The large flexibility of meshfree solution schemes makes them attractive for many kinds of engineering applications, like Additive Manufacturing or cutting processes. While numerous meshfree methods ...were developed over the years, the accuracy and robustness are still challenging and critical issues. Stabilization techniques of various kinds are typically used to overcome these problems, but often require the tuning of unphysical parameters. The Peridynamic Petrov–Galerkin method is a generalization of the peridynamic theory of correspondence materials and offers a stable and robust alternative. In this work, the stabilization free approach is extended to three dimensional problems of finite elasticity. Locking-free mixed formulations for nearly incompressible and incompressible materials are developed and investigated in convergence studies. In general, an efficient implicit quasi-static framework based on Automatic Differentiation is presented. The numerical examples highlight the convergence properties and robustness of the proposed formulations.
NURBS-based isogeometric analysis is applied to 3D frictionless large deformation contact problems. The contact constraints are treated with a mortar-based approach combined with a simplified ...integration method avoiding segmentation of the contact surfaces, and the discretization of the continuum is performed with arbitrary order NURBS and Lagrange polynomial elements. The contact constraints are satisfied exactly with the augmented Lagrangian formulation proposed by Alart and Curnier, whereby a Newton-like solution scheme is applied to solve the saddle point problem simultaneously for displacements and Lagrange multipliers. The numerical examples show that the proposed contact formulation in conjunction with the NURBS discretization delivers accurate and robust predictions. In both small and large deformation cases, the quality of the contact pressures is shown to improve significantly over that achieved with Lagrange discretizations. In large deformation and large sliding examples, the NURBS discretization provides an improved smoothness of the traction history curves. In both cases, increasing the order of the discretization is either beneficial or not influential when using isogeometric analysis, whereas it affects results negatively for Lagrange discretizations.
Error estimation for crack simulations using the XFEM Prange, C.; Loehnert, S.; Wriggers, P.
International journal for numerical methods in engineering,
28 September 2012, Letnik:
91, Številka:
13
Journal Article
Selective Laser Melting (SLM) is an emerging Additive Manufacturing technology for metals. Complex three dimensional parts can be generated from a powder bed by locally melting the desired portions ...layer by layer. The necessary heat is provided by a laser. The laser–matter interaction is a crucial physical phenomenon in the SLM process. Various modeling approaches with different degrees of complexity exist in the literature to represent the laser–matter interaction within a numerical framework. Often, the laser energy is simply distributed into a specified volume. A more precise approach is ray tracing. The laser beam can be divided into moving discrete energy portions (rays) that are traced in space and time. In order to compute the reflection and absorption usually a triangulation of the free surface is conducted. Within meshfree methods, this is a very expensive operation. In this work, a computationally efficient algorithm is developed which avoids triangulation and can easily be combined with meshfree methods. Here, the suggested ray tracing algorithm is exemplary coupled with the stabilized Optimal Transportation Meshfree Method. The importance of ray tracing is evaluated by simulating the fusion of metal powder particles. A comparison of the results with a volumetric heat source approach shows that ray tracing significantly improves the accuracy of absorption and vaporization.
•T-spline isogeometric analysis is adopted to model frictionless contact problems.•Analysis models are generated directly in the design environment.•A convergence study for T-splines and uniform and ...non-uniform NURBS is performed.•The superior accuracy of T-splines with respect to NURBS is demonstrated.
T-spline-based isogeometric analysis is applied to frictionless contact problems between deformable bodies in the context of large deformations. The continuum is discretized with cubic T-splines and cubic NURBS. A Gauss-point-to-surface formulation is combined with the penalty method to treat the contact constraints in the discretized setting. It is demonstrated that analysis-suitable T-splines, coupled with local refinement, accurately approximate contact pressures with far fewer degrees of freedom than NURBS. Both two- and three-dimensional examples are presented. Additionally, all T-spline analysis models are generated using commercially available T-spline modeling software without intermediate mesh generation or geometry clean-up steps.
Cohesive zone (CZ) models have long been used by the scientific community to analyze the progressive damage of materials and interfaces. In these models, non-linear relationships between tractions ...and relative displacements are assumed, which dictate both the work of separation per unit fracture surface and the peak stress that has to be reached for the crack formation. This contribution deals with isogeometric CZ modeling of interface debonding. The interface is discretized with generalized contact elements which account for both contact and cohesive debonding within a unified framework. The formulation is suitable for non-matching discretizations of the interacting surfaces in presence of large deformations and large relative displacements. The isogeometric discretizations are based on non uniform rational B-splines as well as analysis-suitable T-splines enabling local refinement. Conventional Lagrange polynomial discretizations are also used for comparison purposes. Some numerical examples demonstrate that the proposed formulation based on isogeometric analysis is a computationally accurate and efficient technology to solve challenging interface debonding problems in 2D and 3D.
