A bifurcation-based decohesion model for simulating the transition from localization to decohesion with the MPM

Based on recent experimental observations on the formation of localization before delamination, a bifurcation-based decohesion approach is proposed in this paper to simulate the transition from localization to decohesion involved in the delamination process of compressed films. The onset and orientation of discontinuous failure are identified from the discontinuous bifurcation analysis. A discrete constitutive model is then formulated based on the bifurcation analysis to predict the evolution of material failure as decohesion or separation of continuum. The Material Point Method, that does not employ fixed mesh-connectivity, is developed as a robust spatial discretization method to accommodate the multi-scale discontinuities involved in the film delamination. To demonstrate the potential of the proposed approach, a parametric study is conducted to explore the effects of aspect ratio and failure mode on the evolution of failure patterns under different boundary conditions, which provides a better understanding on the physics behind the film delamination process.     

Aspects of computational homogenisation of microheterogeneous materials including decohesion at finite strains

During the last years, the development and application of new composite materials gained more and more importance. For engineering applications it is necessary to get effective material properties of such materials. In this contribution we present some aspects of computational homogenisation procedures of microheterogeneous materials which can show decohesion in a cohesive zone around the particles. Due to the decohesion we get finite deformations and .nite strains within the RVE. The geometrical and material nonlinearities cause the main dif.culties. The homogenization procedure leads to an effective stress strain curve for the RVE, and for the nonlinear elastic case one can also obtain effective material parameters. It is necessary to do statistical tests in order to get a representative result. Here we set a special focus on the adaptive numerical model, the statistical testing procedure and the different boundary conditions (pure tractions and pure displacements) applied on the RVE. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hamiltonian weakly damped autonomous systems exhibiting periodic attractors

The dynamic local stability of autonomous Hamiltonian, weakly damped, lumped-mass (discrete) systems is reconsidered. For such potential(conservative) systems conditions for the existence of limit cycles are discussed by studying the effect of the damping matrix on the Jacobian eigenvalues. New findings that contradict existing results are presented. Thus, undamped stable symmetric systems with the inclusion of slight damping may experience: (a) a double zero eigenvalue bifurcation, a degenerate Hopf bifurcation and a generic (usual) Hopf bifurcation, and (b) a limit cycle (dynamic) mode of instability prior to the static (divergence) mode of instability (failure of Zieglers kinetic criterion). A variety of numerical examples verified by a nonlinear analysis confirm the validity of the theoretical findings presented herein. Received: January 3, 2003; revised: July 14, 2003 and February 17, 2004     

Concurrent homoclinic bifurcation and Hopf bifurcation for a class of planar Filippov systems

This paper investigates both homoclinic bifurcation and Hopf bifurcation which occur concurrently in a class of planar perturbed discontinuous systems of Filippov type. Firstly, based on a geometrical interpretation and a new analysis of the so-called successive function, sufficient conditions are proposed for the existence and stability of homoclinic orbit of unperturbed systems. Then, with the discussion about Poincaré map, bifurcation analyses of homoclinic orbit and parabolic–parabolic (PP) type pseudo-focus are presented. It is shown that two limit cycles can appear from the two different kinds of bifurcation in planar Filippov systems.     

The role of transverse stretching in the delamination fracture of softcore sandwich plates

This paper presents the semi-layerwise analysis of structural sandwich plates with through-width delamination. The mechanical model of rectangular plates is based on the method of four equivalent single layers and the system of exact kinematic conditions. An important improvement compared to a previous formulation is the consideration of linear and quadratic stretching term in the transverse displacement component. Three different delamination scenarios are investigated: core-core failure, face-core delamination and the face-face failure. By applying the first- and second-order laminated plate theories and the principle of virtual work the governing equations are derived. The equilibrium equations are solved under Lévy type boundary conditions using the state-space approach. Solutions for the mechanical fields are provided and compared to 3D finite element results. The energy release rate distributions along the delamination front are also determined using the J-integral. Although the stress resultants by transverse stretching do not influence directly the J-integral, the results indicate that this effect improves the accuracy of the model in general, and substantially influences the results of the first-order plate theory in the case of the face-face delamination.     

Bifurcation analysis of the HIV‐1 within host model

In this paper, a bifurcation solution's analysis is proposed for an HIV‐1 within the host model around its chronic equilibrium point, this is carried out based on Lyapunov–Schmidt approach. It is shown that the coefficient b, which represents the healthy CD4⁺ T‐cells growth rate, is a bifurcation parameter; this means that the rate of multiplication of healthy cells can have serious effects on the qualitative dynamical properties and structural stability of the infection evolution dynamics. Copyright © 2015 John Wiley & Sons, Ltd.     

