Urban crystallization and the morphogenesis of urban territories

We develop the perspective of crystallization as a way to shed a light on the morphogenesis and stabilization of urban territories. We start by describing crystallization as a consolidation of a visible and singular order that establishes certain privileged directions of growth and breaks spatial and temporal symmetries. We then illuminate how crystallization processes unfold at different scales, going through a series of historical cases, from the stabilization of urban regions, to iconic places such as Times Square, New York, and on to large scale linear or path crystals, such the Turia Riverbed Park in Valencia. Building on thesecases, we then discuss crystallization as a phenomenon requiring metastability, and how this metastability relates to different ways and forms of territorial stabilization. Finally, we discuss how crystallization, by making certain figures and directions more salient than others, also plays an important part in the emergence of new scales and in the processes of urban rescaling, that is, how crystallization also contributes to a hierarchical segmentation of the urban environment

Crack path dependence on inhomogeneities of material microstructure

Crack trajectories under different loading conditions and material microstructural features play animportant role when the conditions of crack initiation and crack growth under fatigue loading have to beevaluated. Unavoidable inhomogeneities in the material microstructure tend to affect the crack propagationpattern, especially in the short crack regime. Several crack extension criteria have been proposed in the pastdecades to describe crack paths under mixed mode loading conditions. In the present paper, both the Sihcriterion (maximum principal stress criterion) and the R-criterion (minimum extension of the core plastic zone)are adopted in order to predict the crack path at the microscopic scale level by taking into account microstressfluctuations due to material inhomogeneities. Even in the simple case of an elastic behaviour under uniaxialremote stress, microstress field is multiaxial and highly non-uniform. It is herein shown a strong dependence ofthe crack path on the material microstructure in the short crack regime, while the microstructure of the materialdoes not influence the crack trajectory for relatively long cracks

Discontinuous FE approach and lattice models to describe cracking behaviour in fibre-reinforced brittle materials

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Defect tolerance in soft materials

Abstract The ability of materials to withstand defects like cracks, notches or generic geometric discontinuities, is usually indicated as flaw tolerance, and is a crucial aspect of the safety assessment of structural components. Flaw tolerance in soft materials can be substantially different from that in traditional ones. As a matter of fact, the capacity of highly deformable materials to undergo large deformations with a significant rearrangement of the molecular network at the miscroscale in highly stressed regions can enhance such an ability, leading to an erroneous underestimation of their safety level against defect-driven failure, if traditional methods of analysis are employed. In the present research work, the mechanics of highly deformable notched plates is considered from the fail-safety point-of-view. Experimental, numerical and theoretical remarks are made in order to explain the mechanism of defect resistance in such a class of materials from a physically-based point-of-view

Crack paths in soft thin sheets

Highly deformable materials (elastomers, gels, biological tissues, etc.) are ubiquitous in nature as well as in technology. The understanding of their flaw sensitivity is crucial to ensure a desired safety level. Fracture failure in soft materials usually occurs after the development of an uncommon crack path because of the non-classical near-tip stress field and the viscous effects. In a neo-Hookean material, the true opening stress singularity along the crack path (evaluated normal to the crack line) is of the order , while it is of the order ahead of the crack tip, promoting the appearance of a crack tip splitting leading to a tortuous crack. In the present paper, experimental tests concerning the fracture behavior of highly deformable thin sheets under tension are discussed, and the observed crack paths are interpreted according to the crack tip stress field arising for large deformations. The study reveals that higher strain rates facilitate the development of a simple Mode I crack path, while lower strain rates induce a mixed Mode in the first crack propagation stage, leading to the formation of new crack tips. The above described behavior seems to not be affected by the initial crack size

A unified approach for static and dynamic fracture failure in solids and granular materials by a particle method

The material structure at the microscale reveals the particulate nature of solids. By exploiting the discrete aspect of materials, the so-called particle methods developed and applied to the simulation of solids and liquids have attracted the attention of several researchers in the field of computational mechanics. In the present paper, a particle method based on a suitable force potential is proposed to describe the nature and intensity of the forces existing between particles of either the same solid or different colliding solids. The formulation applies to problems involving both granular materials and solids interacting with granular materials. The above approach is applied to simulate different problems dealing with the 3D dynamic fracture and failure of solids

Effect of fibre arrangement on the multiaxial fatigue of fibrous composites: a micromechanical computational model

Structural components made of fibre-reinforced materials are frequently used in engineering applications. Fibre-reinforced composites are multiphase materials, and complex mechanical phenomena take place at limit conditions but also during normal service situations, especially under fatigue loading, causing a progressive deterioration and damage. Under repeated loading, the degradation mainly occurs in the matrix material and at the fibre-matrix interface, and such a degradation has to be quantified for design structural assessment purposes. To this end, damage mechanics and fracture mechanics theories can be suitably applied to examine such a problem. Damage concepts can be applied to the matrix mechanical characteristics and, by adopting a 3-D mixed mode fracture description of the fibre-matrix detachment, fatigue fracture mechanics concepts can be used to determine the progressive fibre debonding responsible for the loss of load bearing capacity of the reinforcing phase. In the present paper, a micromechanical model is used to evaluate the unixial or multiaxial fatigue behaviour ofstructures with equi-oriented or randomly distributed fibres. The spatial fibre arrangement is taken into account through a statistical description of their orientation angles for which a Gaussian-like distribution is assumed, whereas the mechanical effect of the fibres on the composite is accounted for by a homogenization approach aimed at obtaining the macroscopic elastic constants of the material. The composite material behaves as an isotropic one for randomly distributed fibres, while it is transversally isotropic for unidirectional fibres. The fibre arrangement in the structural component influences the fatigue life with respect to the biaxiality ratio for multiaxial constant amplitude fatigue loading. One representative parametric example is discussed

fracture toughness of highly deformable polymeric materials

Abstract: A fundamental requirement for safety design of structural components is flaw tolerance. In this field, the soft materials have a unique ability to bear external loads despite the presence of defects, due to their pronounced deformability. Unlike traditional materials, which have an enthalpic elasticity, the mechanical response of a polymer-based material is governed by the state of internal entropy of a molecular network which has a great ability to rearrange the material structure and shape so to minimize the local detrimental effect of flaws. For a correct estimation of the fracture toughness of these materials, a proper knowledge of this entropic effect is needed. In the present research, the mechanical behaviour up to failure of silicone-based cracked plates is examined by taking into account the time-dependent effects. Experimental and theoretical aspects are discussed in order to understand the defect tolerance of such materials

a phase field approach for crack modelling of elastomers

Abstract The description of a problem related to an evolving interface or a strong discontinuity requires to solve partial differential equations on a moving domain, whose evolution is unknown. Standard computational methods tackle this class of problems by adapting the discretized domain to the evolving interface, and that creates severe difficulties especially when the interface undergoes topological changes. The problem becomes even more awkward when the involved domain changes such as in mechanical problems characterized by large deformations. In this context, the phase-field approach allows us to easily reformulate the problem through the use of a continuous field variable, identifying the evolving interface (i.e. the crack in fracture problems), without the need to update the domain discretization. According to the variational theory of fracture, the crack grows by following a path that ensures that the total energy of the system is always minimized. In the present paper, we take advantage of such an approach for the description of fracture in highly deformable materials, such as the so-called elastomers. Starting from a statistical physics-based micromechanical model which employs the distribution function of the polymer's chains, we develop herein a phase-field approach to study the fracture occurring in this class of materials undergoing large deformations. Such a phase-field approach is finally applied to the solution of crack problems in elastomers