Application of the Discrete Element Method to crack propagation and crack branching in a vitreous dense biopolymer material

Crack propagation in a vitreous biopolymer material is simulated using the Discrete Element Method (DEM), which models the brittle material as an assembly of particles bonded together. The simulations are compared to experiments combining a high-speed camera monitoring of crack branching together with a micromechancial testing of samples where local mixture mode is generated by introducing a stress concentrator. Our experimental results show unstable crack propagation and branching occurring upon crack deviation by the action of the stress concentrator. The validity of the DEM simulations is checked by comparing its result to the Finite Element Method (FEM) and to an analytical expression under similar conditions. DEM results show a higher sensitivity to mixed mode compared to FEM and a better match with the analytical formulation. Finally, crack branching is correctly predicted using DEM without any specific criterion for the initiation of secondary cracks.     

On the numerical convergence and performance of different spatial discretization techniques for transient elastodynamic wave propagation problems

We present a systematic investigation of several discretization approaches for transient elastodynamic wave propagation problems. This comparison includes a Finite Difference, a Finite Volume, a Finite Element, a Spectral Element and the Scaled Boundary Finite Element Method. Numerical examples are given for simple geometries with normalized parameters, for heterogeneous materials as well as for structures with arbitrarily shaped material interfaces. General conclusions regarding the accuracy of the methods are presented. Based on the essential numerical examples an expansion of the results to a wide range of problems and thus to numerous fields of application is possible.     

An Element Free Galerkin analysis of steady dynamic growth of a mode i crack in elastic–plastic materials

An Element Free Galerkin (EFG) method based formulation for steady dynamic crack growth in elastic–plastic materials is developed. A domain convecting parallel to the steadily moving crack tip is employed. The EFG methodology eliminates the stringent mesh requirements of the Finite Element Method (FEM) for such problems. Both rate-independent materials and rate-dependent materials are considered. The material is characterized by von Mises yielding condition and an associated flow rule. For rate-independent materials, both the influence of crack speeds and that of strain hardening on the mechanics of steady dynamic crack growth are investigated. For rate-dependent materials, only a non-hardening material is considered with emphasis on determining the influence of viscous properties of materials and crack speeds. The influence of strain hardening on steady dynamic crack growth shows the same trends as for steady quasi-static crack growth. The simplifications used in the literature in deriving analytical solutions for high strain-rate crack growth have been examined thoroughly using the numerical results.     

Modeling and simulation of relaxation in viscoelastic open cell materials and structures

Open cell materials with cubic anisotropy and structures made thereof are investigated with respect to their linear viscoelastic properties, in particular their relaxation behavior. The study is concerned with the prediction of the effective behavior which results from the isotropic bulk material properties as well as the cellular architecture. Finite Element Method simulations of three-dimensional structures are employed to predict the effective response to a wide range of loading modes in the time domain.For predicting the properties of the cellular materials and structures by the Finite Element Method different modeling strategies are employed. The first approach is a periodic unit cell method modeling an infinite medium by means of periodic boundary conditions. This way the entire effective linear viscoelastic constitutive behavior can be computed. However, it is not possible to capture effects as being attributed to traction free faces and load introduction in specimens or structures. A second approach follows to account for these effects by generating finite sample models to represent situations which occur in experimental testing. Finally, an analytical constitutive material law is developed to model linear viscoelasticity for cubic anisotropy in the time domain. It is implemented into the commercial Finite Element software ABAQUS/Standard and the material parameters are gained from the unit cell investigations. This enables the simulation of structures, parts, and components which consist or contain such cellular materials.     

