of e.g. shape stability. It is for example difficult to predict the internal growth stress field within the tree stem. Growth stresses are progressively generated during the tree growth and they are highly influenced by climate, biologic and material related factors. To increase the knowledge of the stress formation a finite element model was created to study how the growth stresses develop during the tree growth. The model is an axisymmetric general plane strain model where material for all new annual rings is progressively added to the tree during the analysis. The material model used is based on the theory of small strains (where strains refer to the undeformed configuration which is good approximation for strains less than 4%) where so-called biological maturation strains (growth-related strains that form in the wood fibres during their maturation) are used as a driver for the stress generation. It is formulated as an incremental material model that takes into account elastic strain, maturation strain, viscoelastic strain and progressive stiffening of the wood material. The results clearly show how the growth stresses are progressively generated during the tree growth. The inner core becomes more and more compressed whereas the outer sapwood is subjected to slightly increased tension. The parametric study shows that the growth stresses are highly influenced by the creep behaviour and evolution of parameters such as modulus of elasticity, micro fibril angle and maturation strain.

A theory for analysing the shape stability of sawn timber was implemented in a finite element program. To illustrate the types of results that can be obtained, the behaviour of a board during drying was simulated. The simulation yields information about unfavourable deformations and stresses during the drying process. To investigate factors that influence drying deformations, a parameter study was performed in which the influence of different constitutive models and different material parameters was studied. In addition, the influence of the spiral grain angle was examined.

Numerical simulations were performed to investigate how the annual ring orientation affects the shape stability of sawn timber. The influence of radial variations in the basic properties and the spiral grain is also studied. The knowledge obtained can contribute to more effective use of the raw material through allowing boards having properties that would yield bad shape stability to be sorted out. Possibilities for improving shape stability through gluing pieces of wood together are examined as well.

Different methods of real-time fibre-network visualisation have been studied. Using an extrusion-based method yields very good results, but for large networks the frame rate becomes unacceptably low. To increase the number of fibres that can be visualised in real time, a textured billboard method has been implemented. With this method, an average performance gain of 60% has been achieved, using an OpenGL implementation.