A numerical study of hypoelastic and hyperelastic large strain viscoplastic Perzyna type models

For the case of metals with large viscoplastic strains, it is necessary to define appropriate constitutive models in order to obtain reliable results from the simulations. In this paper, two large strain viscoplastic Perzyna type models are considered. The first constitutive model has been proposed by Ponthot, and the elastic response is based on hypoelasticity. In this case, the kinematics of the constitutive model is based on the additive decomposition of the rate deformation tensor. The second constitutive model has been proposed by García Garino et al., and the elasticresponse is based on hyperelasticity. In this case, the kinematics of the constitutive model is based on the multiplicativedecomposition of the deformation gradient tensor. In both cases, the resultant numerical models have been implemented in updated Lagrangian formulation. In this work, global and local numerical results of the mechanical response of both constitutive models are analyzed and discussed. To this end, numerical experiments are performed and different parameters of the constitutive models are tested in order to study the sensitivity of the resultantalgorithms. In particular, the evolution of the reaction forces, the effective plastic strain, the deformed shapes and the sensitivity of the numerical results to the finite element mesh discretization have been compared and analyzed. The obtained results show that both models have a very good agreement and represent very well the characteristic of the viscoplastic constitutive model.     

Effective moduli of hyperelastic porous media at large deformation

Summary.  Among the parameters affecting the overall material properties of porous media, the most significant involve the micromechanical morphology, the matrix material behavior and the applied load range. Considering a unit cell for the porous medium, several approaches of the material response are developed, which yield the effective properties of the medium. Numerical results are presented and compared with experimental or analytical data available in literature. Proposed formulations impose several material characterizations ranging from linear elastic to incompressible hyperelastic. In the case of nonlinear materials, a special formulation has been developed permitting prediction of the porous material moduli. This formulation considers a special nonlinear form for the strain energy function under specific loading conditions. The proposed method yields simple formulas approximating the effective moduli of porous media, which are useful for design purposes. Received August 3, 2001; revised August 14, 2002 Published online: January 16, 2003 Acknowledgements The first of the authors is grateful to his mentor Dr. Paul J. Blatz for his encouragement all these years for continuous research on the nonlinear theories of hyperelastic materials.     

Solution of large deformation contact problems with friction between Blatz-Ko hyperelastic bodies

The present paper is devoted to the analysis of the contact problems with Coulomb friction and large deformation between two hyperelastic bodies. One approach to separate the material nonlinearity and contact nonlinearity is presented. The total Lagrangian formulation is adopted to describe the geometrically nonlinear behavior. Nondifferentiable contact potentials are regularized by means of the augmented Lagrangian method. Numerical examples are carried out in two cases: rigid-deformable contact and deformable-deformable contact with large slips. The numerical results prove that the proposed approach is robust and efficient concerning numerical stability.     

Assessment on assorted hyper-elastic material models applied for large deformation soft finger contact problems

Modeling of soft finger contact mechanics is a prerequisite for gripper design. Realism of soft finger deformations depends extremely on the selection of appropriate hyper-elastic material model for soft materials. The essential criterion for a good mathematical model for hyper elasticity is its ability to match the measured strain energy curves under different deformations over a large range. Selecting an appropriate material law for a given material combination is one of the most difficult tasks in soft finger contact modeling. The present study is devoted for comparing seven popular hyper-elastic non-linear material models (Mooney–Rivlin, Ogden, Yeoh, Neo-Hookean, Gent, Polynomial and Aruda–Boyce model) and selection of the most appropriate model based on experimental data for modeling of soft contact problems. Present results clearly reveal that Ogden and Neo-Hookean model are more suitable for these problems and in line with the experimental results. Finite element technique is employed for critical comparison of various hyper-elastic material models.     

