Multiple Failure Criteria Research Articles

Anisotropic damage evolution in solid fractures: A novel phase field approach with multiple failure criteria and directional-dependent structural tensor

This study proposes a novel phase-field fracture model based on unified phase field theory, aiming to overcome current limitations in simulating material complex fracture behaviors. Through this model, analytical solutions for two-dimensional bars subjected to tensile or compressive stresses are provided, enabling the coupling of multiple failure criteria and further proficient simulation of mode-I, mode-II, and mixed mode-I/II fractures, effectively addressing challenges faced in modelling materials with different or complex failure modes under various loading conditions. Furthermore, to account for the strong anisotropic failure behavior of materials, a novel directional-dependent structural tensor is proposed. The tensor correlates fracture energy with crack surface orientation, facilitating precise characterization of material damage evolution with multiple potential crack orientations. This tensor ensures the consistency of phase-field fracture evolution with predefined fracture patterns. The effectiveness of the proposed model is validated through case studies, emphasizing its robustness and superior predictive capability in capturing fracture behavior under various conditions. This research provides a more accurate and universally applicable approach for simulating material failure, particularly for complex or multiple failure mode material failure simulations.

The effect of the stress equilibrium factor on the composite case of the solid rocket motor

In this paper, based on the composite structure design and analysis software ANSYS ACP, the layup design for the composite cases of the equal pole hole solid rocket motor with different stress equilibrium factors is carried out. The finite element software ANSYS Workbench is used to study in detail the effects of stress equilibrium factor on the stress level, failure degree, and burst pressure prediction of the case under a certain internal pressure. The results show that reducing the value of the stress equilibrium factor can reduce the stress level of each winding layer along the main direction of the material in the motor case and gradually transfer the maximum stress of the case along the fiber direction from the weak stress zone to the cylinder section. This is beneficial for improving the burst pressure of the case and making the burst point located in the cylinder section. However, whether the case failure is related to the selected failure theory and strength criterion, the failure results and burst pressure obtained using different failure theories and strength criteria may be different, which indicates that each failure criterion has its scope of application and limitations. Under the Tsai-Wu criterion, using the stress equilibrium equation to calculate the stress equilibrium factor can just ensure that each winding layer of the motor case does not fail under the working pressure. In summary, when designing a composite case and predicting its failure, in addition to considering whether the stress equilibrium factor taken is conducive to meeting the design requirements for the strength of the case, it is also necessary to consider the use of multiple failure criteria to study the failure of the case. Obviously, arbitrarily selecting the stress equilibrium factor is not appropriate in the above process. By analyzing the influence of the stress equilibrium factor on the strength and failure condition of the motor case, it can provide an effective reference for the design of a composite case for SRM.

Fuzzy seismic fragility analysis of underground structures considering multiple failure criteria

To avoid the deficiency of a single failure criterion and deterministic thresholds of limit states in seismic fragility analysis of underground structures, a method of fuzzy seismic fragility analysis of underground structures considering multiple failure criteria is proposed by combining fuzzy-random theory and copula theory. In this method, probabilistic seismic demand and capacity analyses based on different failure criteria are first performed. Then, the fuzziness of the limit states of different failure criteria is characterized by using membership functions, and the fuzzy seismic fragility of underground structures considering a single failure criterion with different membership functions is further calculated. On this basis, the copula function and the combination of membership functions are optimized to characterize the correlation between multiple failure criteria and establish fuzzy seismic fragility curves considering multiple failure criteria. Taking the Daikai subway station as the background, the effects of different failure criteria and the fuzziness of limit states on the seismic fragility are discussed, and the optimal combination of membership functions that characterizes the fuzziness of limit states under the failure criteria of deformation and strength is also presented. The results show that the failure criteria and fuzziness of limit states have significant effects on the seismic fragility of underground structures, and the combination of trigonometric membership functions is the optimal combination that characterizes the fuzziness of multiple failure criteria. Moreover, the fuzzy seismic fragility of underground structures considering multiple failure criteria is more sensitive to the fuzziness of limit states under frequent earthquakes and basic earthquakes, while the multiple failure criteria and the correlation between different failure criteria have more significant effects on the fuzzy seismic fragility considering multiple failure criteria under rare earthquakes and extremely rare earthquakes.