Cosserat model for periodic masonry deduced by nonlinear homogenization

The paper deals with the problem of the determination of the in-plane behavior of periodic masonry material. The macromechanical equivalent Cosserat medium, which naturally accounts for the absolute size of the constituents, is derived by a rational homogenization procedure based on the Transformation Field Analysis. The micromechanical analysis is developed considering a Cauchy model for masonry components. In particular, a linear elastic constitutive relationship is considered for the blocks, while a nonlinear constitutive law is adopted for the mortar joints, accounting for the damage and friction phenomena occurring during the loading history. Some numerical applications are performed on a Representative Volume Element characterized by a selected commonly used texture, without performing at this stage structural analyses. A comparison between the results obtained adopting the proposed procedure and a nonlinear micromechanical Finite Element Analysis is presented. Moreover, the substantial differences in the nonlinear behavior of the homogenized Cosserat material model with respect to the classical Cauchy one, are illustrated.     

Quasi-static simulations of compact polydisperse particle systems

The Discrete Element Method (DEM) was originally devised by Cundall and Strack (1979), as a technique to examine the micromechanics of granular media with the anticipation that this would lead to more physically reliable continuum theories to describe the quasi-static deformation of granular material such as sand. However, the methodology models the evolution of a system of particles as a dynamic process. Consequently there have been numerous publications of the application of DEM to an increasingly wider v...     

压电结构的主动控制仿真与实验研究

结合有限元方法研究了直接负速度反馈和基于LQR(二次线性最优控制)的独立模 态空间主动控制方法来控制结构的振动, 采用一种新的仿真方法：PATRAN与MATLAB 联合仿真,对这两种方法进行主动控制数值仿真. 用MATLAB的xPC实时控制,进 行了主动板的振动控制实验,验证了采用上述控 制仿真方法的正确性. 各种结果表明用压电结构进行振动主动控制效果明显.     

A Projected Finite Element Update Method for Inverse Identification of Material Constitutive Parameters in transversely Isotropic Laminates

In this paper, a novel application of Finite Element Update Method (FEUM) is proposed for the inverse identification of material constitutive parameters in transversely isotropic laminates. Two-dimensional Digital Image Correlation (2D–DIC) is used for full-field measurements which is required for the identification process. Instead of measuring the in-plane displacements, which is a well-known application of 2D–DIC, we seek to measure the pseudo-displacements resulting from out-of-plane (towards camera) deflection of plate under a point load. These pseudo-displacements are basically the perspective projection of the three dimensional displacement fields on the image-plane of the image acquisition system. The cost function in this method is defined in terms of these projections instead of the true displacements – and hence the name Projected Finite Element Update Method (PFEUM). In this article, identification of in-plane elastic moduli of Carbon Fiber Reinforced Plastic (CFRP) plate has been performed using plate bending experiments which show pre-dominantly out-of-plane deflection with little contribution from the in-plane displacements. Identification results are validated by direct experimental measurements of the unknown elastic constants as well as theoretical estimates based on volume ratio of constituents. The results show good conformance between estimated and target values for at least three material parameters namely E₁, E₂ and G₁₂. Effects of experimental noise on parameter estimates has also been evaluated to explain the observed deviation in estimated parameters with current test configuration.     

利用无网格伽辽金法分析材料稳态蠕变问题

稳态蠕变是高温环境下材料的一个重要的考虑问题，它也是材料破坏的一种重要形式。由于存在划分网格，利用传统有限元法模拟稳态蠕变有一定的不足之处。作为一种新兴的数值模拟方法，无网格法不需要划分单元，只需将求解问题离散成独立的结点，计算过程可以局部细化。利用连续介质的虚功原理，将无网格伽辽金法应用于稳态蠕变的数值模拟，推导了稳态蠕变的无网格伽辽金法控制方程。利用罚参数来实现稳态蠕变的不可压缩条件和本质边界条件，能够保证求解过程中刚度矩阵的对称正定性。通过实例的计算结果表明，无网格伽辽金法在求解稳态蠕变时具有较高的计算精度，结果与理论解结果吻合，而且前后处理较为简单。     

Zusammengesetzte Scheiben aus verschiedenartigen Werkstoffen gleicher Querkontraktionszahl und ihre Berechnung nach der Singularitätenmethode

Übersicht Der Spanmmgs- und der Verformungszustand zusammengesetzter Scheiben aus verschiedenartigen Werkstoffen gleicher Querkontraktionszahl werden mit Hilfe der Integralgleichungsmethode (BEM) berechnet.Unter Verwendung von Kräfte- oder Versetzungssingularitäten wird das Problem auf ein System Fredholmseher Integralgleichungen 2. Art zurückgeführt, das numerisch gelöst wird. An zwei Beispielen wird die Anwendbarkeit des Verfahrens gezeigt.

