J. M. A. César de Sá

A new volumetric and shear locking‐free 3D enhanced strain element

This paper focuses on the development of a new class of eight‐node solid finite elements, suitable for the treatment of volumetric and transverse shear locking problems. Doing so, the proposed elements can be used efficiently for 3D and thin shell applications. The starting point of the work relies on the analysis of the subspace of incompressible deformations associated with the standard (displacement‐based) fully integrated and reduced integrated hexahedral elements. Prediction capabilities for both formulations are defined related to nearly‐incompressible problems and an enhanced strain approach is developed to improve the performance of the earlier formulation in this case. With the insight into volumetric locking gained and benefiting from a recently proposed enhanced transverse shear strain procedure for shell applications, a new element conjugating both the capabilities of efficient solid and shell formulations is obtained. Numerical results attest the robustness and efficiency of the proposed approach, when compared to solid and shell elements well‐established in the literature.

New enhanced strain elements for incompressible problems

A new enhanced strain element, based on the definition of extra compatibles modes of deformation added to the standard four-node finite element, is initially presented. The element is built with the objective of addressing incompressible problems and avoiding locking effects. By analysing at the element level the deformation modes which form a basis for the incompressible subspace the extra modes of deformation are proposed in order to provide the maximum possible dimension to that subspace. Subsequently another new element with more degrees of freedom is formulated using a mixed method. This is done by including an extra field of variables related to the derivatives of the displacement field of the extra compatible modes defined previously. The performance of the elements proposed is assessed in linear and non-linear situations. Copyright ( 1999 John Wiley & Sons, Ltd.

Numerical modelling of ductile plastic damage in bulk metal forming

Abstract This work addresses the computational aspects of a model for rigid–plastic damage. The model is a modification of a previous established model formulated by Perzyna (Recent Advances in Applied Mechanics, Academic Press: New York, 1966, p. 243–377 (Chapter 9)) which is here extended to include isotropic damage. Such an extension is obtained by incorporating the constitutive equations introduced by Lemaitre (J. Eng. Mater. Technol. 107 (1985) 83; Comput. Meth. Appl. Mech. Eng. 51 (1985) 31; A Course on Damage Mechanics, Springer, Berlin, Heidelberg, New York, 1996) for ductile plastic damage into the original model. In its original version (J. Eng. Mater. Technol. 107 (1985) 83; Comput. Meth. Appl. Mech. Eng. 51 (1985) 31) this model does not distinguish tension and compression in the damage evolution law, so it was necessary to introduce a refinement proposed by Ladeveze (in: J.P. Boehler, (Ed.), Proceedings of CNRS International Colloquium 351 Villars-de-Lans, France (Failure Criteria of Structured Media, 1983, p. 355) and Lemaitre (A Course on Damage Mechanics, Springer, Berlin, Heidelberg, New York, 1996) which takes into account the partial crack closure effect with isotropic damage. The accuracy of the computational model, developed for the analysis of the material degradation in bulk metal forming processes, is shown through the discussion of the results of two examples, allowing to compare the simulation results with experimental and numerical results obtained by other authors.

A gradient model for finite strain elastoplasticity coupled with damage

This paper describes the formulation of an implicit gradient damage model for finite strain elastoplasticity problems including strain softening. The strain softening behavior is modeled through a variant of Lemaitres damage evolution law. The resulting constitutive equations are intimately coupled with the finite element formulation, in contrast with standard local material models. A 3D finite element including enhanced strains is used with this material model and coupling peculiarities are fully described. The proposed formulation results in an element which possesses spatial position variables, nonlocal damage variables and also enhanced strain variables. Emphasis is put on the exact consistent linearization of the arising discretized equations.A numerical set of examples comparing the results of local and the gradient formulations relative to the mesh size influence is presented and some examples comparing results from other authors are also presented, illustrating the capabilities of the present proposal.