Perturbations and Hopf bifurcation of the planar discontinuous dynamical system

The objective of the paper is to obtain results on the behavior of a specific plane discontinuous dynamical system in the neighbourhood of the singular point. A new technique of investigation is presented. Conditions for existence of the foci and centres are proposed. The focus-centre problem and Hopf bifurcation are considered. Appropriate examples are given to ilustrate the bifurcation theorem.     

Blast Damage Simulation With the Discontinuous Galerkin Finite Element Method of Bond⁃Based Peridynamics北大核心CSCD

近场动力学是一种积分型非局部的连续介质力学理论,已广泛应用于固体材料和结构的非连续变形与破坏分析中,其数值求解方法主要采用无网格粒子类的显式动力学方法.近年来,弱形式近场动力学方程的非连续Galerkin有限元法得到发展,该方法不仅可以描述考察体的非局部作用效应和非连续变形特性,还可以充分利用有限单元法高效求解的特点,并继承了有限元法能直接施加局部边界条件的优点,可有效避免近场动力学的表面效应问题.该文阐述了键型近场动力学的非连续Galerkin有限元法的基本原理,导出了计算列式,给出了具体算法流程和细节,计算模拟了脆性玻璃板动态开裂分叉问题,并对爆炸冲击荷载作用下混凝土板的毁伤过程进行了计算分析.研究结果表明,该方法能够再现爆炸冲击荷载作用下结构的复杂破裂模式和毁伤破坏过程,且具有较高的计算效率,是模拟结构爆炸冲击毁伤效应的一种有效方法.     

Existence and stability of the grazing periodic trajectory in a two-degree-of-freedom vibro-impact system

This paper investigates the existence and stability of the grazing periodic trajectory in a two-degree-of-freedom vibro-impact system. The criterion for existence of grazing period-n motion is presented. A local analysis based on the discontinuity-mapping approach is employed to derive a normal form Poincaré mapping near the grazing trajectory. Based on the above approach, a condition of stability can be formulated, such that a grazing trajectory will be discontinuous if the condition is unfulfilled. The predicted grazing bifurcations are in agreement with the numerical results. In particular, comparison of the grazing bifurcation diagrams of the normal form Poincaré mapping and the simulation diagrams of the original differential equation illustrates the validity of the discontinuity-mapping approach.     

Viscosity Solution of the Hamilton-Jacobi Equation Arising from a Thin Film Blistering Model

The paper deals with a dynamical nonlinear model describing the self-driven delamination of compressed thin films. Some assumptions on the buckled shape allow us to describe the moving boundary of the film by a single Hamilton-Jacobi equation. We prove the existence and uniqueness of a viscosity solution to the associated evolution problem.     

Periodic motions in a simplified brake system with a periodic excitation

In this paper, periodic motions for a simplified brake system under a periodical excitation are investigated, and the motion switchability on the discontinuous boundary is discussed through the theory of discontinuous dynamical systems. The onset and vanishing of periodic motions are discussed through the bifurcation and grazing analyses. Based on the discontinuous boundary, the switching planes and the basic mappings are introduced, and the mapping structures for periodic motions are developed. From the mapping structures, the periodic motions are analytically predicted and the corresponding local stability and bifurcation analysis is completed. Periodic motions will be illustrated for verification of analytical predictions. In addition, the relative force distributions along the displacement are illustrated for illustrations of the analytical conditions of motion switchability on the discontinuous boundary.     

A level set approach to the wearing process of a nonconvex stone

We study the geometric evolution of a nonconvex stone by the wearing process via the partial differential equation methods. We use the so-called level set approach to this geometric evolution of a set. We establish a comparison theorem, an existence theorem, and some stability properties of solutions of the partial differential equation arising in this level set approach, and define the flow of a set by the wearing process via the level set approach.Received: 15 February 2002, Published online: 6 June 2003Mathematics Subject Classification: 53C44, 35K65Hitoshi Ishii: was supported in part by the Grant-in-Aid for ScientificResearch no. 1244004412304006JSPSToshio Mikami: was supported in part by the Grant-in-Aid for Scientific Research no. 1364009612440044JSPS     

A few typical delamination patterns of compressed thin films

In this paper we consider compressed flat thin films on rigid substrates. Residual compressive stresses arising e.g. from temperature loading are the driving quantities of the irreversible delamination process. A Reissner–Mindlin shell formulation is used as a model for the thin film, since small geometrical imperfections are considered to initiate buckling. For the interface we postulate the existence of a cohesive free energy as a function of the opening displacement vector and internal variables. The irreversible delamination process is described using a cohesive law of exponential type, where the parameters depend on the combination of the modes I, II and III. In order to analyse the delamination process exactly we use the energy criterion of the steady-state growth. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Principal Asymptotics in the Problem on the Andronov–Hopf Bifurcation and Their Applications

New formulas are obtained for the principal asymptotics of bifurcation solutions in the problem on the Andronov–Hopf bifurcation, leading to new algorithms for studying bifurcations in the general setting. The approach proposed in the paper allows one to consider not only the classical problems about bifurcations of codimension one but also some problems concerning bifurcations of codimension two. A new approach to the analysis of bifurcations of cycles in systems with homogeneous nonlinearities is proposed. As an application, we consider the problem on the bifurcation of periodic solutions of the van der Pol equation.     

