Application of the Cosserat continua to numerical studies on the properties of the materials

The finite element models of Cosserat continuum in two- and three-dimensions are presented. The size effects of a cantilever beam and a micro-rod, the well-posedness, the mesh-independent solutions of the boundary value problems with non-associated elastoplastic and strain softening constitutive behavior, and the progressive failure of the two- and three-dimensional vertical excavations are studied. Numerical results illustrate that the proposed Cosserat continuum models are capable of reflecting the size effects of micro-structures, preserving the well-posedness of the boundary value problem characterized by the strain localization, ensuring mesh-independent solutions, and simulating the entire progressive failure process occurring in engineering structures.     

On error estimator and adaptivity in the meshless Galerkin boundary node method

In this article, a simple a posteriori error estimator and an effective adaptive refinement process for the meshless Galerkin boundary node method (GBNM) are presented. The error estimator is formulated by the difference between the GBNM solution itself and its L ²-orthogonal projection. With the help of a localization technique, the error is estimated by easily computable local error indicators and hence an adaptive algorithm for h-adaptivity is formulated. The convergence of this adaptive algorithm is verified theoretically in Sobolev spaces. Numerical examples involving potential and elasticity problems are also provided to illustrate the performance and usefulness of this adaptive meshless method.     

On the numerical evaluation of Eshelby's tensor and its application to elastoplastic fibrous composites

A numerical evaluation of Eshelby's S tensor for an ellipsoidal inclusion imbedded in a general anisotropic matrix material is performed. The numerical scheme is valid for any degree of matrix anisotropy and for any aspect ratio of the ellipsoid, including the extreme cases of cracks and cylindrical inclusions. The influence of matrix anisotropy on the evaluation of S is tested extensively for cylindrical inclusions by considering plasticity induced anisotropy in the instantaneous properties of an elastic-plastic matrix material. The Mori-Tanaka averaging method is used to study the influence of the evaluation of S on the prediction of instantaneous effective properties of fibrous composites with elastic fibres and elastic-plastic matrix.     

RVE computations with error control and adaptivity: the power of duality

The goal of computational homogenization is to obtain the macro-scale response, normally in terms of macro-scale stress for given macro-scale deformation, via RVE-computations. In this paper we investigate, in a systematic manner, the effects of Dirichlet and Neumann boundary conditions on the RVE. Adaptive computations are carried out with respect to, in particular, control of the error in the macro-scale stress tensor. This requires the corresponding dual solutions. As a new result, it is shown how the same dual solutions can be conveniently used in computing the algorithmic tangent stiffness tensor, thereby demonstrating the “power of duality”.     

A review of error estimation and adaptivity in the boundary element method

When using the boundary element method, the accuracy of the numerical solution depends critically on the discretization of the boundary into elements (panels). The distribution of the panels is one of the most important decisions taken when analyzing a problem, but still the vast majority of users employ empirical guidelines to distribute the panels. This paper reviews the various adaptive schemes that have been proposed for boundary elements. Numerical results are obtained for infinite fluid flow problems and free surface problems and are used to assess the reliability and effectiveness of each method.     

On a variational formulation of problems in the classical continuum mechanics of solids

The basic equations of linear elasticity, of mildly non-linear elasticity and of plastic flow are reduced to a generalization of Hamilton's canonical formalism. Complementary variational principles are deduced. Numerical applications of these principles are demonstrated in some simple cases.     

Applications of inherent strain and interface element to simulation of welding deformation in thin plate structures

Welding-induced distortion not only reduces largely manufacturing accuracy but also decreases significantly productivity due to correction works. If welding distortion can be predicted through a simple and practical method beforehand, the predictions will be helpful for taking active as well as appropriate measures to control the dimension accuracy. Based on inherent strain theory and interface element formulation, we developed a practical prediction system to compute the accumulated distortion during the welding assembly process in the current study. Using the developed prediction method, we calculated the welding distortion in a thin plate structure with considering both the shrinkage due to heat input and the gap/misalignment generated during assembly process. Meanwhile, we investigated the influences of assembly sequence and gap correction on the final distortion.     

