Abstract

The  main objective of the research presented in this work is the formulation, analysis and implementation of efficient numerical algorithms for dissipate dynamical systems in solids mechanics. The dissipate structure exhibited by the systems considered is described in detail for the coupled thermoviscoplastic problem including phase change phenomena and extended to the frictional thermomechanical contact problem.

Abstract

In this work shall be presented a stabilized finite element method to deal with incompressibility in solid mechanics. A mixed formulation involving pressure and displacement fields is used and a continuous linear interpolation is considered for both fields. To overcome the Ladyzhenskaya-Babuska-Brezzi condition, a stabilization technique based on the orthogonal sub-grid scale method is introduced. The main advantage of the method is the possibility of using linear triangular finite elements, which are easy to generate for real industrial applications. Results are compared with several improved formulations, as the enhanced assumed strain method (EAS) and the Q1P0-formulation, in nearly incompressible problems and in the context of linear elasticity and J2-plasticity.

Abstract

El objetivo de este trabajo es desarrollar e implementar una formulación específica, robusta y precisa de elementos, capaz de abordar el problema de incompresibilidad en mecánica de sólidos, con modelos constitutivos elásticos y elasto-plásticos J2, tanto en el contexto de las deformaciones infinitesimales como de las grandes deformaciones.

Abstract

This paper deals with the numerical simulation of Friction Stir Welding (FSW) processes. FSW techniques are used in many industrial applications and particularly in the aeronautic and aerospace industries, where the quality of the joining is of essential importance. The analysis is focused either at global level, considering the full component to be jointed, or locally, studying more in detail the heat affected zone (HAZ).The analysis at global (structural component) level is performed defining the problem in the Lagrangian setting while, at local level, an apropos kinematic framework which makes use of an efficient combination of Lagrangian (pin), Eulerian (metal sheet) and ALE (stirring zone) descriptions for the different computational sub-domains is introduced for the numerical modeling. As a result, the analysis can deal with complex (non-cylindrical) pin-shapes and the extremely large deformation of the material at the HAZ without requiring any remeshing or remapping tools.A fully coupled thermo-mechanical framework is proposed for the computational modeling of the FSW processes proposed both at local and global level. A staggered algorithm based on an isothermal fractional step method is introduced.To account for the isochoric behavior of the material when the temperature range is close to the melting point or due to the predominant deviatoric deformations induced by the visco-plastic response, a mixed finite element technology is introduced. The Variational Multi Scale (VMS) method is used to circumvent the LBB stability condition allowing the use of linear/linear P1/P1 interpolations for displacement (or velocity, ALE/Eulerian formulation) and pressure fields, respectively. The same stabilization strategy is adopted to tackle the instabilities of the temperature field, inherent characteristic of convective dominated problems (thermal analysis in ALE/Eulerian kinematic framework).At global level, the material behavior is characterized by a thermo-elasto- viscoplastic constitutive model. The analysis at local level is characterized by a rigid thermo-visco-plastic constitutive model. Different thermally coupled (non-Newtonian) fluid-like models as Norton-Hoff, Carreau or Sheppard-Wright, among others are tested.To better understand the material flow pattern in the stirring zone, a (Lagrangian based) particle tracing is carried out while post-processing FSW results.A coupling strategy between the analysis of the process zone nearby the pin-tool (local level analysis) and the simulation carried out for the entire structure to be welded (global level analysis) is implemented to accurately predict the temperature histories and, thereby, the residual stresses in FSW.

Abstract

This paper deals with the computational modeling and numerical simulation of the material flow around the probe tool in a Friction Stir Welding (FSW) process. Within the paradigmatic framework of the multiscale stabilization methods, suitable subgrid scale stabilized coupled thermomechanical formulations have been developed using an Eulerian description. Norton-Hoff and Sheppard-Wright thermo-rigid-viscoplastic constitutive material models have been considered. Constitutive equations for the subgrid scale models have been proposed and an approximation of the subgrid scale variables has been given. In particular Algebraic Subgrid Scale (ASGS) and Orthogonal Subgrid Scale (OSGS) methods for P1/P1/P1 linear elements have been considered. Furthermore, it has been shown that well known classical stabilized formulations, such as the Galerkin Least-Squares (GLS) or Streamline Upwind/Petrov-Galerkin (SUPG) methods, can be recovered as particular cases of the multiscale stabilization framework considered. Within the framework of a product formula algorithm, the resulting algebraic system of equations has been solved using a staggered procedure, in which a mechanical problem, defined by the plastic strain rate incompressibility equation and the quasi-static linear momentum balance equation, is solved at a constant temperature and a thermal problem, defined by the energy balance equation, is solved keeping constant the mechanical variables. The computational model has been implemented in the in-house developed FE software COMET. An assessment of the influence of the thermal deformation in the formulation has been carried out. Results obtained show that the influence of the thermal deformation is very small and can be neglected, getting a fully incompressible formulation. Finally, the computational model implemented in COMET has been validated through a number of examples, including a 3D numerical simulation of a FSW process. Numerical results obtained have been compared with experimental results available in the literature. A good agreement on the temperature distribution has been obtained and predicted peak temperatures compare well, both in value and position, with the experimental results available.

Abstract

The use of stabilization methods is becoming an increasingly well-accepted technique due to their success in dealing with numerous numerical pathologies that arise in a variety of applications in computational mechanics. In this monograph a multiscale finite element method technique to deal with pressure stabilization of nearly incompressibility problems in nonlinear solid mechanics at small and finite deformations J2 plasticity is presented. A mixed formulation involving pressure and displacement fields is used as starting point. Within the finite element discretization setting, continuous linear interpolation for both fields is considered. To overcome the Babuˇska-Brezzi stability condition, a multiscale stabilization method based on the Orthogonal Subgrid Scale (OSGS) technique is introduced. Suitable nonlinear expression of the stabilization parameters are proposed. The main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements, which are easy to generate and, therefore, very convenient for practical industrial applications. Numerical results obtained using the OSGS stabilization technique are compared with results provided by the P1 standard Galerkin displacements linear triangular/tehrahedral element, P1/P1 standard mixed linear displacements/ linear pressure triangular/tetrahedral element and Q1/P0 mixed bilinear/ trilinear displacements/constant pressure quadrilateral/hexahedral element for 2D/3D nearly incompressible problems in the context of nonlinear small and finite deformation J2 plasticity models.

Abstract

This work describes a novel formulation for the solution of problems involving shear band localization using a local isotropic J2 continuum damage model and mixed linear simplex (triangles and tetrahedral). A simple isotropic local J2 damage constitutive model is considered, either with linear or exponential softening.