Thermomechanical surface instability at the origin of surface fissure patterns on heated circular MDF samples

When a flat sample of medium density fibreboard (MDF) is exposed to radiant heat in an inert atmosphere, primary crack patterns suddenly start to appear over the entire surface before pyrolysis and any charring occurs. Contrary to common belief that crack formation is due to drying and shrinkage, it was demonstrated for square samples that this results from thermomechanical instability. In the present paper, new experimental data are presented for circular samples of the same MDF material. The sample was exposed to radiant heating at 20 or 50 kW/m2, and completely different crack patterns with independent Eigenmodes were observed at the two heat fluxes. We show that the two patterns can be reproduced with a full 3-D thermomechanical surface instability model of a hot layer adhered to an elastic colder foundation in an axisymmetric domain. Analytical and numerical solutions of a simplified 2-D formulation of the same problem provide excellent qualitative agreement between observed and calculated patterns. Previous data for square samples together with the results reported in the present paper for circular samples confirm the validity of the model for qualitative predictions, and indicate that further refinements can be made to improve its quantitative predictive capability.Comment: 9 pages, 13 figures. New title and abstract, added experimental and simulation details and figures, conclusions unchanged. Matches the version published in Fire And Material

Thermomechanical surface instability at the origin of surface fissure patterns on heated circular MDF samples

When a flat sample of medium density fibreboard (MDF) is exposed to radiant heat in an inert atmosphere, primary crack patterns suddenly start to appear over the entire surface before pyrolysis and any charring occurs. Contrary to common belief that crack formation is due to drying and shrinkage, it was demonstrated for square samples that this results from thermomechanical instability. In the present paper, new experimental data are presented for circular samples of the same MDF material. The sample was exposed to radiant heating at 20 or 50 kW/m2, and completely different crack patterns with independent Eigenmodes were observed at the two heat fluxes. We show that the two patterns can be reproduced with a full 3-D thermomechanical surface instability model of a hot layer adhered to an elastic colder foundation in an axisymmetric domain. Analytical and numerical solutions of a simplified 2-D formulation of the same problem provide excellent qualitative agreement between observed and calculated patterns. Previous data for square samples together with the results reported in the present paper for circular samples confirm the validity of the model for qualitative predictions, and indicate that further refinements can be made to improve its quantitative predictive capability.Comment: 9 pages, 13 figures. New title and abstract, added experimental and simulation details and figures, conclusions unchanged. Matches the version published in Fire And Material

On Finite Element Computations of Contact Problems in Micropolar Elasticity

Within the linear micropolar elasticity we discuss the development of new finite element and its implementation in commercial software. Here we implement the developed 8-node hybrid isoparametric element into ABAQUS and perform solutions of contact problems. We consider the contact of polymeric stamp modelled within the micropolar elasticity with an elastic substrate. The peculiarities of modelling of contact problems with a user defined finite element in ABAQUS are discussed. The provided comparison of solutions obtained within the micropolar and classical elasticity shows the influence of micropolar properties on stress concentration in the vicinity of contact area

Strain gradient continuum mechanics: simplified models, variational formulations and isogeometric analysis with applications

This dissertation is devoted to two families of generalized continuum theories: the first and second strain gradient elasticity theories including the first and second velocity gradient inertia, respectively. First of all, a number of model problems is studied by analytical means revealing the key characters and potential of generalized continuum theories. In particular, the classical Kirsch problem is extended to the case of a simplified first strain gradient elasticity model demonstrating the size dependency of stresses and strains in the vicinity of a round hole in a plate in tension. Within linearly isotropic second strain gradient elasticity theory, instead, a simplified model is proposed, still capable of capturing free surface effects and surface tension, in particular, arising in solids of both nano- and macro-scales. With a series of benchmark problems, including a comprehensive set of stability analyses, the role of higher-order material parameters is revealed. On the way towards computational analysis, the boundary value problems of the fourth- and sixth-order partial differential equations arising in the first and second strain gradient models, respectively, are formulated and analysed in a mathematical variational form within appropriate Sobolev space settings. For numerical simulations, isogeometric Galerkin methods meeting higher-order continuity requirements are implemented in a user element framework of a commercial finite element software. Various benchmarks for statics and free vibrations confirm the optimal convergence properties of the numerical methods, verify the implementation and demonstrate the key properties of the underlying higher-order continuum models. Regarding model validation and applications, thorough analyses of stretching, shearing and vibration phenomena of complex triangular lattices homogenized by the simplified second strain gradient elasticity model reveal the strong size dependency of lattice structures and hence provide pivotal information for practical applications of materials and structures with a microstructure or microarchitecture

CAD-CAE integration and isogeometric analysis: trivariate multipatch and applications

This PhD thesis is focused on the issues related to one of the critical steps during the lifecycle of a product design and manufacturing process: the transition between the geometrical and functional definition of a product, and the virtual prototyping with numerical simulations, also known as CAD (Computer-Aided Design) / CAE (Computer-Aided Engineering) transition. The isogeometric methodologies developed by Hughes et Al. [1, 2] has the ambition to close the gap in CAD/CAE integration, allowing the two environments to underlay on the same framework, taking advantage of the isoparametric concept, widely used in Finite Elements world, coupled with the Non-Uniform Rational B-Splines (NURBS) that are a standard in CAD systems in the mathematical representation of geometries. Even though the first paper was published 10 years ago, the method is not yet used in industrial applications and only few commercial software are able to handle isogeometric elements. In this thesis a step towards the possibility of application in industry by developing a multi-patch coupling method where the geometry at the interface does not allow a compatible mesh. This improvement opens new frontiers for applications in both static and dynamic solutions. Another issue that is analysed in this thesis is the possibility to improve the geometry-to-analysis integration by conversion of the information that comes from CAD software, in terms of representation of the external surfaces, to solid information that is necessary to be suitable for a structural simulation