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Investigation of composed discs with the Boundary Element Method

Summary The state of tensions and displacements in discs which are composed of discs of different material with the same Poisson's ratio is calculated by means of the Boundary Element Method (BEM).Load or dislocation singularities are used to reduce the problem to a system of Fredholm integral equations of the second kind, which is solved numerically. To illustrate the applicability of the method two examples are presented including numerical results.

     

A micro-mechanically based continuum damage model for fatigue life prediction of filled rubbers

This paper presents a continuum damage model based on two mechanisms: decohesion between fillers and matrix at a micro-scale followed by a crack nucleation at a macro-scale. That scenario was developed considering SEM observations and an original experimental procedure based on simple shear and tension specimens. Damage accumulation is related to fatigue life using the continuum damage mechanics (CDM). The material behavior is investigated using the statistical framework introduced by Martinez et al. (2011). A Finite Element implementation is proposed and some numerical examples are provided.     

多层膜结构对硬度实验影响的数值分析

为了研究多层膜结构对纳米微硬度实验的影响,用FEPG对纳米微硬度实验中压头的压入过程进行数值模拟,分析了由TiN,Al,Ti组成的多层膜中软膜材料不同、软膜与硬膜厚度比不同以及多层膜层数不同对膜层体系产生的影响,得出梯度变化的膜层结构能够提高膜层的整体性能,为纳米微硬度实验提供了一定的参考依据．     

Prediction of draft forces in cohesionless soil with the Discrete Element Method

The Discrete Element Method (DEM) is applied to predict draft forces of a simple implement in cohesionless granular material. Results are compared with small-scale laboratory tests in which the horizontal force is measured at a straight blade. This study is focused on the case of cohesionless material under quasi-static conditions.The DEM requires the calibration of the local contact parameters between particles to adjust the bulk material properties. The most important bulk property is the angle of internal friction ?. In the DEM, the shear resistance is limited in the case of spherical particles due to excessive particle rotations. This is cured by retaining rotations of the particles. Although this is known to prevent the material from developing shear bands, the model still turns out to be capable of predicting the reaction force on the blade.In contrast to empirical formulas for this kind of application, the DEM model can easily be extended to more complex tool geometries and trajectories. This study helps to find a simple and numerically efficient setup for the numerical model, capable of predicting draft forces correctly and so allowing for large-scale industrial simulations.     

Simulation of the Mach reflection in supersonic flows by the CE/SE method

This study employs the Space-Time Conservation Element and Solution Element (CE/SE) method to determine the influence of downstream flow conditions on Mach stem height. The results indicate that the Mach stem height depends on the incident shock wave angle and the distance between the trailing edge and the symmetry plane. Furthermore, it is shown that the downstream length ratio and the trailing edge angle do not affect the Mach stem height nor the Mach reflection (MR) configuration, and the Space-Time Conservation Element and Solution Element method is able to simulate the MR as well as many other numerical schemes. Communicated by K. Takayama PACS 47.40.Nm     

A Simplified Quadrature Element Method to compute the natural frequencies of multispan beams and frame structures

In this paper a new version of the Modified Quadrature Element Method (MQEM) is proposed. Like MQEM, the proposed method overcomes the drawback of the distance δ of the Quadrature Element Method (QEM) without introducing further degrees of freedom at the ends of the element as in the Differential Quadrature Element Method (DQEM), but it makes the computational cost of the stiffness matrix (and the mass matrix) lighter and uses a general procedure to generate the sampling points distribution. The method here presented has been applied to compute the fundamental frequencies of some structures.     