Multiscale simulations: application to the heat transfer simulation of sliding solids

Molecular dynamics is a powerful tool allowing the simulation of matter behaviour at the atomic scale. Due to computation time, it is clearly not possible to use molecular dynamics to simulate a forming process. However, atomistic simulations can be used to study and understand the physical phenomena that occur during matter deformation. As an example, heat transfer between the contacting solids in forming processes is one of the important physics phenomena that have to be taken into account in order to do realistic simulations. A multiscale analysis of heat transfer is presented. This analysis leads to two kinds of models: a macroscopic model which can be used for the simulation of the process itself and a microscopic model that is used to determine the parameters of the macroscopic model. In this microscopic model, the friction heat generation phenomena has to be described quite accurately. Friction heat is mainly due to plastic and elastic deformation and adhesion. Thus, to understand the underlying friction heat generation phenomena, atomistic simulations using molecular dynamics are carried out. It is shown that friction heat is the transformation of mechanical work given to the system at the macroscopic scale into potential energy during elastic deformation. This potential energy which is stored in the system is finally transformed into atomic kinetic energy (friction heat) during plastic transformation.     

On strain localization in the high rate extension of nylon fibers

A simple analytical model for the adiabatic high strain rate extension of synthetic textile fibers is presented. The model suggests that, for fibers with particular thermo-mechanical and constitutive properties, initial nominally uniform strain distributions along the fiber will tend to become non-uniform, with localization of axial strain into a thermally softened region. To assess the usefulness of the model in predicting and interpreting fiber behavior, a commercial nylon filament is investigated experimentally. Nylon filaments are extended to break at a low, isothermal strain rate (0.0015 s^–1) and at a high, adiabatic strain rate (70 s^–1). A dimensionless strain localization parameter (SLP), used to characterize the nylon filament in the framework of the model, predicts strain localization to occur during extension at the 70 s^–1 strain rate. Experimental load-extension curves exhibit a sharply reduced elongation-to-break at the high strain rate, consistent with the predicted occurrence of localized, versus uniform, straining. In addition, the transition from homogeneous to localized straining appears to occur at elongations that correspond with the SLP attaining a critical value for onset of localization.     

On the description of ductile fracture in metals by the strain localization theory

Numerical simulations based on the bifurcation and imperfection versions of the strain localization theory are used in this paper to predict the failure loci of metals and applied to an advanced high strength steel subjected to proportional loading paths. The results are evaluated against the 3D unit cell analyses of Dunand and Mohr (J Mech Phys Solids 66(1):133–153, 2014. doi: 10.1016/j.jmps.2014.01.008) available in the literature. The Gurson porous plasticity model (Gurson in J Eng Mater Technol 99(1):2–15, 1977. doi: 10.1115/1.344340) is used to induce strain softening and drive the localization process. The effects of the void growth, void nucleation and void softening in shear are investigated over a large range of stress triaxialities and Lode parameters. A correlation between the imperfection and bifurcation results is established.     

Calculation of stress and strain gradients in the concentration zone in cyclic elastoplastic deformation. 1

A method is proposed of calculating the gradients of true stresses and strains in the stress concentration zone in cyclic elastoplastic deformation of the material based on calculating the true stresses and strains in the stress concentration zone using approximate dependencies. The gradients of the true stresses, calculated using the method of equivalent energy and Neuber's method, are compared with the gradients of elastic stresses. It is shown that this also applies to other materials in which the gradients of the true stresses in cyclic elastoplastic deformation are considerably lower than the gradients of elastic stresses.N. E. Zhukovskii Aviation Institute, Khar'kov. Prochnost' Regional Scientific Research Institute. Translated from Problemy Prochnosti, No. 9, pp. 98–100, September, 1989.     

