Modelling of shear localization in elastic material by means of energy relaxation

A new approach to the problem of shear localization is proposed. It is based on the energy minimization principle associated with micro–structure developments and the micro–shearing of a rank–one laminate which is aligned to shear band. The thickness of the shear band represented by the volume fraction is assumed to tend to zero. The non–convex energy due to the formation of the shear band is solved by energy relaxation in order to ensure that the problem is well–posed. An application of the proposed formulation to isotropic linear elastic material is presented. The capability of the proposed energy relaxation is demonstrated through numerical simulation of a plane strain tension. The numerical results demonstrate that there is no mesh–dependence. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of shear band formation in hyperelastic material by energy relaxation

A theorical framework for the analysis of localized failure in hyperealstic material is presented based on the energy minimization principles associated with micro-structure developments. The theory is predicated upon the assumptions that the thickness of shear band represented by its volume fraction tends to zero as well as that the energy inside shear band is a function of the norm of the deformation gradient. Shear bands are treated as laminates of first order. The existence of shear bands in the structure leads to an ill-posed problem which can be solved by means of energy relaxation. An application of the proposed formulation to Neo-Hookean material is presented. Numerical simulation is shown in order to evaluate the performance of the proposed energy relaxation. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical analysis of shear bands in solids by means of computational homogenization

A novel fully three–dimensional framework for the numerical analysis of shear bands in solids undergoing large deformations is presented. The effect of micro shear bands on the macroscopic material response is computed by means of a homogenization strategy. More precisely, a strain–driven approach which complies well with displacement–driven finite element formulations is adopted. The proposed implementation is based on periodic boundary conditions for the micro–scale. Details about the implementation of the resulting constraints into a three–dimensional framework are discussed. The shear bands occurring at the micro–scale are modeled by a cohesive zone law, i.e., the tangential component of the traction vector governs the relative shear sliding displacement. This law is embedded into a Strong Discontinuity Approach (SDA). To account for realistic sliding modes, multiple shear bands are allowed to form and propagate in each finite element. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

爆炸和冲击载荷下金属材料及结构的动态失效仿真

通过数值模拟研究爆炸冲击载荷下金属材料和结构的动态失效规律,对表征爆炸冲击毁伤效应及设计新型抗冲击结构有重要意义.强动载下金属材料失效涉及材料大变形、热力耦合、材料状态变化等多个复杂物理过程,给数值仿真带来了极大挑战,其中包括裂纹、剪切带等复杂失效模式的几何描述、动态失效准则的确定、塑性与损伤耦合演化的描述等问题.针对...     

Identification of the Material Parameters of a Micropolar Model for Granular Materials

Granular frictional materials show a complex stress‐strain behaviour depending on the stress state and the load history. Furthermore, biaxial experiments exhibit the occurrence of shear band phenomena as the result of the localization of plastic strains. It is well known that the onset of shear bands is associated with microrotations of the granular microstructure, which has a significant influence on the macroscopic behaviour. Consequently, the macroscopic material must result in a micropolar model, which incorporates rotational degrees of freedom. After the formulation of the constitutive equations and the numerical implementation, it is necessary to determine all required material parameters. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non–Isothermal Shear Band Localization in Crystal Plasticity

We analyze the formation of shear bands in plastically deforming single crystals under non-isothermal quasi-static loading conditions. A key feature of the present work is to motivate the constitutive coupled thermomechanical equations for the slip resistance and the slip evolution by micromechanical investigations of defects in crystals. Here, we put particular emphasis on comparative investigations of hardening–softening effects of crystals under non-isothermal conditions, including a quantification of the latent energy storage. Furthermore, we analyze a numerical solution algorithm for the coupled thermomechanical problem and we test the performance on a typical benchmark example of finite-strain single-crystal thermoplasticity: the localization of deformation into a shear band for the case of a rectangular strip. Experimental evidence for this problem is well documented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unsteady shear vibrations of a die for a nonuniform base

A dynamic shear contact problem is examined for uniform and nonuniform bases. A flexible layer on a rigid half-space is chosen as the nonuniform base. The problem is solved on the basis of applied equations for strain. By using this approach, it is possible to reduce the problem to a system of integrodifferential equations. A numerical algorithm is proposed for its solution. Attention is focused on the effect of the flexible layer on the displacement and reaction of the die. The numerical results are analyzed.Translated from Dinamicheskie Sistemy, No. 4, pp. 52–57, 1985.     