Prediction of plane strain fracture of AHSS sheets with post-initiation softening

In this investigation, the three-parameter Modified Mohr–Coulomb (MMC) fracture model and the determination of the material parameters are briefly described. The formulation of the post-initiation behavior is proposed by defining both the explicit softening law and the incremental damage evolution law. As opposed to the existing attempts to simulate slant fracture with material weakening before crack formation, softening is assumed to occur only in the post-initiation range. The justification of this assumption can be provided by the interrupted fracture tests, for example, Spencer et al. (2002).Element deletion with a gradual loss of strength is used to simulate crack propagation after fracture initiation. The main emphasis of the paper is the numerical prediction of slant fracture which is almost always observed in thin sheets. For that purpose, VUMAT subroutines of ABAQUS are coded with post-initiation behavior for both shell elements and plane strain elements. Fracture of flat-grooved tensile specimens cut from advanced high strength steel (AHSS) sheets are simulated by 2D plane strain element and shell element models.     

A semi-analytical solution for the confined compression of hydrated soft tissue

Confined compression is a common experimental technique aimed at gaining information on the properties of biphasic mixtures comprised of a solid saturated by a fluid, a typical example of which are soft hydrated biological tissues. When the material properties (elastic modulus, permeability) are assumed to be homogeneous, the governing equation in the axial displacement reduces to a Fourier equation which can be solved analytically. For the more realistic case of inhomogeneous material properties, the governing equation does not admit, in general, a solution in closed form. In this work, we propose a semi-analytical alternative to Finite Element analysis for the study of the confined compression of linearly elastic biphasic mixtures. The partial differential equation is discretised in the space variable and kept continuous in the time variable, by use of the Finite Difference Method, and the resulting system of ordinary differential equations is solved by means of the Laplace Transform method.     

An endochronic plasticity formulation for filled rubber

The nature of elastomeric material demands the consideration of finite deformations, nonlinear elasticity including damage as well as rate-dependent and rate-independent dissipative properties. While many models accounting for these effects have been refined over time to do better justice to the real behavior of rubber-like materials, the realistic simulation of the elastoplastic characteristics for filled rubber remains challenging.The classical elastic-ideal-plastic formulation exhibits a distinct yield-surface, whereas the elastoplastic material behavior of filled rubber components shows a yield-surface free plasticity. In order to describe this elastoplastic deformation of a material point adequately, a physically based endochronic plasticity model was developed and implemented into a Finite Element code. The formulation of the ground state elastic characteristics is based on Arruda and Boyce (1993) eight-chain model. The evolution of the constitutive equations for the nonlinear endochronic elastoplastic response are derived in analogy to the Bergström–Boyce finite viscoelasticity model discussed by Dal and Kaliske (2009).     

Study of Pressure Sensitive Plastic Flow Behaviour of Gasket Materials

The mechanical behaviour of the materials used as compressible gasket in the ultra high pressure apparatus is investigated. Materials such as pyrophyllite and talc, showing a pressure sensitive plastic flow behaviour were considered and a testing configuration was set up for studying the dependence of their plastic response on the hydrostatic component of the stress tensor, according to the Drucker-Prager criterion. A Finite Element modelling of the test was performed to evaluate the specimen response and the local stress condition, during loading. The Finite Element results were validated by comparison with those of a specific experimental characterisation. A parametric analysis was then carried out, by varying the materials constitutive behaviour, in order to build up a data base of representative curves. In this way an algorithm was developed, with the aim of determining the material constitutive behaviours by the analysis of the experimental data. The proposed procedure was then used to study the mechanical response of different gasket materials.     

A coupled sliding and rolling friction model for DEM calibration

The accuracy of dense Discrete Element Method (DEM) simulations is sensitive to initial density, contact orientation, particle size and shape, and interparticle interaction parameters including contact stiffness, cohesion, coefficients of friction, and coefficients of restitution. Although studies have characterized the effects of individual particle interaction parameters on mechanical responses of loaded granular material, research combining DEM parameters for calibration is scarce. Robust DEM calibration methodology combining sliding and rolling friction coefficients was developed and validated to predict bulk residual soil strength of initially dense DEM particle assemblies.