Solution of large deformation impact problems with friction between Blatz–Ko hyperelastic bodies

Feng et al. [Z.Q. Feng, F. Peyraut, N. Labed, Solution of large deformation contact problems with friction between Blatz–Ko hyperelastic bodies, Int. J. Eng. Sci. 41 (2003) 2213–2225] have proposed a study of contact problems between Blatz–Ko hyperelastic bodies in static cases using the bi-potential method. The extension of this method for dynamic analysis of impact problems is realized in the present work. The total Lagrangian formulation is adopted to describe large strains and large displacements non-linear behavior. A first order algorithm is applied for the numerical integration of the time-discretized equation of motion. Numerical examples are carried out in two cases: rigid–deformable and deformable–deformable–rigid impacts in 2D. Numerical results show that the proposed approach is robust and efficient and the physical energy dissipation phenomena are apparently illustrated.     

Nonlinear material parameter estimation for characterizing hyper elastic large strain models

An automated, systematic, and computationally efficient methodology to estimate the material parameters for characterizing general nonlinear material models for large strain analysis (e.g., hyperelastic and hyper foam materials) is presented. Such constitutive material models often require a large number of material constants to describe a host of physical phenomena and complicated deformation mechanisms. Extracting such material constants for a model from the volumes of data generated in the test laboratory is usually a very difficult, and frustrating. The integrated code COMPARE (that is an acronym of Constitutive Material PARameter Estimator) is being developed to enable the determination of an “optimum” set material parameters by minimizing the errors between the experimental test data and the predicted response. The key ingredients of COMPARE are listed as follows: (i) primal analysis tools (response functionals) for differential form of constitutive models; (ii) sensitivity analysis; (iii) optimization technique of an error/cost function; and (iv) graphical user interface. The code COMPARE casts the estimation of the material parameters as a minimum-error, weighted-multiobjective, optimization problem. Detailed derivations and results generated by applying the proposed technique to a comprehensive set of test data are given. These results have clearly demonstrated the great practical utility of the automated scheme developed. Received 17 September 1999     

Approximation of incompressible large deformation elastic problems: some unresolved issues

Several finite element methods for large deformation elastic problems in the nearly incompressible and purely incompressible regimes are considered. In particular, the method ability to accurately capture critical loads for the possible occurrence of bifurcation and limit points, is investigated. By means of a couple of 2D model problems involving a very simple neo-Hookean constitutive law, it is shown that within the framework of displacement/pressure mixed elements, even schemes that are inf-sup stable for linear elasticity may exhibit problems when used in the finite deformation regime. The roots of such troubles are identified, but a general strategy to cure them is still missing. Furthermore, a comparison with displacement-based elements, especially of high order, is presented.     

大型浮筏姿态及弹性变形控制算法研究

随着浮筏气囊系统趋于大型化,筏体结构刚度不可避免的降低。外界扰动作用下,筏架不仅会偏离平衡位置,还会产生较大的弹性变形,导致设备之间产生相对位移,危及设备运行安全。建立某船舶浮筏气囊隔振装置柔性筏架响应模型,并提出一种基于气囊压力参数识别的控制方法,通过调整气囊压力分布对筏架姿态和弹性形态进行控制。试验结果表明,该方法不仅可以控制筏架姿态平衡,还可以有效抑制筏架的弹性变形,并且具有较高的控制精度。     

Two-dimensional dynamical problems for incompressible isotropic linear elastic solids with time dependent moduli and variable density

Summary This paper describes a new general method of solution of two-dimensional problems involving the dynamical behaviour of incompressible linear elastic solids. As formulated, the solution takes account of density variation with both position and time and a shear modulus which is purely time dependent. Several simple applications are made to problems involving thick cylinders and an infinite plate containing a circular hole.

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Zusammenfassung Diese Arbeit beschreibt eine neue, allgemeine Methode zur Lösung von zweidimensionalen, dynamischen Problemen von inkompressiblen, linear-elastischen Materialien. Die Lösung berücksichtigt die Abhängigkeit der Dichte von Ort und Zeit und die Abhängigkeit des Schubmoduls von der Zeit allein. In einigen einfachen Anwendungen werden Probleme gelöst, die den dicken Zylinder und die unendliche Platte mit einem kreisrunden Loch enthalten.

