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Decohesion processes involved in debonding between yarns and matrix or sliding between contacting yarns constitute important failure mechanisms in woven composites. The geometry of the yarn architecture however makes it difficult to avoid interpenetrations between neighboring yarns in their geometrical description. This motivated recent works using a level set-based methodology to generate smooth geometries without interpenetration for generated Representative Volume Elements (RVEs) and experimental image-based samples. Such tools require introducing gaps between contacting yarns, which may be debatable when taken too large or may be computationally costly for thin gap, locally dictating the mesh size. To avoid this, the yarns contacting surfaces can be discretized using interface elements. Yet, identifying such contacting surfaces is complex. An implicit geometry description based on distance fields is used here to extract a geometry that supports cohesive zones, identifying the interface of yarn-yarn contacts and eliminating the gaps using manipulations on distance fields of the individual yarns. This allows generating conforming tetrahedral meshes with inserted cohesive elements in the contact areas. The methodology is shown to reduce the size of finite element models of woven composite RVEs by over two orders of magnitude, thereby paving the way towards affordable damage simulations on such RVEs., info:eu-repo/semantics/published

Paper sheets reveal pronounced changes in shape and dimensions upon exposure to variations in moisture, which comprises digital printing operations. These are observed in the form of curls, waviness and buckling at the sheet-scale of paper. In digital printing, this undesired behavior is due to the fact that the moisture is rapidly absorbed in paper and thereafter evaporated within a short period of time. These dimensional changes originate from the single fibre level, which affects the fibre network through the inter-fibre bonds (regions where the fibres overlap). At these bonds, an interaction of the hygroscopic and mechanical response of the fibres occurs, entailing micro-stresses and associated sheet-scale deformations. In order to understand this macro-scale behavior of paper, it is essential to study the complex fibrous network at the micro-scale.In Chapter 2, a level-set based XFEM approach is used to model the hygro-elastic response of complex fibrous networks in a two dimensional framework. The fibres are assumed to be completely bonded in the inter-fibre bonds. The fibre edges are described by the zero level-set of a higher dimensional function. The level-set method coupled with X-FEM captures the geometrical description of the fibres adequately with a lower system size, since the discretization is decoupled from the geometry. Therefore, LS-XFEM formalism is shown to be successful in modeling the hygo-mechanical response of complex networks of fibres. During the manufacturing process of paper, when the pulp is dried under restraint, internal stresses/strains are developed as explained by the fibre segment activation mechanism. Upon exposure to a moisture cycle (e.g. during printing), these strains are released at the fibre level which induces permanent deformations at the macro-scale accompanied by dimensional instabilities. To capture such phenomena, a rate-independent kinematic hardening plasticity model is developed for the individual fibres in Chapter, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

Partial differential equations having diffusive, convective and reactive terms appear naturally in the modeling of a large variety of processes of practical interest in several branches of science such as biology, chemistry, economics, physics, physiology and materials science. Moreover, in some instances several species or components interact with each other requiring to solve strongly coupled systems of convection-diffusion-reaction equations. Of special interest for us is the numerical treatment of the advection dominated continuum dislocation transport equations used to describe the plastic behavior of crystalline materials.Analytical solutions for such equations are extremely scarce and practically limited to linear equations with homogeneous coefficients and simple initial and boundary conditions. Therefore, resorting to numerical approximations is the most affordable and often the only viable strategy to deal with such models. However, when classical numerical methods are used to approximate the solutions of such equations, even in the simplest one dimensional case in the steady state regime for a single equation, instabilities in the form of node to node spurious oscillations are found when the convective or reactive terms dominate over the diffusive term.To address such issues, stabilization techniques have been developed over the years in order to handle such transport equations by numerical means, overcoming the stability difficulties. However, such stabilization techniques are most often suited for particular problems. For instance the Streamline Upwind Petrov-Galerkin method, to name only one of the most well-known, successfully eliminates spurious oscillations for single advection-diffusion equations when its advective form is discretized, but have been shown useless if the divergence form is used instead. Additionally, no extensive work has been carried out for systems of coupled equations. The reason for this immaturity is the lack of a maximum princ, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

info:eu-repo/semantics/nonPublished

info:eu-repo/semantics/nonPublished