Optimal Cracks: How to Crack Any Software in Minutes

A novel high-throughput strategy was developed to determine the calcium precipitation activity (CPA) of mineralization bacteria used for self-healing of concrete cracks. A bacterial strain designated as H4 with the highest CPA of 94.8 % was screened and identified as a Bacillus species based on 16S rDNA sequence and phylogenetic tree analysis. Furthermore, the effects of certain influential factors on the microbial calcium precipitation process of H4 were evaluated. The results showed that lactate and nitrate are the best carbon and nitrogen sources, with optimal concentrations of approximately 25 and 18 mM, respectively. The H4 strain is able to maintain a high CPA in the pH range of 9.5-11.0, and a suitable initial spore concentration is 4.0 10(7) spores/ml. Moreover, an ambient Ca(2+) concentration greater than 60 mM resulted in a serious adverse impact not only on the CPA but also on the growth of H4, suggesting that the maintenance of the Ca(2+) concentration at a low level is necessary for microbial self-healing of concrete cracks.

Optimal Cracks

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Materials and methods: Fifty distobuccal roots of human maxillary first molars were divided into five groups; Group I: PTG Full rotation, Group II: PTG in OTR, Group III: PTN Full rotation, Group IV: PTN in OTR, Group V: unprepared (control group). After mechanical preparation, the distobuccal roots were sectioned horizontally at 3, 6, and 9 mm from the apex. Images were captured using a stereomicroscope at 25X to determine the presence or absence of dentinal cracks. Friedman test was used to compare between root sections followed by Wilcoxon signed-rank test for pairwise comparison. Kruskal-Wallis test was used to compare between tested rotary systems followed by pairwise comparison with Dunn Bonferroni correction (α = 0.05).

Results: Crack development was significantly higher in PTG using OTR motion 36.7% followed by PTN using OTR 33.3%, while the control group showed no cracks. PTG and PTN with full rotation showed crack development with 23.3% and 13.3%, respectively.

Conclusions: The type of motion kinematics used during mechanical preparation have an impact on dentinal crack formation. Nickel-titanium instruments with larger taper tend to induce more cracks.

Assessing the resilience of a road network is instrumental to improve existing infrastructures and design new ones. Here, we apply the optimal path crack model (OPC) to investigate the mobility of road networks and propose a new proxy for resilience of urban mobility. In contrast to static approaches, the OPC accounts for the dynamics of rerouting as a response to traffic jams. Precisely, one simulates a sequence of failures (cracks) at the most vulnerable segments of the optimal origin-destination paths that are capable to collapse the system. Our results with synthetic and real road networks reveal that their levels of disorder, fractions of unidirectional segments and spatial correlations can drastically affect the vulnerability to traffic congestion. By applying the OPC to downtown Boston and Manhattan, we found that Boston is significantly more vulnerable than Manhattan. This is compatible with the fact that Boston heads the list of American metropolitan areas with the highest average time waste in traffic. Moreover, our analysis discloses that the origin of this difference comes from the intrinsic spatial correlations of each road network. Finally, we argue that, due to their global influence, the most important cracks identified with OPC can be used to pinpoint potential small rerouting and structural changes in road networks that are capable to substantially improve urban mobility.

Sequence of removed links during the OPC process for 66 square lattices under weak disorder in traveling times (β=0.002) and different values of the fraction p of unidirectional links, namely, (a) p=0, (b) p=0.4, and (c) p=1. Before the collapse of the system, all links in red were part of an optimal path, at least, once, from the bottom (origin) to the top (destination) of the lattice. Those removed are indicated with white circles in the middle, numbered according to the OPC removal sequence as explained in the main text. The number of removed links clearly decreases with p. The dashed line in (a) corresponds to the fracture backbone that is always present as a result of the OPC process applied to fully bidirectional networks (p=0) [17].

Schematic representation of the OPC process for a realization of a origin (O) destination (D) in downtown Boston. Before the collapse of the network, all links in black or red were part of an optimal path, at least, once. Those removed are in red and indicated with white circles in the middle, numbered according to the OPC removal sequence as explained in the main text.