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Remeshing strategies for large deformation problems with frictional contact and nearly incompressible materials

We present a framework to efficiently solve large deformation contact problems with nearly incompressible materials by implementing adaptive remeshing. Specifically, nodally integrated elements are employed to avoid mesh locking when linear triangular or tetrahedral elements are used to facilitate mesh re‐generation. Solution variables in the bulk and on contact surfaces are transferred between meshes such that accuracy is maintained and re‐equilibration on the new mesh is possible. In particular, the displacement transfer in the bulk is accomplished through a constrained least squares problem based on nodal integration, while the transfer of contact tractions relies on parallel transport. Finally, a residual‐based error indicator is chosen to drive adaptive mesh refinement. The proposed strategies are applicable to both two‐dimensional or three‐dimensional analysis and are demonstrated to be robust by a number of numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

A novel method for the measurement of elastic moduli of fibres

The elastic modulus of fibres used in composite materials is a parameter of prime importance in the determination of overall mechanical behaviour. However, evaluation of Young’s modulus, E, of a fibre is a delicate operation given the small dimensions (diameter typically a few tens of microns), and therefore low forces involved in tensile testing. This article treats a novel method of modulus assessment involving the bending of fibres, clamped at one extremity, by forced vibrations. The fibre behaves as a beam, and when the forced oscillations approach (one of) the resonant frequency(ies) of the fibre, the bending amplitude increases. Classical beam theory allows evaluation of Young’s modulus from knowledge of resonant frequency, and fibre dimensions and density. Preliminary application of the technique using fibres of E-glass, having well known elastic characteristics, has given good results and shown its inherent potential. Subsequently, the technique developed was used on recycled fibres in order to obtain their Young’s modulus and to assess their loss of mechanical properties when compared to virgin fibres.     

Automation of finite element formulations for large deformation contact problems

The aim of this paper is to present a general method for automation of finite element formulations of large deformation contact problems. A new automatic‐differentiation‐based notation is introduced that represents a bridge between the classical mathematical notation of contact mechanics and the actual computer implementation of contact finite elements. Automation of derivation of the required formulas (e.g. element residual and tangent matrix) combined with automatic code generation makes the finite element implementation possible at a moderate effort. Accordingly, several 3D contact formulations have been implemented in this work, including penalty and augmented Lagrangian treatments of contact constraints, and several contact smoothing techniques. A typical benchmark problem could thus be executed in an objective way leading to a comprehensive study of the efficiency and the accuracy of various formulations of 3D contact finite elements. Copyright © 2010 John Wiley & Sons, Ltd.     

A polygonal finite element method for modeling arbitrary interfaces in large deformation problems

In this paper, a polygonal-FEM technique is presented in modeling of arbitrary interfaces in large deformations. The method is used to model the internal interfaces and arbitrary geometries using a uniform non-conformal mesh. The technique is applied to capture discontinuous deformations in the non-conformal elements, which are cut by the interface in a uniform regular mesh. In this approach, a uniform non-conformal mesh is decomposed into sub-elements that conform to the internal interfaces. The geometry of interface is used to produce various triangular, quadrilateral and pentagonal elements at the intersection of interface with regular FE mesh, in which the extra degrees-of-freedom are defined along the interface. The level set method is employed to describe the material geometry on the background mesh. The technique is used to extrude any arbitrary geometry from an initial background mesh and model under different external effects. An important feature of the technique is the decomposition of the uniform non-conformal mesh to the polygonal-FEM mesh, which is conformed to the material interfaces. Finally, several numerical examples are analyzed to demonstrate the efficiency of proposed technique in modeling arbitrary interfaces in large deformations.     