Finite Elements Analysis of Biomechanical Behavior of the Bracket in a Gradual Horizontal Periodontal Breakdown—A Comparative Analysis of Multiple Failure Criteria

This study assessed the stress distribution (in eighty-one 3D models of the second lower premolar) in a stainless-steel bracket and enamel crown under 0.5 N of intrusion, extrusion, rotation, translation, and tipping during a horizontal periodontal breakdown of 0–8 mm. The FEA simulations (totaling 405) employed five failure criteria and assessed the adequacy and accuracy of Von Mises (VM), Tresca (T), Maximum Principal (S1), Minimum Principal (S3), and Hydrostatic Pressure. T and VM criteria showed no change in stress display areas during the periodontal breakdown, seeming to be more correct and adequate than the other three (with unusual stress displays). Both VM and T (found to be more adequate) generated maximum stress areas on the attachment side and the entire base of the bracket, confirming the non-homogenous stress distribution areas and the risks of bond failure. Rotation, translation, and tipping were the most stressful movements and showed slightly lower quantitative values for 8 mm bone loss when compared with the intact periodontium, while intrusion and extrusion showed the opposite behavior (slight increase). Periodontal breakdown did not influence the stress display in the bracket and its surrounding enamel area during the five orthodontic movements.

Cortical and Trabecular Bone Stress Assessment during Periodontal Breakdown-A Comparative Finite Element Analysis of Multiple Failure Criteria.

Background and Objectives: This numerical analysis investigated the biomechanical behavior of the mandibular bone as a structure subjected to 0.5 N of orthodontic force during periodontal breakdown. Additionally, the suitability of the five most used failure criteria (Von Mises (VM), Tresca (T), maximum principal (S1), minimum principal (S3), and hydrostatic pressure (HP)) for the study of bone was assessed, and a single criterion was identified for the study of teeth and the surrounding periodontium (by performing correlations with other FEA studies). Materials and Methods: The finite element analysis (FEA) employed 405 simulations over eighty-one mandibular models with variable levels of bone loss (0-8 mm) and five orthodontic movements (intrusion, extrusion, tipping, rotation, and translation). For the numerical analysis of bone, the ductile failure criteria are suitable (T and VM are adequate for the study of bone), with Tresca being more suited. S1, S3, and HP criteria, due to their distinctive design dedicated to brittle materials and liquids/gas, only occasionally correctly described the bone stress distribution. Results: Only T and VM displayed a coherent and correlated gradual stress increase pattern for all five movements and levels of the periodontal breakdown. The quantitative values provided by T and VM were the highest (for each movement and level of bone loss) among all five criteria. The MHP (maximum physiological hydrostatic pressure) was exceeded in all simulations since the mandibular bone is anatomically less vascularized, and the ischemic risks are reduced. Only T and VM displayed a correlated (both qualitative and quantitative) stress increase for all five movements. Both T and VM displayed rotation and translation, closely followed by tipping, as stressful movements, while intrusion and extrusion were less stressful for the mandibular bone. Conclusions: Based on correlations with earlier numerical studies on the same models and boundary conditions, T seems better suited as a single unitary failure criterion for the study of teeth and the surrounding periodontium.

Numerical validation and optimization of hybrid composite beam hull using multiple failure criteria