Superconvergence and the use of the residual as an error estimator in the BEM. II: Collocation,numerical integration and error indicators

We show for a variety of integral equations that the residual can be used as an error estimator provided the Sloan iterate of the approximation superconverges. This generalizes a result given by Geng el al. [J. Acoust. Soc. Am. 100 (1996) 355]. When the solution technique is Galerkin's method we show that the superconvergence of the Sloan iterate can be established under quite general conditions. For collocation this is more difficult and we discuss a generalization of a result of Brunner [J. Comp. Appl. Math. 67 (1996) 185] for doing this. Using ideas of Schulz [Über lokale and globale Fehlergschätzungen für adaptive randelment Methoden, PhD thesis, Mathematisches Institute A, University of Stuttgart, 1997] it is shown how to localize these results to provide asymptotically exact local error indicators. It is also shown that it is important to consider the effect of numerical integration errors, as such errors can destroy superconvergence.     

Evolution of solids fraction surfaces in tapping: simulation and dynamical systems analysis

We report our findings on the evolution of solids fraction in a tapped system of inelastic, frictional spheres as a function of the applied acceleration obtained via discrete element simulations. Animations of the simulation data reveal the propagation of a wave initiated from the base that causes local rearrangements of the particles ultimately leading to the development of a dense microstructure. We also describe the analysis of dynamical models capable of predicting the simulated behavior, and advanced visualization techniques for revealing the dynamics.     

Approximate determination of the state of stress and strain in an elastoplastic body weakened by cracks

Conclusion An approximate approach has been given for determining the parameters of the state of stress and strain in the region around a crack vertex by the use of boundary interpolation and equivalent states.The approach can be used for any force shcme, which greatly extends the scope for applying nonlinear failure in mechanics in research on viability and working life for structural components and machines.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 6, pp. 44–50, November–December, 1989.     

The evaluation of the error term in some numerical quadrature formulae: An addendum

In a previous paper the author deduced a method of evaluating the error term arising in some quadrature formulae. This method depended on the analytic evaluation of a Hilbert transform. The result is now extended to all quadrature formulae used for the calculation of integrals over finite intervals by approximating the Hilbert transform.     

Thermomechanical characterization of stress localization in glass: An experimental and numerical study

Thermoelastic stress analysis and quantitative calorimetry are full‐field noncontact techniques widely used to study the thermomechanical behaviour of materials. The first one linearly relates the sum of the principal stresses to the temperature variation, and the second one can be used to measure the mechanical dissipation. However, brittle materials such as glass are a priori bad candidates for these techniques. Indeed, their low‐temperature variations under loading lead to very noisy infrared images, and their brittle mechanical behaviour does not allow to deform them significantly. In the present paper, the thermomechanical characterization of a holed glass sample under cyclic loading is performed. A preliminary new filtering methodology has been applied to the thermal movie to remove the noise. The stress field obtained from the thermoelastic stress analysis is well correlated to the finite element model showing that this technique is adapted to study the thermoelastic response of brittle materials. Finally, the corresponding calorimetric response has been determined by using a simplified formulation of the heat diffusion equation. This permits to quantify heat sources and to carry out energy balances.     

Granular packing: numerical simulation and the characterisation of the effect of particle shape

The packing of granular particles is investigated using a combined finite-discrete element approach. One of the aims of this paper is to present an application of a recently improved numerical simulation technique for deformable granular material with arbitrary shapes. Our study is focused on the influence of the effect of the particle shape on (1) the emergent properties of a granular pack (packing density, coordination number, force distribution), and on (2) the spatial distribution of the stress. A set of simulations that mimick the sedimentation process is carried out, with varying input parameters, such as contact friction and particle shape. It is shown that the eccentricity of the particles not only significantly influences the final density of the pack but also the distribution of the stress and the contact forces. The presence of surface friction increases the amount of disorder within the granular system. Stress heterogeneities and force chain patterns propagate through the particles more efficiently than for the frictionless systems. The results also suggest that for the monodisperse systems investigated the coordination number is one of the factors that controls the distribution of the stress within a granular medium.