A comparative study of mathematical models for gas-solid non-catalytic reactions

Experimental data on desulphurisation of a simulated coal gas mixture containing 200 ppm H₂S, using CuO/ZnO mixed oxide sorbent in a fluidised bed reactor, are used to evaluate four representative structural models for gas-solid non-catalytic reactions. The four models chosen for evaluation are the spherical changing-grain-size model of Georgakis and co-workers, the rectangular grains version of the general formulation of Szekely and co-workers, the single-pore model of Ramachandran and Smith and the random pore model of Bhatia and Perlmutter. All the model parameters except the reaction rate constant are calculated from experimental measurements or from literature correlations. The rate constant alone is adjusted so as to obtain good agreement between the model and the experiment. It is shown that at any given temperature all the models describe the data well. However, the random pore model predicts conversions lower than experiment at large times while the rectangular grains model predicts conversions higher than experiment for small times. The rate constants decrease as temperature increases indicating an inadequacy of all the models in this regard. The models also predict much smaller variations in conversion with change in particle size than those observed experimentally.     

A two material constant,nonlinear elastic stress constitutive equation including the effect of compressibility

A new constitutive equation for compressible, nonlinear elasticity is derived. The stress-deformation relation takes the final form $\text{σ}{}_{\mathrm{ij}}\text{=}\text{3k}\text{2J}\text{(J}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{- 1) δ}{}_{\mathrm{ij}}\text{+}\text{μ}\text{J}\text{(B}{}_{\mathrm{ij}}\text{- j}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{δ}{}_{\mathrm{ij}}\text{)}$ where B_ij is the left Cauchy-Green deformation tensor. J is the Jacobean of the deformation, and k and μ are the two governing mechanical properties having the same interpretation as in linear, isotropic elasticity theory. In this nonlinear theory, k and μ are separately determinable from large deformation conditions of pure dilatation and simple shear, respectively. Under isochoric conditions, the distortional part of the theory takes the form of the kinetic theory of rubber elasticity. Under conditions of small volume change, the theory coincides with the molecular theory of Flory derived for elastomers, but given explicit from only in the one dimensional case.     

A buckling-based metrology for measuring the elastic moduli of polymeric thin films

As technology continues towards smaller, thinner and lighter devices, more stringent demands are placed on thin polymer films as diffusion barriers, dielectric coatings, electronic packaging and so on. Therefore, there is a growing need for testing platforms to rapidly determine the mechanical properties of thin polymer films and coatings. We introduce here an elegant, efficient measurement method that yields the elastic moduli of nanoscale polymer films in a rapid and quantitative manner without the need for expensive equipment or material-specific modelling. The technique exploits a buckling instability that occurs in bilayers consisting of a stiff, thin film coated onto a relatively soft, thick substrate. Using the spacing of these highly periodic wrinkles, we calculate the film's elastic modulus by applying well-established buckling mechanics. We successfully apply this new measurement platform to several systems displaying a wide range of thicknessess (nanometre to micrometre) and moduli (MPa to GPa).     

A generalized self consistent model for effective elastic moduli of human dentine

Closed-form expressions are presented for effective material properties of human dentine in this paper. The derivation is based a Generalized Self Consistent Method and the strain energy principle. The Generalized Self Consistent Model for cell model of fiber-reinforced composites is extended to the case of hollow cylinder model and the corresponding cell model is chosen to consist of a circular hollow cylinder filled with liquid or gas phase, which surrounded by a circular cylindrical shell of matrix phase. Each layer of cylindrical shell is here considered as a kind of composite consisting of collagen fibrils, with mineralized hydroxyapatite, loosely connected to their neighbours, and water (or gas in the case of dry dentine composite). Using the cell model, the effect of Poisson’s ratio and volume fraction of intertubular dentine on effective mechanical constants is analyzed. Results obtained from the proposed model are compared with those from other models such as nano-indentation method.     

大变形刚-柔耦合系统仿真和实验研究

通过气浮台和梁系统的刚-柔耦合动力学实验研究完备的几何非线性模型和一次近似模型在大变形情况下的适用性.首先从Green应变与位移的非线性关系式出发,用绝对节点坐标法建立了弹性梁的完备的几何非线性动力学模型,并考虑结构阻尼建立了气浮台和梁系统的刚-柔耦合动力学方程,然后利用非接触式的运动测量仪和应变仪测量特征点的速度、角速度和应变,通过理论和实验结果的数值对比验证了几何非线性动力学模型的正确性,在此基础上进一步分析基于小变形的一次近似模型的适用性.