Guillermo J. Creus

Simulation of 3D metal-forming using an arbitrary Lagrangian–Eulerian finite element method

Abstract The arbitrary Lagrangian–Eulerian (ALE) formulation is an efficient alternative to deal with the finite element mesh distortion that occurs in an updated Lagrangian (UL) formulation when simulating metal-forming processes. Uncoupling mesh movement from material movement, the ALE operator can be split into an UL step followed by an Eulerian step. Deformation due to loading is calculated in the UL step (without convective terms) and the mesh movement (relative to the material) is imposed by nodal relocation techniques in the Eulerian step. In this paper, the authors propose two relocation techniques, similar to an r-refinement, that can move internal and external nodes (including non-planar surface nodes) of eight-node hexahedral elements of structured meshes, while keeping the body volume approximately constant. In this manner, an improved mesh is obtained. Data transfer between the UL mesh and the relocated mesh is performed by using either an expansion of stresses in a Taylor’s series or a new search algorithm that avoids iterative solutions. Two examples, one static and one dynamic, are presented and their results compared with known solutions.

Geometrically nonlinear finite element analysis of viscoelastic composite materials under mechanical and hygrothermal loads

Abstract The time-dependent response of polymeric matrix laminated composites subject to mechanical and hygrothermal loads is considered. The analysis is based on an incremental total Lagrangian formulation which allows the treatment of finite displacements and small strains. A three-dimensional degenerated finite element model is employed to analyze the plates and shells. The material is considered as linear viscoelastic and hygrothermal-rheologially simple. Numerical examples for isotropic and graphite-epoxy laminated plates and shells are presented.

FINITE ELEMENT ANALYSIS OF THREE-DIMENSIONAL CONTACT AND IMPACT IN LARGE DEFORMATION PROBLEMS

Abstract An algorithm that models three-dimensional contact with friction, including cases where large deformations occur is proposed. The algorithm is an extension to three-dimensions of an algorithm for contact previously proposed by Ponthot and Hogge [1] . The present algorithm can be used in implicit or explicit codes, when contact between a rigid and a deformable body or among deformable bodies (multibody contact) is to be determined. The penalty method is used as the contact–friction formulation. Constitutive relations for contact–friction and integration of these relations in a corotational reference system are detailed. In order to provide a good convergence rate, the contact–friction stiffness matrices used are consistent with the time integration process. A simple and fully explicit form was obtained for these matrices. For contact problems involving rigid and deformable bodies, interpenetrations are detected using an iterative procedure. For frictionless multibody contact, a new element that simplifies the gap calculation, eliminating iterative procedures, is proposed. Comparison with benchmark results and the solution of practical examples demonstrate the effectiveness of the algorithm.

Viscoelastic failure analysis of composite plates and shells

The present paper describes a numerical method for modeling the failure behavior of composite laminates in the presence of large displacements and creep. Geometrical nonlinear finite elements are used for the discretization. The modeling of material behavior includes thermal, hygroscopic and viscoelastic effects, using an efficient state variable representation. Incremental damage is determined and used to calculate a modified stiffness matrix. Thus, the procedure can be used to analyze, for example, buckling, creep buckling and creep buckling including damage. A detailed formulation, computational procedures and examples to check the accuracy of the code are presented.

Direct evaluation of singular integrals in boundary element analysis of thick plates

Abstract This work presents the derivation of the asymptotic expansions for two dimensional elasticity and plate bending problems fundamental solutions, applied to the direct evaluation of BEM singular integrals. Interesting conclusions arise from the resulting analytical expressions, regarding the actual order of singularity of the kernel functions. The expansions were tested for a number of plate bending benchmarks, showing good agreement to analytical solutions for thin and thick plates. The convergence behavior for constant, linear and quadratic elements is analyzed and compared with other integration techniques.

Modeling of the Mechanical Behavior of Metallic Foams: Damage Effects at Finite Strains

This work applies Gurson model to the simulation of damage in metallic foams. In the first part, two approaches for Gurson model application, i.e., the hypoelastic and the hyperelastic formulations are compared. Then, a study on the minimum number of cells to be employed in an experimental test to adequately simulate the behavior of the cellular material in tension is presented. Finally, considering that compression is the dominant loading in impact situations, a simulation including damage effects of a compression test on a cellular metal sample is shown and compared with experimental results.

Nonlinear viscoelastic analysis of thin-walled beams in composite material

Abstract Laminated composites of polymeric matrix show anisotropic viscoelastic behaviour, enhanced by temperature and humidity effects. The consideration of anisotropy and viscoelasticity are important for the determination of deformations and, as a consequence, of deformation-related phenomena, as elastic and creep buckling. This paper studies the behaviour of thin-walled beams of composite material under flexure and buckling, taking account of creep effects. The analysis uses a nonlinear viscoelastic finite element code with shell elements, whose basic formulation is given. The use of shell elements allows a better representation of constitutive properties and boundary conditions. Comparison with available analytical results is made for several cases like flexure of an I beam, buckling of beam columns and lateral buckling of this beams. The results show good correlation.

Rheological Models: Integral and Differential Representations

Viscoelastic relations may be expressed in both integral and differential forms. Integral forms are very general and appropriate for theoretical work. Differential forms are related to rheological models that provide a more direct physical interpretation of viscoelastic behavior. In this chapter we describe the most usual rheological models, deduce their differential equations and, by solving them, we find the corresponding integral representations. These relations will be set in a more computational friendly form in Chap. 3 and extended to three-dimensional situations in Chap. 4 and then used in analytical and computational solutions.

Solutions with Abaqus

To help the reader to practice with a professional computer code, we use Abaqus to solve a few problems in viscoelasticity (small and large strains). First we relate Abaqus procedure to the general formulation given in this book and then we provide detailed instructions to run the code.

Aging Damage Effects on Composite Structures

High performance composite materials have many well‐known structural advantages. On the other hand, questions about durability and aging are still a subject of discussion and much needed research. As a consequence, in the last few years there have been available a growing amount of information on composites aging considering effects as temperature, oxidation, UV radiation, permanent loading etc. Much of this research is performed at the materials level, by materials scientists and it is not directly applicable to the design stage. In this paper, we use an analytical‐numerical framework for the compilation, interpretation and application of experimental data to actual engineering analysis and design. The formulation includes elastic anisotropic relations; aging viscoelastic anisotropic constitutive equations in terms of state variables; age‐adjusted failure and degradation criteria; all in a setting of large displacements with small strains. These equations are set in a form adequate for numerical analysis...