XFEM-VCCT for Composite Delamination

ObjectiveIn order to accurately assess the ice resistance experienced by an icebreaker during continuous icebreaking when sailing in a level ice zone, and understand the characteristics of different prediction methods, this paper uses the empirical formula method, numerical simulation method and ship model test method to evaluate an icebreaker's continuous sailing in smooth ice and predict the ice resistance. MethodIn this paper, the nonlinear finite element software DYNA is used to construct ice numerical simulation models based on the traditional finite element and cohesive element methods respectively, and simulations are performed of the bending fracture and interaction process that occurs when level ice interacts with an icebreaker. At the same time, using the empirical formula method, three different empirical formulas are used to calculate the ice resistance, and a sensitivity analysis of the parameters affecting the prediction results of the empirical formula method is also carried out. ResultsThe study finds that ice resistance shows an upward trend with the increase in speed, ice thickness and bending strength. Among them, ice thickness has the greatest influence on ice resistance. Among the three empirical formulas, the prediction results of the Lindqvist formula are closer to the ship model test results, while those of the Vance and Lewis formulas are more conservative. The traditional finite element and cohesive element methods obtain more accurate ice resistance prediction results when the thickness is small. When the thickness is large, the error is about 25%. In case of small ice thickness and high speed, the ice resistance value predicted by the cohesive element method is more accurate than that of the traditional finite element method, and the accuracy error is within 10% compared with the ship model test results. ConclusionIn the actual ice resistance prediction, the empirical formula method and numerical simulation method can be combined to take into account the accuracy and efficiency of the prediction results.

To investigate the influence of the crack dip angle on the strength of rock specimens, uniaxial compression tests were conducted on granite specimens containing pre-existing cracks. The strain energy evolution during the loading process was analyzed, and the loading-induced cracking process was simulated using the cohesive element method. Both the experimental and numerical results indicate that cracks significantly impact the plastic-yielding stage of the stress–strain curve more than the initial and elastic deformation stages. When the crack dip angle is less than 45°, the stress concentration near the crack is significant, which is an important factor affecting the strength and elastic strain energy distribution of rock specimens. When the crack dip angle is greater than 45°, the degree of stress concentration decreases, and the uniformity of the elastic strain energy distribution and the possibility of crack bifurcation increase. Combining the energy theory with the cohesive element method helps comprehensively understand the initiation, propagation, and coalescence of microcracks near pre-existing crack tips. These research results can provide a reference for geotechnical engineering design and structural stability assessment.

The zero-thickness cohesive element method (CEM) is a powerful way to simulate crack propagation. However, it suffers from artificial compliance issue and alters the wave speed in dynamic analyses. In this article, we show that the CEM formulation can be correlated to the Babuška and Zlámal, discontinuous Galerkin formulation, and switching to symmetric interior penalty Galerkin (SIPG) formulation improves the accuracy of wave speed approximation. Moreover, we demonstrate the SIPG formulation can better control the nodal jumps between element interfaces with a lower cost than CEM. A convergence study is carried out to support this SIPG robustness.

A continuum damage mechanics framework for modeling the effect of crystalline anisotropy on rolling contact fatigue

The major processes that occur when level ice interacts with sloping structures (especially wide structures) are the fracturing of ice and upcoming ice fragments accumulating around the structure. The cohesive zone method, which can simulate both fracture initiation and propagation, is a potential numerical method to simulate this process. In this paper, as one of the numerical methods based on the cohesive zone theory, the cohesive-element–based approach was used to simulate both the fracturing and upcoming fragmentation of level ice. However, simulating ice and sloping structure interactions with the cohesive element method poses several challenges. One often-highlighted challenge is its convergence issue. Numerous attempts by different researchers have been invested in this issue either to prove or improve its convergence. However, these researchers work in different fields (e.g., fracture of concrete, ceramic, or glass fiber) with different scales (e.g., from a ceramic ring to a concrete block). As an attempt to study the cohesive element method's application in the current ice-structure interaction context (i.e., an engineering scale up to hundreds of meters), the mesh dependency of the cohesive element method was alleviated by both creating a mesh with a crossed triangle pattern and utilizing a penalty method to obtain the initial stiffness for the intrinsic cohesive elements. Furthermore, two potential methods (i.e., introduction of a random ice field and bulk energy dissipation considerations) to alleviate the mesh dependency problem were evaluated and discussed. Based on a series of simulations with the different aforementioned methods and mesh sizes, the global ice load history is obtained. The horizontal load information is validated against the test results and previous simulation results. According to the comparison, the mesh objectivity alleviation with different approaches was discussed. As a preliminary demonstration, the results of one simulation are summarized, and the load contributions from different ice-structure interaction phases are illustrated and discussed.

Microstructure-based modelling of hydraulic fracturing in silicified metamorphic rock using the cohesive element method

Ice loads are an important and decisive factor for the safe operation of offshore wind turbines (OWTs). In severe environment load cases, it shall lead to prominent ice-induced vibration and ice-induced fatigue failure of OWT structures. Based on the cohesive element method (CEM) and considering the pile–soil interaction used by nonlinear distributed springs, the full interaction model of the ice and monopile OWT structure with an ice-breaking cone in a cold sea region is established in this study. Furthermore, the Tsai-Wu failure criterion and the empirical failure formula of maximum plastic failure strain are used to describe the mechanical behavior of ice bending failure in the collision simulation tool LS-DYNA, and the dynamic ice loads under different ice velocities and cone angles are statistically analyzed. Finally, according to the interaction process between sea ice and OWT containing the ice-breaking cone, the dynamic response of OWT under the combined wind and ice loads is studied, and the most reasonable ice-breaking cone angle is determined. The results show that the method adopted in this paper can well simulate the bending failure process of sea ice. Concurrently, the cone angle has a significant impact on the dynamic response and damage of the OWT, and the recommended optimal cone angle is 60.