Fatigue cracked primary aircraft structural parts that cannot be replaced need to be repaired by other means. A structurally efficient repair method is to use adhesively bonded patches as reinforcements. This paper considers optimal design of such patches by minimizing the crack extension energy release rate. A new topology optimization method using this objective is developed as an extension of the standard SIMP compliance optimization method. The method is applied to a cracked test specimen that resembles what could be found in a real fuselage and the results show that an optimized adhesively bonded repair patch effectively reduces the crack energy release rate.

For the aero structural applications motivating the developments in this paper, except for very short cracks, small scale yielding conditions can be assumed to prevail, meaning that inelastic deformations are restricted to a small regime at the crack front, and that the behavior of the crack is governed by the elastic stress state in the material surrounding this plastic zone, see e.g. Anderson (2017). In such a linear elastic fracture mechanics context, the intensity of the loading as seen from the crack can be described by the stress intensity factors \(K_I\), \(K_II\) and \(K_III\), which for a plane geometry characterizes the stress singularity in tearing, in-plane shearing and out-of-plane shearing. For a general geometry and loading, however, a more direct description of the crack driving force is the energy release rate G, specifying the energy available for crack growth. In terms of equilibrium potential energy \(\Pi \), seen as function of a crack area A, we may write \(G=-\partial \Pi /\partial A\). For a plane geometry and for an isotropic material the stress intensity factors and G are related as

The paper is organized as follows: Section 2 introduces the finite element discretized structural problem. We use the basic definition of crack energy release rate as the sensitivity of the potential energy with respect to crack extension, and derive its sensitivity with respect to design changes. Such first and second variations of energy with respect to change of domain due to crack extension, and its relation to, e.g., the J-integral, is discussed in Nguyen (2000). In Section 3 the general structural optimization problem is introduced. Basic facts concerning SIMP penalization, filter regularization and the optimality criteria method are given. Calculation of the crack energy release rate as well as its sensitivity requires the sensitivity of the stiffness matrix with respect to crack extension. This is accomplished by the so-called virtual crack extension method (Parks 1974; Hellen 1975). In Section 4 we present numerical examples corresponding to two test specimen geometries and loadings. We present optimal repair patch geometries created by both an essentially standard compliance optimization formulation and the novel formulation that uses the crack energy release rate as objective. The more advanced specimen is chosen to resemble conditions that can be expected in a real fuselage. The model includes an adhesive layers that bonds the repair patches to the cracked specimen. Finally, summary and conclusions are given in Section 5.

This may be accomplished by simple interval reduction. The algorithm then returns to calculate a new trial design. Convergence is assumed when the maximum absolute difference between \(\rho _i^k\) and \(\rho _i^k + 1\) falls below a prescribed value, or after a fixed number of iterations. The need for a non-positive \(S(\boldsymbol \rho ^k)\) follows from the iteration formula (9) if the Lagrangian multiplier is assumed positive: a fact that can be expected as long as a larger available volume V implies a lower optimal objective function value.

In order to retain a pure tearing state of the crack after adding repair patches for the specimen shown in Fig. 3, we use symmetry, which means that two identical patches are added on each side of the cracked specimen. A second symmetry plane through the crack is also used. The length of the specimen, in the direction of the distributed force, shown as green arrows in Fig. 3, is 650 mm, and the width is 120 mm. The thickness of the plate is 3 mm and the length of the crack, shown as a red color line in the figure, is 10 mm. The design domain for topology optimization, i.e., the volume that, due to the two symmetry planes, could be occupied by half of one of the final optimized repair patches, is of size 80 \(\times \) 60 \(\times \) 25 mm. In Fig. 4, where one of the symmetries are retained, optimal repair patches are shown in blue. The problem has been solved for different mesh refinements and for both objective functions discussed in Section 3. The volume of the optimal structure, i.e., the constant V of problem \((\mathbb P)\), is chosen as 1/5 times the volume of the design domain. All used meshes consist of 27-node brick elements. The results presented here are for the problem of minimizing crack energy release rate, i.e., using \(f_g\) as objective. Results for classical stiffness maximization are presented for the more advanced test specimen in the next subsection. However, it should be noted that a repair patch that is optimal for such an objective will mostly tend to reduce the global lengthening of test specimen, instead of reducing crack opening, and, therefore, material tends to be placed away from the crack. 2ff7e9595c