We present a general framework for the analysis and modelling of frictional contact involving composite materials. The study has focused on composite materials formed by a matrix of rubber and ...synthetic or metallic fibres, which is the case of standard tires. We detail the numerical treatment of incompressibility at large deformations that rubber can experience, as well as the stiffening effect that properly oriented fibres will induce within the rubber. To solve the frictional contact between solids, a Dual Augmented Lagrangian Multiplier Method is used together with the Mortar method. This ensures a variationally consistent estimation of the contact forces. A modified Serial-Parallel Rule of Mixtures is employed to model the behaviour of composite materials. This is a simple and novel methodology that allows the blending of constitutive behaviours as diverse as rubber (very low stiffness and incompressible behaviour) and steel (high stiffness and compressible behaviour) taking into account the orientation of the fibres within the material. The locking due to the incompressibility constraint in the rubber material has been overcome by using Total Lagrangian mixed displacement-pressure elements. A collection of numerical examples is provided to show the accuracy and consistency of the methodology presented when solving frictional contact, incompressibility and composite materials under finite strains.
In this contribution, methods of computing the macroscopic tangent that is required in multiscale volumetric homogenization problems are investigated. A condensation procedure that employs the ...tangent information from the microscale finite element analysis is derived within a special framework where deformation controlled boundary conditions in micromechanical testing are enforced via the penalty method. The developed methodology is demonstrated by sample macroscale problems in the context of the multilevel finite element strategy. Due to the high memory allocation costs that the condensation procedure induces, a perturbation procedure is developed based on a minimal number of micromechanical tests. Results from the condensation and perturbation procedures are compared for sample infinitesimal and finite deformation inelasticity problems and the algorithmic consistency of the macroscopic tangent with the evolution of the macroscopic stress is discussed. It is shown that the ability to compute the macroscopic tangent can also be employed to construct a stress controlled micromechanical testing procedure.
In this paper three-dimensional geometrical models for concrete are generated taking the random structure of aggregates at the mesoscopic level into consideration. The generation process is based ...upon Monte Carlo's simulation method wherein the aggregate particles are generated from a certain aggregate size distribution and then placed into the concrete specimen in such a way that there is no intersection between the particles. For high volume fractions of aggregates, new algorithms for generating realistic concrete models are proposed.
The generated geometrical models are then meshed using the aligned approach in which the finite element boundaries are coincident with materials interfaces and therefore there are no material discontinuities within the elements.
The finite element method (FEM) is used in the direct computation of the effective properties of concrete. The results obtained from the numerical simulations and the subsequent homogenisation are then compared with experimental data. Furthermore numerical simulations of the damage and fracture process of concrete are performed using an isotropic damage model to model the progressive degradation of concrete. Finally, a concrete block is investigated where numerical and experimental results are discussed.
Flexoelectricity, which represents the spontaneous electric polarization induced by the strain gradient, is a universal electromechanical coupling effect regardless of symmetry in all dielectric ...material. In solid dielectric material, the contribution from flexoelectricity can be due to four related phenomena: static and dynamic bulk flexoelectricity, surface flexoelectricity and surface piezoelectricity. While the surface flexoelectric effect can be negligible, the magnitude of the remaining three phenomena are comparable. Presently, the role of the static bulk flexoelectric and surface piezoelectric effects in the energy harvesters has been intensively studied, the contribution from dynamic flexoelectric effect remains unclear. In this work, based on the conventional beam theory, equations of motion considering dynamic flexoelectric effect are investigated. Consequently, the free vibration of the simply supported beam is studied in order to examine the influence of the dynamic flexoelectricity on natural frequency. From the numerical studies, it is found that dynamic flexoelectric effect is more influential on thick beam model and higher vibration modes. In addition, the results show that the relation between the static and dynamic flexoelectric coefficients can also alter the free vibration response.
•We investigate the role of dynamic flexoelectric coefficient in piezoelectric nanostructures.•The energy associated with flexodynamic tensor is included into the kinetic energy.•Based on beam theory, the equation of motion for Timoshenko and Euler-Bernoulli beam models is derived.•Free vibration analysis shows that the dynamic flexoelectricity is more influential on the thick beam and higher vibration modes.
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