A Phase-Field Model of Ductile Fracture at Finite Strains

This work outlines a variational-based framework for the phase field modeling of ductile fracture in elastic-plastic solids at large strains. The phase field approach regularizes sharp crack discontinuities within a pure continuum setting by a specific gradient damage model with geometric features rooted in fracture mechanics. Based on the recent works [1, 2], the phase field model of ductile fracture is linked to a formulation of gradient plasticity at finite strains in order to ensure the crack to evolve inside the plastic zones. The thermodynamic formulation is based on the definition of a constitutive work density function including the stored elastic energy and the dissipated work due to plasticity and fracture. The proposed canonical theory is shown to be governed by a rate-type minimization principle, which determines the coupled multi-field evolution problem. Another aspect is the regularization towards a micromorphic gradient plasticity-damage setting which enhances the robustness of the finite element formulation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Quasi-Stationary Phase-Field Model with Micro-Movements

This note addresses the global strong solvability of a phase-field system arising in connection with the phase transition theory recently proposed by Frémond. The novelty of this modelization consists in considering the macroscopic effect of the microscopic movements of particles of the system that undergoes the phase transition. In particular, we outline the basic features of this model and deal with the upcoming nonlinear PDE system in the one-dimensional setting by means of an approximation—a priori estimates—passage to the limit procedure.     

A Phase-Field Model Based on a Three-Phase-Lag Heat Conduction

Our aim in this article is to study a phase-field system based on a three-phase-lag for the thermal flux vector. In particular, we prove the existence and uniqueness of solutions and then study the spatial behavior of the solutions in a semi-infinite cylinder, when such solutions exist.     

Direct and Inverse Problems for a Phase-Field Model with Memory

We consider a semilinear integrodifferential system in non-normal form. Such a system is a generalization of the one that arises in the phase-field theory with memory. We prove an abstract existence and uniqueness theorem and a continuous dependence result for the direct problem. Reformulating the direct problem in a suitable way we prove that the identification problem admits a unique solution.     

A New Model of Coupled Hindmarsh-Rose Neurons

A new model of two coupled neurons is presented by the partly di?usive HindmarshRose equations. The solution semi?ow exhibits globally absorbing characteristics. As the main result, the self-synchronization of the coupled neurons at a uniform rate is proved, which can be extended to complex neuronal networks.     

A Regularized Sharp Interface Model for Martensitic Phase Transformations at Large Strains

The macroscopic mechanical behavior of many functional materials crucially depends on the formation and evolution of their microstructure. When considering martensitic shape memory alloys, this microstructure typically consists of laminates with coherent twin boundaries. We suggest a variational-based phase field model for the dissipative evolution of microstructure with coherence-dependent interface energy and construct a suitable gradient-extended incremental variational framework for the proposed dissipative material. We use our model to predict laminate microstructure in martensitic CuAlNi. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strong （Weak） Exact Controllability and Strong （Weak） Exact Observability for Quasilinear Hyperbolic Systems

Numerical approximations of Cahn-Hilliard phase-field model for the two-phase incompressible flows are considered in this paper.Several efficient and energy stable time discretization schemes for the coupled nonlinear Cahn-Hilliard phase-field system for both the matched density case and the variable density case are constructed,and are shown to satisfy discrete energy laws which are analogous to the continuous energy laws.     

Asymptotic Behaviour for a Phase-Field Model with Hysteresis in One-Dimensional Thermo-Visco-Plasticity

The asymptotic behaviour for t of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress law and also in the phase evolution equation are described by using the mathematical theory of hysteresis operators.     

板的大变形分析的混合变分泛函*

本文导出了板在大变形分析的混合变分表达式,在本式中,平衡方程和协调方程是分别用应力函数和位移分量等同满足的,而应力应变关系是在最小二乘方的意义上满足的.解了一个例,并和文献中已知的结果进行了比较.此外,我们写出了特别适用于板的屈曲失稳分析的泛函,并举例题解证明理论的有效.     

非线性弹性大变形问题的率型解法

本文分别采用Ｊａｕｍａｎｎ应力率、Ｔｒｕｅｓｄｅｌｌ应力率和Ｇｒｅｅｎ－Ｎａｇｈｄｉ应力率导出了非线性各向同性弹性体的率型本构表达形式，通过对Ｍｏｏｎｅｙ－Ｒｉｖｌｉｎ材料的简单剪切大变形分析表明，三种率型的本构关系均与全量本构关系相等价。文中还给出了相应的率型变分原理，并采应Ｒｉｔｚ法，数值求解了受单轴拉伸的矩形橡皮薄膜的大变形问题．     

热-力耦合原子-连续关联模型的框架及其算法

对热-力耦合的原子-连续关联模型进行了系统研究,给出了计及热-力耦合行为的金属微-纳米构件内材料的瞬态弹性常数,应力、应变、比热容等物理量的具体计算公式及其算法.利用原子运动中的“结构形变”部分来研究微-纳米尺度下多晶原子团簇的非均匀结构变形.将原子团簇晶格结构的变形与连续体的变形关联起来,在准简谐近似假设下,推导出依赖于微观结构变形和热振动的自由能密度、熵密度、内能密度表达式,从而给出了微-纳米尺度下的瞬态热-力学参数.     

正交各向异性板的非对称大变形问题

从各向异性板的基本理论出发,推导出正交各向异性圆板的非对称大变形基本方程,利用Fourier级数把问题的偏微分方程转化为一组可积分求解的非线性常微分方程,并给出利用迭代法求解该问题的基本方法.     