Elastic wave propagation energy dissipation characteristics analysis on the viscoelastic damping material structures embedded with acoustic black hole based on semi-analytical homogeneous asymptotic method

Elastic wave energy dissipation and absorption properties of viscoelastic damping material (VDM) composite plates embedded with acoustic black hole (ABH) are analyzed in this paper. Considering the periodic distribution of the ABH-embedded VDM structure in the composite plate, semi-analytical homogeneous asymptotic theory is applied, which transforms the macroscopic to a microscopic problem. In-plane variables of the composite structure are defined and generated by the third-order shear deformation theory of Reddy, and the equilibrium equations are derived by extended Hamilton's principle and the internal balance is consequently determined by representative volume element theory. Determining the constitutive equations of the composite laminate structure allow the equivalent shear and strain equilibrium equations to be achieved. Subsequently, the complex equivalent stiffness is defined according to the general Hooke's law, and the dimensionless equivalent loss tangent tanδ of the composite sandwich plate is finally evaluated from the equivalent loss and storage modulus. The ABH and VDM layer factors which affect tanδ are thoroughly analyzed and discussed. The investigation can supply a new efficient method to dissipate and absorb propagation wave energy with a wide bandwidth at low frequency. Additionally, the analysis is validated by numerical simulation and Galerkin methods.     

Treatment of the composite fabric’s shaping using a Lagrangian formulation

In this paper, we are interested in the simulation of prepreg composite deformation by deep-drawing and laying-up. It uses new bi-component finite elements made of woven material in which the nodal interior loads are deduced from fibre tensile strain energy and not polymerized resin membrane energy. Specific treatment is used to analyze the frictional-contact problem between the deformable prepreg composite and the steel rigid tools. The frictional-contact method is based on the Lagrangian formulation and the preconditioned conjugate gradient method. Some numerical tests are given to investigate the performance of the numerical strategies.     

Material stability analysis of particle methods

Material instabilities are precursors to phenomena such as shear bands and fracture. Therefore, numerical methods that are intended for failure simulation need to reproduce the onset of material instabilities with reasonable fidelity. Here the effectiveness of particle discretizations in reproducing of the onset of material instabilities is analyzed in two dimensions. For this purpose, a simplified hyperelastic law and a Blatz–Ko material are used. It is shown that the Eulerian kernels used in smooth particle hydrodynamics severely distort the domain of material stability, so that material instabilities can occur in stress states that should be stable. In particular, for the uniaxial case, material instabilities occur at much lower stresses, which is often called the tensile instability. On the other hand, for Lagrangian kernels, the domain of material stability is reproduced very well. We also show that particle methods without stress points exhibit instabilities due to rank deficiency of the discrete equations. AMS subject classification 74S30     

Caracterización de la delaminación en materiales compuestos mediante la teoría de mezclas serie/paralelo

This paper presents a new procedure to deal with the delamination problem found in laminated composites, based in a continuum mechanics formulation. The procedure proposed obtains the composite constitutive performance with the Serial/Parallel mixing theory, developed by F. Rastellini. This theory characterizes composite materials by coupling the constitutive behaviour of the composite components, imposing an iso–strain relation among the components in the fibre (or parallel) direction and an iso-stress relation in the remaining directions (serial directions). The proposed procedure uses a damage formulation to characterize the constitutive behaviour of matrix component in order to obtain the stress-strain performance of this material.With these two formulations, the delamination phenomenon is characterized naturally by the numerical simulation, being unnecessary the definition of special elements or computationally expensive techniques like the definition of contact elements or mesh separation. Matrix failure, as a result of the stress state found in it, leads to a reduction of the stiffness and strength capacity of the composite in its serial directions, among them, the shear component. This stiffness reduction provides a composite performance equivalent to what is found in a delaminated material.To prove the ability of the formulation proposed to solve delamination problems, the End Notch Failure test is numerically simulated and the results obtained are compared with experimental ones. The agreement found in the results with both simulations, numerical and experimental, validate the proposed methodology to solve the delamination problem.     

A numerical approach for the simulation of ductile fracture with embedded discontinuities

In the present study, a computational approach for the numerical simulation of ductile fracture within the framework of the finite element method is proposed. In the developed macroscopic formulation, the inelastic behavior in the bulk of the material is described by the finite elasto‐plastic material model proposed in [4]. The failure process is modeled by introducing discontinuities when a special local fracture criterion is satisfied. The discontinuities are incorporated via special triangular finite elements with embedded interfaces following the line of [2]. Finally, the numerical procedure is evaluated for a twodimensional representative test problem. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Plane harmonic wave propagation in three-dimensional composite media

An important characteristic of waves propagating through periodic materials is the existence of stop bands. A stop band implies the range of frequencies over which a medium completely reflects all incident waves and there is no transmission. Predicting stop band phenomena in periodic materials is regarded as the first step toward designing composite microstructures capable of propagating energy in a predetermined manner. In this paper a global–local modeling methodology previously proposed by the authors is used to successively predict stop bands in three-dimensional composite media. Numerical results reveal that the first stop band of the considered microstructures occurs where an acoustic shear mode veers with the lowest optical branch of the same symmetry class.     

A biobjective optimization model for routing in mobile ad hoc networks

In this paper, the problem of finding optimal paths in mobile ad hoc networks is addressed. More specifically, a novel bicriteria optimization model, which allows the energy consumption and the link stability of mobile nodes to be taken into account simultaneously, is presented. In order to evaluate the validity of the proposed model, a greedy approach is devised. Some preliminary computational experiments have been carried out, in a simulation environment. The numerical results are very encouraging, showing the correctness of the proposed model. Indeed, the selection of a shorter route leads to a more stable route, but to a greater energy consumption. On the other hand, if longer routes are selected the route fragility is increased, but the average energy consumption is reduced.     

