Modeling of the competition between shear yielding and crazing in glassy polymers Estevez, R.; Tijssens, M.G.A.; van der Giessen, E. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. AbstractFracture in amorphous glassy polymers involves two mechanisms of localized deformations: shear yielding and crazing. We here investigate the competition between these two mechanisms and its consequence on the material's fracture toughness. The mechanical response of the homogeneous glassy polymer is described by a constitutive law that accounts for its characteristic softening upon yielding and the subsequent progressive orientational strain hardening. The small scale yielding, boundary layer approach is adopted to model the local finite-deformation process in front of a mode I crack. The concept of cohesive surfaces is used to represent crazes and the traction-separation law incorporates craze initiation, widening and breakdown leading to the creation of a microcrack. Depending on the craze initiation sensitivity of the material, crazing nucleates at the crack tip during the elastic regime or ahead of the crack. As the crazes extend, plasticity develops until an unstable crack propagation takes place when craze fibrils start to break down. Thus, the critical width of a craze appears to be a key feature in the toughness of glassy polymers. Moreover, the opening rate of the craze governs the competition between shear yielding and brittle failure by crazing.

This article addresses one of the major constraints imposed by additive manufacturing processes on shape optimization problems -that of overhangs, i.e. large regions hanging over void without sufficient support from the lower structure. After revisiting the 'classical' geometric criteria used in the literature, based on the angle between the structural boundary and the build direction, we propose a new mechanical constraint functional, which mimics the layer by layer construction process featured by additive manufacturing technologies, and thereby appeals to the physical origin of the difficulties caused by overhangs. This constraint, as well as some variants, are precisely defined; their shape derivatives are computed in the sense of Hadamard's method and numerical strategies are extensively discussed, in two and three space dimensions, to efficiently deal with the appearance of overhang features in the course of shape optimization processes.

To cite this version:Charles Dapogny, Alexis Faure, Georgios Michailidis, Grégoire Allaire, Agnes Couvelas, et al.. Geometric constraints for shape and topology optimization in architectural design.Abstract. This work proposes a shape and topology optimization framework oriented towards conceptual architectural design. A particular emphasis is put on the possibility for the user to interfere on the optimization process by supplying information about his personal taste. More precisely, we formulate three novel constraints on the geometry of shapes; while the first two are mainly related to aesthetics, the third one may also be used to handle several fabrication issues that are of special interest in the device of civil structures. The common mathematical ingredient to all three models is the signed distance function to a domain, and its sensitivity analysis with respect to perturbations of this domain; in the present work, this material is extended to the case where the ambient space is equipped with an anisotropic metric tensor. Numerical examples are discussed in two and three space dimensions.

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In recent years the phase-field method and the coupled energy and stress-based criterion have attracted much attention due to their adaptability in modeling fractures. Both approaches have been successfully used to determine crack initiation and have compared well with real-life experiments. The phase-field method diffuses the crack surface into the volume of the solid, thus making the solution viable through variational techniques. The diffusion is controlled by an internal length scale, which is primarily considered to be a numerical aid without any real physical meaning. In this paper, we question the consideration that the internal length is only a numerical parameter, and assess its mechanical significance with the help of the coupled criterion. Through elaborate benchmark examples, the correlation between the two methods is demonstrated based on the critical loading, the crack topology, and the crack arrest length. We reveal that independently of the chosen aspect, the phase-field approach and the coupled criterion present excellent correspondence. We show that the correlation between tensile strength and length scale is unique for the standard phase-field formulation. Interestingly, we find that both stress and energy criteria are satisfied in the phase-field fracture, and this is explained by demonstrating the alteration in global energy release rate due to the regularization introduced by the smeared model.

This article considers the modelling of the effective properties of the constituent material of structures fabricated by additive manufacturing technologies; the influence of these properties on the design optimization process is analyzed, and the opportunities that they offer in this context are investigated. On the one hand, emphasizing on the case where the particular material extrusion techniques are used for the construction, we propose a model for the anisotropic material properties of shapes depending on the (user-defined) trajectory followed by the machine tool during the assembly of their 2d layers. On the other hand, we take advantage of the potential of additive manufacturing technologies for constructing very small features: we consider the optimization of the infill region of a shape with given external contour with the goal to improve at the same time its lightness and its robustness. The optimized and constraint functionals of the domain involved in the shape optimization problems in both contexts are rigorously analyzed, notably by relying on the notion of signed distance function. Eventually, several numerical experiments are conducted in two dimensions to illustrate the main points of the study.