A study of prebiotic evolution

A very simple model prebiotic system is explored, both, to elucidate the full complexity of its dynamic behavior, and from the standpoint of what a thermal analysis can tell us about evolution more generally. The system consists of a coacervate containing a four variable enzymatic oscillator that is driven by a single input concentration. The reaction scheme is “nested”; i.e., by “turning on” one reaction at a time we can go from a two‐variable system, to one of three variables, to one of four, each developing more complex behavior. The four‐variable system is shown to have at least five distinct genera of complex attractors within the range examined. Two of these coexist for the same parameter values; the other three are substantially separated in the bifurcation space. The fixed points, characteristic roots, Lyapunov exponents, stability (dissipation), Kaplan‐Yorke dimensions, and correlation dimensions are all calculated for each attractor. A six‐variable amplification of the reaction scheme is considered as a simple model of nucleation in a coacervate and is shown to totally stabilize the corresponding attractor. An Evolutionary Potential is proposed that is wholly beyond the purview of classical thermostatics, yet incorporates entropy effects via Clausius' strong version of the Second Law. It is shown that the latter is a necessary condition for the sort of structuring characteristic of living systems. © 2003 Wiley Periodicals, Inc. Complexity 8: 45–67, 2003     

Simulation of Buckling-Induced Failure in Composite Laminates

This contribution presents a simple model for the analysis of buckling–induced failure in thin–walled composite laminates in the framework of the finite element method. The plies are modeled with shear deformable geometrically non–linear four–node shell elements which are layered according to the classical laminate theory. Shear locking effects are reduced via the well–known assumed natural strains (ANS) approach. A ply discount model is applied for the successive failure of the plies. The cohesive zone approach which is implemented in so–called interface elements is employed for delamination. The failure processes are history dependent leading to non–recurring stiffness degradation in areas where damage is detected. A numerical example with experimental evidence highlights the performance and applicability of the proposed model. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Microscale mechanics for metal thin film delamination along ceramic substrates

The metal thin film delamination along metal/ceramic interface in the case of large scale yielding is studied by employing the strain gradient plasticity theory and the material microscale effects are considered. Two different fracture process models are used in this study to describe the nonlinear delamination phenomena for metal thin films. A set of experiments have been done on the mechanism of copper films delaminating from silica substrates, based on which the peak interface separation stress and the micro-length scale of material, as well as the dislocation-free zone size are predicted.     

Bifurcations and multistability in the extended Hindmarsh–Rose neuronal oscillator

We report on the bifurcation analysis of an extended Hindmarsh–Rose (eHR) neuronal oscillator. We prove that Hopf bifurcation occurs in this system, when an appropriate chosen bifurcation parameter varies and reaches its critical value. Applying the normal form theory, we derive a formula to determine the direction of the Hopf bifurcation and the stability of bifurcating periodic flows. To observe this latter bifurcation and to illustrate its theoretical analysis, numerical simulations are performed. Hence, we present an explanation of the discontinuous behavior of the amplitude of the repetitive response as a function of system’s parameters based on the presence of the subcritical unstable oscillations. Furthermore, the bifurcation structures of the system are studied, with special care on the effects of parameters associated with the slow current and the slower dynamical process. We find that the system presents diversity of bifurcations such as period-doubling, symmetry breaking, crises and reverse period-doubling, when the afore mentioned parameters are varied in tiny steps. The complexity of the bifurcation structures seems useful to understand how neurons encode information or how they respond to external stimuli. Furthermore, we find that the extended Hindmarsh–Rose model also presents the multistability of oscillatory and silent regimes for precise sets of its parameters. This phenomenon plays a practical role in short-term memory and appears to give an evolutionary advantage for neurons since they constitute part of multifunctional microcircuits such as central pattern generators.     

基于断裂能的岩土节理弹性-软化塑性本构模型

基于准脆性材料的断裂力学和塑性理论,提出了用于岩土节理软化行为描述的弹性软化塑性本构模型.模型的主要特点是:1)节理材料的软化塑性和扩容特性直接与断裂失效过程相联系,所采用的材料参数比已有的弹塑性软化模型所用的参数少;2)模型可以描述混合断裂失效及相应的摩擦滑动,具有较广的适用性.