Fracture simulation using a nonlocal particle model

Extensive researches have been done to simulate crack initialization, propagation, branching, and coalesce from different engineering disciplines. Various numerical methods have been developed, which can be generally grouped into two categories: the continuum-based methods and the discontinuous approaches. For cracking problems, the classical finite element method (FEM) uses mesh matching and remeshing techniques which is computationally very expensive. The cohesive elements does not require very dense mesh near the crack tip region, but usually requires the crack path as a priori knowledge for the computational efficiency. eXtended FEM (XFEM) treats the discontinuity via level sets method and enrich the crack tip elements with analytical solution for the stress or displacement from linear elastic fracture mechanics. Arbitrary crack branching and coalesce is still challenging in the XFEM framework. The discontinuous approaches, such as lattice spring models and peridynamics, can handle fracture problems very efficiently. No additional criteria are needed as the crack growth is a natural outcome of the system evolution. As the elongation of the connecting bonds exceeds the critical value, it breaks and the crack propagates automatically. However, there are some other issues with the discontinuous approaches, such as restriction on effective Poisson’s ratio and crack path preference. A Volume-Compensated Particle Method (VCPM) was proposed by Chen et al. to solve these issues within the discontinuous framework. In the VCPM, both pairwise and nonlocal potentials are used to describe interactions among particles. One unique issue in the regular lattice particle method is the directional preference of the crack propagating path due to the regular lattice topology. The objective of this study is to investigate a general formulation using the VCPM concept to eliminate/reduce the crack path preference in the fracture simulation

Unified framework for microstruture evolution and property quantification

In this study, a novel unified framework for the study of both microstructural evolution and the mechanical property quantification is proposed. The multistate Potts model is used to simulate the microstructural evolution, whereas a volume-compensated particle method (VCPM) is used for the mechanical property quantification of the steady state microstructure. The VCPM proposed by Chen and colleagues was originally developed for the investigation of the fracture phenomenon of solid materials. The model was also successfully extended to study the elastoplastic properties of solids by introducing a volume conservation scheme. In the VCPM framework, the domain of interest is discretized into regular unit cells according to the triangle and square packing for 2D and simple cubic, body centered cubic and face-centered cubic packing for 3D. Both local pair-wise and nonlocal multibody potential are proposed to account for the interactions between particles. The multistate Potts models have been used extensively to model a variety of microstructural phenomena, such as the grain growth in a single or multiple-phase system, recrystallization, solidification, and many others. The space-filling array of regular cells is used to represent the Potts domain which is the same as the one used in VCPM. The microstructure evolves such that the system Hamiltonian is minimized. To consider different external effects on the states of the microstructure, different energy terms can be introduced into the system Hamiltonian, such as surface energy to account for the interface effect and strain energy for the grain orientation. Once the final steady state is obtained using the multistate Potts model, usually some other techniques, such as FEM, are used to calculate the effective properties of the microstructural system. It requires the mapping between the FEM meshes and the microstructure. The mapping is very difficult, especially for the interface mapping when the microstructure is very complex. In this study, the VCPM is coupled with the multistate Potts model to simulate the microstructural evolution and quantify the effective mechanical properties of the system within one framework. No mapping between these two models is required since they share the same underlying domain structures. The nonlocal potential proposed in VCPM is introduced into the multistate Potts model as an alternative of the original strain energy term. By doing this, effective simulation of the microstructure evolution for multiple-phase materials can be achieved. Given the final microstructure, the VCPM simulation is carried out to calculate the effective properties of the obtained system

Nonlinear stability of continuously stratified quasi-geostrophic flow

Nonlinear stability theorems analogous to Arnol'd's second stability theorem are established for continuously stratified quasi-geostrophic flow with general nonlinear boundary conditions in a vertically and horizontally confined domain. Both the standard quasi-geostrophic model and the modified quasi-geostrophic model (incorporating effects of hydrostatic compressibility) are treated. The results establish explicit upper bounds on the disturbance energy, the disturbance potential enstrophy, and the disturbance available potential energy on the horizontal boundaries, in terms of the initial disturbance fields. Nonlinear stability in the sense of Liapunov is also established

Freeze-thaw damage evaluation and model creation for concrete exposed to freeze–thaw cycles at early-age

Concrete subjected to freeze–thaw cycles action at early-age will suffer serious physical damage, resulting in degradation of the concrete’s performance. The subsequent curing conditions after early-age freeze–thaw cycles (E-FTCs) are critical to the development of the properties of frost-damaged concrete. Four test environments were set up for this study, based on different numbers of E-FTCs and subsequent curing conditions. The later-age resistance to freeze–thaw of concrete exposed to E-FTCs was evaluated by analysing the influence of precuring times and curing conditions. Results show that the earlier the FTCs occur, the worse the later-age freeze–thaw resistance is. In particular, for the frost-damaged concrete with a pre-curing time of 18 h, its freeze–thaw resistance is significantlypublishedVersio

Nonlinear stability of multilayer quasi-geostrophic flow

New nonlinear stability theorems are derived for disturbances to steady basic flows in the context of the multilayer quasi-geostrophic equations. These theorems are analogues of Arnol’d's second stability theorem, the latter applying to the two-dimensional Euler equations. Explicit upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy in terms of the initial disturbance fields. An important feature of the present analysis is that the disturbances are allowed to have non-zero circulation. While Arnol’d's stability method relies on the energy–Casimir invariant being sign-definite, the new criteria can be applied to cases where it is sign-indefinite because of the disturbance circulations. A version of Andrews’ theorem is established for this problem, and uniform potential vorticity flow is shown to be nonlinearly stable. The special case of two-layer flow is treated in detail, with particular attention paid to the Phillips model of baroclinic instability. It is found that the short-wave portion of the marginal stability curve found in linear theory is precisely captured by the new nonlinear stability criteria