The number of structurally deficient bridges continues to increase due to corrosion of steel sections and concrete rebar, therefore the replacement of decaying structures and the development of innovative systems have become of high priority to extend the life span of newly built bridges. Hybrid Composite Beam (HCB) produced by Hillman is one of those systems that use a combination of materials i.e., concrete, steel, and Glass Fiber-Reinforced Polymer (GFRP) to integrate each main advantage in a single bridge beam structure. Despite its several apparent advantages; it is not widely spread as expected within the last decade. The HCB is manufactured of self-consolidating concrete (SCC), which is poured in the shape of a traditional arch and tied at its ends by high-strength tendons. A durable FRP composite hull encapsulates the SCC arch and the high-strength tying tendons in order to create a structural beam element for bridge applications. The HCB's design aims to provide pure compressive stresses to the concrete and pure tensile stresses to the steel. The current study performs a deep numerical investigation of the FRP hull instead of other components comprehensively studied. Numerical validation is performed for the deflection results on the experimentally tested Knickerbocker HCB Bridge, the deformations are validated at four stages of HCB manufacturing and testing. Further, the FRP hull strength ratios are quantified for the worst value of four failure criteria. The results showed an excess use of FRP material, where more than 90% of FRP areas have strength ratios of 5 to 50. The FRP hull thickness is minimized using Genetic Algorithm optimization under the worst case of loading. The results achieved more than 60% decrease in FRP weight, that led to only 20% cost difference between traditional precast concrete and HCB girders. It is finally concluded that the overdesign of FRP hull contributed to the high cost of HCB usage consequently inefficient market spread.

Virtual modelling integrated phase field method for dynamic fracture analysis

A non-deterministic phase field (PF) virtual modelling framework is proposed for three-dimensional dynamic brittle fracture. The developed framework is based on experimental observations, accurate numerical modelling, and virtually foreseeable dynamic fracture prediction module through the machine learning algorithm. The uncertain system inputs, including variabilities of material properties, are incorporated into dynamic fracture analysis. Phase field method is implemented to simulate the dynamic fracture behaviours of 3D cracked structures with variabilities and then to create the training database for virtual damage model. The virtual damage model omits the physical finite element approximation process and reveals the virtual governing relationship between the variational system inputs and fracture responses. This advantage enables the virtual model to provide reliable crack propagation prediction based on either experiment-based or numerical simulation and greatly improves the computational efficiency of dynamic fracture analysis. To establish the accurate virtual model in the training process, a newly developed extended support vector regression (X-SVR) method with T-spline polynomial kernel functions is adopted for its outstanding performance in handling complex high-dimensional problems. Based on different real-world engineering scenarios, multiple fracture failure criteria, both strength-based and serviceability-based, are selected and demonstrated in numerical investigations to visualise the proposed framework's workflow. The effectiveness as well as accuracy are verified by these examples, and it is observed that the computational efficiency of dynamic fracture analysis is greatly improved. With the proposed framework, a continuously updating dynamic fracture surveillance system can be potentially built for practical applications.

Probabilistic Fatigue Fragility Curves for Overhead Transmission Line Conductor-Clamp Assemblies

The residual life of transmission line overhead conductors under conditions of fretting fatigue is an important asset management issue for electric network operators. The current industry practice for overhead conductor residual life estimation relies heavily on experimentally generated fatigue curves or rule-based expert systems. The current experiment-based methods do not consider specific conductor-clamp configurations and are based on the simple flexion model. This approach results in large uncertainties in service life predictions and are limited to a failure criterion based on the first wire failure in the conductor. Rule-based expert systems also have limited applicability since they lack physical representation of the fretting fatigue process. Given the limitations of the current methods, the objective of this work is to propose a framework that combines physics-based models and probability theory to estimate the residual life of overhead conductors considering either single or multiple wire failure criteria. To illustrate this procedure, a finite element model of a Bersfort conductor-clamp system is used to assess the contact conditions and internal stress states in the wires of the conductor. Results from the numerical model are then used to develop a fretting fatigue criterion that is a function of the contact energy dissipation mechanisms, contact stresses, and the plain fatigue resistance of the wires. Probability of failure of each contact point between wires and between wires and clamp is computed using the fretting fatigue criterion. With this information, the most probable locations of fretting fatigue failure are identified in the conductor. The predictions for the locations of failure are validated with available literature data for the same conductor-clamp configuration. Given the probabilities of failures at each contact point, the probability of failure of the conductor is derived with the Poisson binomial distribution. Fragility curves are presented for the first through the third wire failures in the conductor. The fragility curves are validated through comparisons with available literature data on the same conductor-clamp configuration. Fatigue curves are also generated from the fragility model for the first wire failure and compared against experimentally generated fatigue curves.