火场-结构联合分析简化模型及其应用研究

为在建筑结构火灾反应分析中考虑实际火场特性,并简化火场分析模型与结构有限元分析模型之间的复杂对应关系,提出并建立了火场温度及对流辐射边界的热传导分析时空模型(STM)和基于时空模型的火场-结构联合分析方法。该方法根据火场模型计算出室内火场温度分布场以及对流辐射边界场离散数据,通过双向正交多项式进行拟合来得到不同时刻的构件边界连续时空模型,再通过时空模型进行热传导分析和热力耦合分析,从而实现火场-结构联合分析方法。在验证其合理性的基础上,通过ABAQUS子程序UTEMP和DFLUX实现其分析过程,并进行了北京某档案馆工程的应用分析,结果表明该方法可以较好地联合火场模拟与结构分析用于结构火灾安全评价。     

A Large-Deformation Phase-Field Approach for the Modeling of Magneto-Sensitive Elastomers

Magneto-sensitive materials show magneto-mechanical coupled response and are thus of increasing interest in the recent age of smart functional materials. Ferromagnetic particles suspended in an elastomeric matrix show realignment under the influence of an external applied field, in turn causing large deformations of the substrate material. The magneto-mechanical coupling in this case is governed by the magnetic properties of the inclusion and the mechancial properties of the matrix. The magnetic phenomenon in ferromagnetic materials is governed by the formation and evolution of domains on the micro scale. A better understanding of the behavior of these particles under the influence of an external applied field is required to accurately predict the behavior of such materials. In this context it is of particular importance to model the macro scopic magneto-mechanically coupled behavior based on the micro-magnetic domain evolution. The key aspect of this work is to develop a large-deformation micro-magnetic model that can accurately capture the microscopic response of such materials. Rigorous exploitation of appropriate rate-type variational principles and consequent incremental variational principles directly give us field equations including the time evolution equation of the magnetization, which acts as the order parameter in our formulation. The theory presented here is the continuation of the work presented in [1, 7] for small deformations. A summary of magneto-mechanical theories spanning over multiple scales has been presented in [4]. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

活体大变形的能量原理

活体是具有自组织和自调控能力的生命系统.讨论活体的能量原理包含有力学和热力学原理两大部分.经典的小变形力学和可逆平衡态热力学理论巳不足于描述活体的运动.本文从大变形非对称应力理论力学描述活体宏观运动的力学能量原理.有关不可逆热力学问题将另文讨论.     

环面薄膜的膨胀失稳

本文从有限弹性理论出发对超弹性薄膜轴对称大变形问题进行了一般的数学描述.基于本文所导出的基本方程,应用打靶法数值地分析了Mooney-Rivlin型类橡胶环面薄膜的大变形膨胀失稳问题.给出了上、下极限载荷和位移载荷曲线.     

橡皮环大变形接触问题

本文借助于子结构技术解决了大变形橡皮环和弹性薄极具有摩擦的接触问题,研究了摩擦系数、极厚对橡皮环变形的影响。     

A Deformation Model for Dispersely Failing Elastoplastic Unidirectionally Reinforced Composites

A calculation model is proposed for unidirectionally reinforced elastoplastic composites capable of gradually accumulating disperse microdamages under loading. The composite is assumed to be a homogeneous transversely isotropic solid. To describe its elastoplastic behavior, an incremental plasticity theory with a nonlinear combined hardening mechanism is invoked. At each point of the solid, its damage is characterized by a centrally symmetric scalar function on a unit sphere. This function is approximated by a fourth-rank tensor, which is used for describing the degradation of the elastic properties of the solid due to the accumulation of disperse microdamages. It is shown how to determine, using the known experimental data, all material constants appearing in the theoretical relations suggested.     

A Coupled System of Integrodifferential Equations Arising in Liquidity Risk Model

We study the mathematical aspects of the portfolio/consumption choice problem in a market model with liquidity risk introduced in (Pham and Tankov, Math. Finance, 2006, to appear). In this model, the investor can trade and observe stock prices only at exogenous Poisson arrival times. He may also consume continuously from his cash holdings, and his goal is to maximize his expected utility from consumption. This is a mixed discrete/continuous time stochastic control problem, nonstandard in the literature. We show how the dynamic programming principle leads to a coupled system of Integro-Differential Equations (IDE), and we prove an analytic characterization of this control problem by adapting the concept of viscosity solutions. This coupled system of IDE may be numerically solved by a decoupling algorithm, and this is the topic of a companion paper (Pham and Tankov, Math. Finance, 2006, to appear).     

基于曲率插值的大变形梁单元

线性梁单元的形函数在单元大转动时会引起虚假应变,不适用于几何非线性分析．传统的几何非线性梁单元由于位移插值和转角插值的相干性,常常引起剪切闭锁等问题．该文 提出了一种平面大变形梁单元,通过单元域内的曲率插值以及曲率与节点位移之间的函数关系,将单元节点力和节点位移表示为节点曲率的函数．由于曲率插值本质上是对梁的应变进行插值,保证了单元任意刚体运动不会产生虚假的节点力;且将梁的截面形心位移表示为曲率的函数,避免了传统单元中的剪切闭锁问题．因而所提方法特别适用于梁的几何非线性分析．数值算例说明了所提方法的正确性和有效性.