考虑损伤的修正梯度弹性理论

梯度弹性理论在描述材料微结构起主导作用的力学行为时具有显著优势,将其与损伤理论相结合,可在材料破坏研究中考虑微结构的影响.基于修正梯度弹性理论,将应变张量、应变梯度张量和损伤变量作为Helmholtz自由能函数的状态变量,并在自然状态附近对自由能函数作Taylor展开,进而由热力学基本定律,推导出修正梯度弹性损伤理论本构方程的一般形式.编制有限元程序,模拟土样损伤局部化带的发展演化过程.结果表明,修正梯度弹性损伤理论消除了网格依赖性;损伤局部化带不是与损伤同时发生,而是在损伤发展到一定程度后再逐渐显现出来.     

Finite-element modeling of the particle clustering effect in a powder-metallurgy-processed ceramic-particle-reinforced metal matrix composite on its mechanical properties

A new numerical method is proposed to predict the effect of particle clustering on grain boundaries in a ceramic- particle-reinforced metal matrix composite on its mechanical properties, and micromechanical finite-element simulation of stress–strain responses in composites with random and clustered arrangements of ceramic particles are carried out. A particular material modeled and analyzed is a TiC-particle-reinforced Al matrix composite processed by powder metallurgy. A representative volume element of a composite microstructure with 5 vol.% TiC is reconstructed based on the tetrakaidecahedral grain boundary structure by using a modified random sequential adsorption. The model proposed in this study accurately represents the stress concentrations and particle-particle interactions during deformation of the powder-metallurgy-processed composite. A comparison with the random-arrangement model shows that the present numerical approach is more accurate in simulating the behavior of the composite material.     

A strong discontinuity based adaptive refinement approach for the modeling of crack branching

In the current work, the physical phenomena of dynamic fracture of brittle materials involving crack growth, acceleration and consequent branching is simulated. The numerical modeling is based on the approach where the failure in the form of cracks or shear bands is modeled by a jump in the displacement field, the so called ‘strong discontinuity’. The finite element method is employed with this strong discontinuity approach where each finite element is capable of developing a strong discontinuity locally embedded into it. The focus in this work is on branching phenomena which is modeled by an adaptive refinement method by solving a new sub-boundary value problem represented by a finite element at the growing crack tip. The sub-boundary value problem is subjected to a certain kinematic constraint on the boundary in the form of a linear deformation constraint. An accurate resolution of the state of material at the branching crack tip is achieved which results in realistic dynamic fracture simulations. A comparison of resulting numerical simulations is provided with the experiment of dynamic fracture from the literature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite element simulations of window Josephson junctions

This paper deals with the numerical simulation of the steady state two dimensional window Josephson junctions by finite element method. The model is represented by a sine-Gordon type composite PDE problem. Convergence and error analysis of the finite element approximation for this semilinear problem are presented. An efficient and reliable Newton-preconditioned conjugate gradient algorithm is proposed to solve the resulting nonlinear discrete system. Regular solution branches are computed using a simple continuation scheme. Numerical results associated with interesting physical phenomena are reported. Interface relaxation methods, which by taking advantage of special properties of the composite PDE, can further reduce the overall computational cost are proposed. The implementation and the associated numerical experiments of a particular interface relaxation scheme are also presented and discussed.     

Strain-gradient viscoplasticity in one-dimensional structural dynamics

Based on the static theory of strain-gradient viscoplasticity proposed by [1], a one-dimensional dynamic analysis is derived for finite element computation of isotropic hardening materials. The kinetic energy is assumed to be composed of the conventional and internal kinetic energy. The internal energy is described phenomenologically in terms of the equivalent plastic strain in order to capture the heterogeneity of plastic flow. Herein, the microscopic density is assumed to be related to the macroscopic one through a microscopic-inertia parameter. The macroscopic- and microscopic-force balances including inertia effects are derived. The performance of the proposed formulation is illustrated through the numerical simulation of a one-dimensional dynamic problem. A parameter study to find the microscopic-inertia parameter is carried out. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Decomposition Methodology Applied to the Multi-Area Optimal Power Flow Problem

This paper describes a decomposition methodology applied to the multi-area optimal power flow problem in the context of an electric energy system. The proposed procedure is simple and efficient, and presents some advantages with respect to other common decomposition techniques such as Lagrangian relaxation and augmented Lagrangian decomposition. The application to the multi-area optimal power flow problem allows the computation of an optimal coordinated but decentralized solution. The proposed method is appropriate for an Independent System Operator in charge of the electric energy system technical operation. Convergence properties of the proposed decomposition algorithm are described and related to the physical coupling between the areas. Theoretical and numerical results show that the proposed decentralized methodology has a lower computational cost than other decomposition techniques, and in large large-scale cases even lower than a centralized approach.