Study on Multiple Failure Criteria of Asphalt Mixtures in Complex Stress States

AbstractAn asphalt mixture is always in a complex stress state during the service life of pavement. Its resistance can be objectively characterized only by applying the strength theory to establish...

Stress Analysis of Variable Ram Blowout Prevention Valves

Summary Variable ram blowout prevention (VRBOP) valves are elastomeric material-based flow control devices used in offshore oil drilling applications as the primary safety mechanism to respond to high wellbore pressure emergency situations. During their operation, the elastomer deforms and distorts extensively to form a tight seal around the drillpipe. Because of the large deformation and distortion of the elastomer, developing a Lagrangian-based finite element analysis model to simulate the operation of a VRBOP valve is quite challenging. The finite elements of the Lagrangian finite element mesh degrade in quality because they deform with the material when the deformation becomes excessive. This leads to poor convergence of the numerical solution. In this study, we first demonstrate that the numerical convergence issues can be resolved by using a suite of modeling techniques: explicit integration scheme, Ogden second-order hyperelastic constitutive model for the elastomer, and the selection of appropriate values for element sizes and other modeling parameters. After resolving the convergence issues, we used the model to study the sealing efficiency and material failure of a VRBOP valve for two different operating temperatures and drillpipe diameters. The sealing efficiency is studied using two performance criteria: the uniformity of the sealing pressure around the drillpipe and the magnitude of the overall deformation of the elastomer. For the material failure analysis of the elastomer, we used multiple failure criteria. The results of this study provide many new insights that have the potential to improve VRBOP valve design. For instance, results show that elevated temperature improves the sealing efficiency of a VRBOP valve because of the higher flexibility of the elastomer at elevated temperatures. Likewise, the wellbore pressure also improves the sealing efficiency. However, all these improvements in sealing pressure come with the risk of a higher probability of material failure.

Optimal bivariate mission abort policy for systems operate in random shock environment

For many safety-critical systems such as aircrafts, nuclear power plants and human space flights, system survival has higher priority over mission completion. For the purpose of enhancing the survivability of safety-critical systems, a mission can be aborted when a certain malfunction condition is satisfied and a rescue procedure is initialized immediately. As the configuration and operating environment for most mission-oriented systems are becoming increasingly complex, multiple failure criteria are commonly observed. This paper investigates the optimal mission abort policy for systems executing missions in a random environment combining cumulative shock model and run shock model. The mission is aborted when the cumulative number of valid shocks reaches a critical value or the number of consecutive valid shocks exceeds a preset level. Under the proposed bivariate mission abort policy, mission success probability and system survivability are evaluated. Two optimization models are constructed to minimize the expected total cost and maximize the mission success probability while providing a desired system survivability. In addition, two heuristic abort policies that only consider single abort criterion are illustrated to justify the advantage of the constructed bivariate mission abort policy. A case study on an aircraft performing transportation task is presented to illustrate the obtained results.

Multi-state balanced systems with multiple failure criteria

The concept of balanced systems has been evolved with many meanings recently, and the research on this topic is a hot and significant issue in the reliability field. In this paper, the system consisting of two components does not fail immediately when it is unbalanced. An imminent unbalanced state is defined that the system experienced before reaching its final failure. According to the sojourn time of the system in the imminent unbalanced state and the number of transitions from the balanced to imminent unbalanced states, two new failure criteria are proposed. Combined with the situation where the system components may be permanently damaged, three types of competing risk models are developed for multi-state balanced systems with multiple failure criteria, which are time threshold models, count threshold models and the mixed threshold model. The closed-form formulas of reliability indexes of the multi-state balanced system under five proposed models are obtained by using the theory of aggregated stochastic processes, such as the probability density function of the system lifetime. The extensions to systems with multiple components are discussed. Finally, numerical examples are provided to illustrate the proposed model and the obtained results.