The size of the fully developed process zone (FDPZ) is needed for the arrangement of displacement sensors in fracture experiments and choosing element size in numerical models using the cohesive element method (CEM). However, the FDPZ size is generally not known beforehand. Analytical solutions for the exact FDPZ size only exist for highly idealised bodies, e.g. semi-infinite plates. With respect to fracture testing, the CEM is also a potential tool to extrapolate laboratory test results to full-scale while considering the size effect. A numerical CEM-based model is built to compute the FDPZ size for an edge crack in a finite square plate of different lengths spanning several magnitudes. It is validated against existing analytical solutions. After successful validation, the FDPZ size of finite plates is calculated with the same numerical scheme. The (FDPZ) size for finite plates is influenced by the cracked plate size and physical crack length. Maximum cohesive zone sizes are given for rectangular and linear softening. Further, for this setup, the CEM-based numerical model captures the size effect and can be used to extrapolate small-scale test results to full-scale.

Shale gas is a cutting edge energy source for development, and reserves are abundant. However, shale microcracks develop and tend to form macroscopic fractures during drilling, which can cause severe wellbore instability. Therefore, in combination with rock mechanics theory and fracture mechanics theory, the cohesive element method is adopted to establish a numerical model for differential crack propagation due to bottomhole pressure on the basis of the B-K fracture criterion. The propagation pattern of cracks around a wellbore is simulated, and the influences of rock mechanical parameters, the initial crack length, the direction of crack distribution, and minimum horizontal stress on crack propagation are analyzed. The research results indicate that the larger the Young’s modulus of shale is, the easier it is for cracks to propagate. The Poisson’s ratio of shale has a large influence on crack widening, but its effect on the crack length is weak. The larger the angle between the crack and the maximum horizontal stress is, the more difficult it is for the crack to propagate. The greater the minimum horizontal stress is, the more difficult it is for cracks to propagate. The initial crack length has a weak effect on crack propagation.

A continuum damage failure model for hydraulic fracturing of porous rocks

The simulation of hydraulic fracturing by the conventional ABAQUS cohesive finite element method requires a preset fracture propagation path, which restricts its application to the hydraulic fracturing simulation of a naturally fractured reservoir under full coupling. Based on the further development of a cohesive finite element, a new dual-attribute element of pore fluid/stress element and cohesive element (PFS-Cohesive) method for a rock matrix is put forward to realize the simulation of an artificial fracture propagating along the arbitrary path. The effect of a single spontaneous fracture, two intersected natural fractures, and multiple intersected spontaneous fractures on the expansion of an artificial fracture is analyzed by this method. Numerical simulation results show that the in situ stress, approaching angle between the artificial fracture and natural fracture, and natural fracture cementation strength have a significant influence on the propagation morphology of the fracture. When two intersected natural fractures exist, the second one will inhibit the propagation of artificial fractures along the small angle of the first natural fractures. Under different in situ stress differences, the length as well as aperture of the hydraulic fracture in a rock matrix increases with the development of cementation superiority of natural fractures. And with the increasing of in situ horizontal stress differences, the length of the artificial fracture in a rock matrix decreases, while the aperture increases. The numerical simulation result of the influence of a single natural fracture on the propagation of an artificial fracture is in agreement with that of the experiment, which proves the accuracy of the PFS-Cohesive FEM for simulating hydraulic fracturing in shale gas reservoirs.

Chapter 6 - Damage tolerance and fatigue durability of scarf joints

Predicting mixed mode damage propagation in snowpack using the extended cohesive damage element method

Many current studies on the numerical simulation of ship-ice collisions, the cohesive element method and the finite element method (CEM-FEM) are mostly used to establish the sea ice model. However, due to the complex mechanical properties of sea ice and the influence of various physical factors, the cohesive element with a single parameter cannot well reflect the mechanical properties of sea ice. Based on this, a cohesive sea ice model based on mixed fracture strength parameters was established in LS-DYNA software and numerically simulated. It was found that the failure modes of the mixed parameter cohesive element sea ice model are primarily extrusion and bending failure, and the crack extension direction shows randomness, and the sea ice failure appears obviously different. In addition, under the same working conditions, the ice-breaking resistance of the cohesive unit of the mixed parameters is in good agreement with the empirical formula of Lindqvist.

In materials, the evolution of crack surfaces is intimately linked with the self‐contact occurring between them. The developed contact forces not only mitigate the effect of stress concentration at crack tip but also contribute significantly to the transfer of shear and normal stresses. In this article, we present a numerical framework to study the simultaneous process of fracture and self‐contact between fracturing surfaces. The widely used approach, where contact constraints are enforced with the cohesive element traction separation law, is demonstrated to fail for relative displacements greater than the characteristic mesh length. A hybrid approach is proposed, which couples a node‐to‐segment contact algorithm with extrinsic cohesive elements. Thus, the fracture process is modeled with cohesive elements, whereas the contact and the friction constraints are enforced through a penalty‐based method. This hybrid cohesive‐contact approach is shown to alleviate any mesh topology limitations, making it a reliable and physically based numerical model for studying crack propagation along rough surfaces.