A Ductile Damage Nonlocal Model of Integral-type at Finite Strains: Formulation and Numerical Issues

This contribution is devoted to the formulation and numerical implementation of a ductile damage constitutive model enriched with a thermodynamically consistent nonlocal theory of integral type. In order to describe ductile deformation, the model takes finite strains into account. To model elasticity, a Hencky-like hyperelastic free energy potential coupled with nonlocal damage is adopted. The thermodynamic consistency of the model is ensured by applying the first and second thermodynamical principles in the global form and the dissipation inequality can be re-written in a local form by incorporating a nonlocal residual that accounts for energy exchanges between material points of the nonlocal medium. The thermodynamically consistent nonlocal model is compared with its associated classical formulation (in which nonlocality is merely incorporated by averaging the damage variable without resorting to thermodynamic potentials) where the thermodynamical admissibility of the classical formulation is demonstrated. Within the computational scheme, the nonlocal constitutive initial boundary value problem is discretized over pseudo-time where it is shown that well established numerical integration strategies can be straightforwardly extended to the nonlocal integral formulation. A modified Newton-Raphson solution strategy is adopted to solve the nonlinear complementarity problem and its numerical implementation, regarding the proposed nonlocal constitutive model, is presented in detail. The results of two-dimensional finite element analyses show that the model is able to eliminate the pathological mesh dependence inherently present under the softening regime if the local theory is considered.

An efficient algorithm to estimate optimal preform die shape parameters in forging

An optimisation method for design of intermediate die shapes needed in some forging operations is presented. The basic problem consists of finding an optimal two‐step forging sequence by automatically designing the shape of the preforming tools. The optimisation problem is defined based on an inverse formulation. The objective function of the optimisation problem is a function describing the quality of the obtained part by measuring the die underfill. The finite element method is used to simulate the forging problem. The optimisation method is based on a modified sequential unconstrained minimisation technique and a gradient method. The sensitivity‐dependent algorithm requires computing the derivatives of the objective function with respect to the design variables defining the preform shapes. A direct differentiation method has been developed for this purpose. The optimisation scheme is demonstrated with two axisymmetric forging examples in which optimal preform dies are obtained.

Simulation model for hot and cold forging by mixed methods including adaptive mesh refinement

Uses a rigid viscoplastic formulation to simulate hot and cold forging processes. The finite element solution uses mixed methods in which the independent variables can be velocities, pressures and deviatoric stresses. Uses interface elements both in the mechanical and the thermal analysis, to take into account the effects of contact and friction, thermal conductivity of lubricants and heat generated by friction. The code developed includes an adaptive mesh refinement, triggered by an error estimator based on energy norms evaluated from nodal stress values, recovered from a local continuous polynomial expansion, and those given by the numerical solution. Assesses the code developed, using experimental results.

A comparison of shear mechanisms for the prediction of ductile failure under low stress triaxiality

Purpose – The purpose of this paper is to perform a numerical assessment of two recently proposed extensions of the Gurson‐Tveegard‐Needleman ductile damage constitutive model under low stress triaxiality.Design/methodology/approach – One of the most widely used ductile damage models is the so‐called Gurson‐Tveegard‐Needleman model, commonly known as GTN model. The GTN model has embedded into its damage formulation the effects of nucleation, growth and coalescence of micro‐voids. However, the GTN model does not include void distortion and inter‐void linking in the damage evolution. To overcome this limitation, some authors have proposed the introduction of different shear mechanisms based on micromechanical grounds or phenomenological assumptions. Two of these constitutive formulations are reviewed in this contribution, numerically implemented within a quasi‐static finite element framework and their results critically appraised.Findings – Through the analysis of the evolution of internal variables, such a...

Enhanced Assumed Strain Shell and Solid‐Shell Elements: Application in Sheet Metal Forming Processes

Reliable numerical analysis of sheet metal forming processes using commercial finite element programs involves a variety of fields within computational mechanics area. Material models, contact algorithms, robust and fast incremental and iterative solution techniques are among the key factors that a finite element package must rely upon. Nevertheless, the finite element formulation itself still represents a milestone of crucial importance in the overall quality of the final solution. As sheet metal forming processes present very strong test cases to the performance of finite elements, robust formulations are then desired. In this work, classes of finite elements involving only the Enhanced Assumed Strain (EAS) method are analyzed. Starting from an innovative approach to eliminate transverse shear locking in shell elements (S4E6P5 shell element) and going through a new approach for a volumetric and transverse shear locking‐free solid‐shell element with a low number of internal variables (HCiS12 solid‐shell ...

Analysis of reinforced concrete with external composite strengthening

A finite element model for the analysis of reinforced concrete with external composite materials strengthening is presented in this paper. The model is based on a concrete material model, external unidirectional composites, the Ahmad Shell element and geometric and material non-linearities. The first-order shear-deformation theory is used, in order to describe the deformation of the shell under the total lagrangian formulation. An example of a RC plate without and with external FRP reinforcement is presented and discussed.