System Reliability Evaluation of a Bridge Structure Based on Multivariate Copulas and the AHP–EW Method That Considers Multiple Failure Criteria

The system reliability evaluation of a bridge structure is a complicated problem. Previous studies have commonly used approximate estimation methods, such as the wide bounds method and the narrow bounds method, but neither could obtain an accurate result. In recent years, the copula theory has been introduced into the system reliability evaluation, which can obtain more accurate results than the approximate methods. However, most studies simply construct binary copula functions to consider the joint failure of two failure modes. For a complex bridge structure composed of multiple components and failure modes, the joint failure of multiple failure modes needs to be considered. Before evaluating the system reliability, it is necessary to determine the failure criteria of the system. Different failure criteria for simply supported beam bridges have been proposed. However, there is no standard available to determine which failure criterion to choose, and the selection of failure criteria is ambiguous. In this paper, a novel method is proposed to evaluate the system reliability of a simply supported beam bridge by considering multiple failure criteria based on multivariate copulas and the analytic hierarchy process entropy weight (AHP–EW) method. The method first considers multiple failure criteria comprehensively and constructs multivariate copulas for the joint failure of multiple components in a bridge system reliability evaluation. The AHP–EW method is a comprehensive weighting method combining the analytic hierarchy process and entropy weight methods, which is used to establish the hierarchical analysis model between system reliability and multiple failure criteria. By considering the joint failure of multiple failure modes in the system reliability evaluation under a single failure criterion, multivariate copula functions were constructed. In order to verify the applicability of the proposed bridge system reliability method, a simply supported reinforced concrete (RC) hollow slab bridge composed of nine slab segments was selected as the numerical example. The results indicate that the method proposed in this paper could evaluate the bridge system reliability more comprehensively and reasonably.

Reliability and Failure Probability Functions of the Consecutive-k-out-of-m-from-n: F System with Multiple Failure Criteria | اقتران موثوقية و اقتران احتمال فشل النظام التتابعي k-out-of-m-from-n: F متعدد معايير الفشل

Reliability and Failure Probability Functions of the Consecutive-k-out-of-m-from-n: F System with Multiple Failure Criteria | اقتران موثوقية و اقتران احتمال فشل النظام التتابعي k-out-of-m-from-n: F متعدد معايير الفشل

Reliability and Failure Probability Functions of the Consecutive-k-out-of-m-from-n: F System with Multiple Failure Criteria | اقتران موثوقية و اقتران احتمال فشل النظام التتابعي k-out-of-m-from-n: F متعدد معايير الفشل

Reliability and Failure Probability Functions of the Consecutive-k-out-of-m-from-n: F System with Multiple Failure Criteria | اقتران موثوقية و اقتران احتمال فشل النظام التتابعي k-out-of-m-from-n: F متعدد معايير الفشل

Reliability And Failure Probability Functions Of The Consecutive-k-out-of-m-from-n: F System With Mul-tiple Failure Criteria

The consecutive-k-out-of-m-from-n: F system with multiple failure criteria consists of n sequentially ordered components (K= (k1, k2,..., kH), m = (m1, m2,..., mH)). The system fails if among any m1, m2,..., mH consecutive components there are at least k1, k2,..., kH components in the failed state. In this paper, the ordinary consecutive-k-out-of-m-from-n: F system played a pivotal role in achieving the reliability and failure probability functions of the consecutive-k-out-of-m-from-n: F linear and circular system with multiple failure criteria. We proved that the failure states of the multiple failure criteria system is a union of all failure state of the consecutive-ki-out-of-mi-from-n: F system, while the functioning state is an intersection of the functioning states of the consecutive-ki-out-of-mi-from-n: F system for . The maximum number of failed components of the functioning consecutive k-out-of-m-from-n: F system with multiple failure criteria is computed.

Multiple failure criteria-based fragility curves for structures equipped with SATMDs

In this paper, a procedure to develop fragility curves of structures equipped with semi-active tuned mass dampers (SATMDs) considering multiple failure criteria has been presented while accounting for the uncertainties of the input excitation, structure and control device parameters. In this procedure, Latin hypercube sampling (LHS) method has been employed to generate 30 random SATMD-structure systems and nonlinear incremental dynamic analysis (IDA) has been conducted under 20 earthquakes to determine the structural responses, where failure probabilities in each intensity level have been evaluated using Monte Carlo simulation (MCS) method. For numerical analysis, an eight-story nonlinear shear building frame with bilinear hysteresis material behavior has been used. Fragility curves for the structure equipped with optimal SATMDs have been developed considering single and multiple failure criteria for different performance levels and compared with that of uncontrolled structure as well as structure controlled using passive tuned mass damper (TMD). Numerical analysis has shown the capability of SATMDs in significant enhancement of the seismic fragility of the nonlinear structure. Also, considering multiple failure criteria has led to increasing the fragility of the structure. Moreover, it is observed that the influence of the uncertainty of input excitation with respect to the other uncertainties is considerable.

Seismic capacity evaluation of a sliding isolation concrete rectangular liquid-storage structure

Considering fluid-structure interaction (FSI), material nonlinearity and liquid sloshing nonlinearity, a nonlinear calculation model of sliding isolation concrete rectangular liquid-storage structure (CRLSS) with limiting devices is established. Failure criteria for sliding isolation CRLSS are summarised and defined, and a method for evaluating seismic capacity of sliding isolation CRLSS is proposed. Under near-field pulse-like earthquake, near-field no-pulse earthquake and far-field earthquake, seismic capacities of no-isolation structure, pure sliding isolation structure and sliding isolation structure are studied, comparatively. Results show that the seismic capacity of CRLSS is weakest under the actions of near-field pulse-like earthquakes; when the height of the reserved no-liquid wall is sufficiently large, sliding isolation can convert the main failure mode of the CRLSS from wall crack to excessive structure displacement, and the reasonable design of limiting device can reduce the failure probability of the sliding isolation CRLSS caused by excessive structure displacement. Besides, it is more reasonable to evaluate the seismic capacity of the system considering multiple failure criteria, and liquid level height and limiting device are the two important factors that affect the failure probability of the sliding isolation CRLSS.

Global optimal reliability index of implicit composite laminate structures by evolutionary algorithms

With uncertainty, reliability assessment is fundamental in structural optimization, because optimization itself is often against safety. To avoid Monte Carlo methods, the Reliability Index Approach (RIA) approximates the structural failure probability and is formulated as a minimization problem, usually solved with fast gradient-methods, at the expense of local convergence, or even divergence, particularly for highly dimensional problems and implicit physical models. In this paper, a new procedure for global convergence of the RIA, with practical efficiency, is presented. Two novel evolutionary operators and a mixed real-binary genotype, suitable to hybridize any Evolutionary Algorithm with elitist strategy, are developed. As an example, a shell laminate structure is presented and the results validated, showing good convergence and efficiency. The proposed method is expected to set the basis for further developments on the design optimization of more complex structures with multiple failure criteria.

Finite element analysis of composite laminates subjected to low-velocity impact based on multiple failure criteria

Progressive damage models based on continuum damage mechanics are used in combination with cohesive elements to explore the effect of three different failure criteria including Chang-Chang, Hashin and Puck criteria, on the structural response and the failure mechanisms of composite laminates subjected to low-velocity impact. Three different failure criteria and damage evolution laws based on equivalent strain are used for intralaminar damage models, and the delamination is simulated by the bilinear cohesive model based on quadratic criteria. A new numerical optimization method combining analytical approximation and Golden section Search has been applied in Puck criteria to search the fracture plane. Numerical analysis is performed on two composite laminates specimens with different materials, layups and impact energy to study the impact force-time, force-displacement and absorbed energy, computational cost, as well as the damage evolution behaviors of fiber, matrix and delamination. The numerical results with three different failure criteria show acceptable accord with available experimental data, which validate the accuracy of the proposed damage model. Moreover, this research can be helpful to select appropriate failure criteria in the progressive failure analysis of composite laminates under low velocity impact.