A micromechanical constitutive model for ductile fracture: numerical treatment and calibration strategy

This contribution describes the numerical treatment and calibration strategy for a new micromechanical damage model, which employs two internal damage variables. The new micromechanical model is based on Gurson's theory incorporating the void volume fraction as one damage parameter and a shear mechanism, which was formulated considering geometrical and phenomenological aspects, as the second internal damage variable. The first and the second damage variables are coupled in the constitutive formulation in order to affect the hydrostatic stress and deviatoric stress contributions, respectively. Both internal damage variables are independent and, as a consequence, they also require independent nucleation mechanisms for each one in order to trigger the growth contribution. These mechanisms require the determination of material parameters that are obtained through two calibration points: one for high and the other for low stress triaxiality. This is in contrast to other damage models that typically require one calibration point. In the first part of this paper, theoretical aspects of the constitutive formulation are presented and discussed. Then, an implicit numerical integration algorithm is derived, based on the operator split methodology, together with a methodology to perform the calibration of all material parameters. In order to assess the performance of the new model, the “butterfly” specimen was used and the 1045 steel was employed under a wide range of stress triaxiality. The results obtained from the numerical simulations are presented such as: the evolution of both damage parameters, the evolution of the equivalent plastic strain, the reaction versus displacement curve and the contour of the effective damage parameter. From the comparison of the numerical results with experimental evidence, it will be highlighted that the present formulation is able to predict accurately the location of fracture onset and the level of the associated equivalent plastic strain at fracture

A Study For Efficiently Solving Optimisation Problems With An Increasing Number Of Design Variables

Coupling optimisation algorithms to Finite Element Methods (FEM) is a very promising way to achieve optimal metal forming processes. However, many optimisation algorithms exist and it is not clear which of these algorithms to use. This paper investigates the sensitivity of a Sequential Approximate Optimisation algorithm (SAO) proposed in [1-4] to an increasing number of design variables and compares it with two other algorithms: an Evolutionary Strategy (ES) and an Evolutionary version of the SAO (ESAO). In addition, it observes the influence of different Designs Of Experiments used with the SAO. It is concluded that the SAO is very capable and efficient and its combination with an ES is not beneficial. Moreover, the use of SAO with Fractional Factorial Design is the most efficient method, rather than Full Factorial Design as proposed in [1-4]

A dual mortar-based contact formulation applied to finite plastic strains – Complas XI

Significant progress has been made on computational contact mechanics over the past decade. Many of the drawbacks that were inherent to the standard node-tosegment element strategy, such as locking/over-constraint and non-physical jumps in the contact forces due to the discontinuity of the contact surface, have been systematically overcome. In particular, the formulation of the mortar finite element method [1], which has allowed the establishment of efficient segment-to-segment approaches [2, 3] when applied to the discretization of a contact surface, has promoted significant advance. However, the regularization schemes used with the mortar element (e.g. the Penalty method, the Lagrange multipliers method or combination of them) still cause unwanted side-effects such as: ill-conditioning, additional equations in the global system or a significant increase in the computational time for solution. In order to circumvent these shortcomings, Wohlmuth [4] has proposed the use of dual spaces for the Lagrange multipliers allowing the local elimination of the contact constraints. As a consequence, the Lagrangian multipliers can be conveniently condensed and no additional equations are needed for the solution of the global system of equations. H´’ueber et al. [5], Hartmann et al. [6], Popp et al.[7] and Gitterle et al [8]. have later combined this methodology with an active set strategy and obtained improved results in terms of convergence rate. Despite the successful application of the dual mortar formulation to contact problems, the advances presented in the literature have, to the authors knowledge, only been employed for the simulation of elastic problems. However, contact between bodies has a strong influence in many applications (e.g., metal forming and cutting) where finite inelastic strains play a crucial role. Therefore, the main goal of the present work is both the application and assessment of the dual mortar method in problems where contact takes place coupled with finite plastic strains

A dual mortar-based contact formulation applied to finite plastic strains – Complas XI

Significant progress has been made on computational contact mechanics over the past decade. Many of the drawbacks that were inherent to the standard node-tosegment element strategy, such as locking/over-constraint and non-physical jumps in the contact forces due to the discontinuity of the contact surface, have been systematically overcome. In particular, the formulation of the mortar finite element method [1], which has allowed the establishment of efficient segment-to-segment approaches [2, 3] when applied to the discretization of a contact surface, has promoted significant advance. However, the regularization schemes used with the mortar element (e.g. the Penalty method, the Lagrange multipliers method or combination of them) still cause unwanted side-effects such as: ill-conditioning, additional equations in the global system or a significant increase in the computational time for solution. In order to circumvent these shortcomings, Wohlmuth [4] has proposed the use of dual spaces for the Lagrange multipliers allowing the local elimination of the contact constraints. As a consequence, the Lagrangian multipliers can be conveniently condensed and no additional equations are needed for the solution of the global system of equations. H´’ueber et al. [5], Hartmann et al. [6], Popp et al.[7] and Gitterle et al [8]. have later combined this methodology with an active set strategy and obtained improved results in terms of convergence rate. Despite the successful application of the dual mortar formulation to contact problems, the advances presented in the literature have, to the authors knowledge, only been employed for the simulation of elastic problems. However, contact between bodies has a strong influence in many applications (e.g., metal forming and cutting) where finite inelastic strains play a crucial role. Therefore, the main goal of the present work is both the application and assessment of the dual mortar method in problems where contact takes place coupled with finite plastic strains

A micromechanical constitutive model for ductile fracture: numerical treatment and calibration strategy

This contribution describes the numerical treatment and calibration strategy for a new micromechanical damage model, which employs two internal damage variables. The new micromechanical model is based on Gurson's theory incorporating the void volume fraction as one damage parameter and a shear mechanism, which was formulated considering geometrical and phenomenological aspects, as the second internal damage variable. The first and the second damage variables are coupled in the constitutive formulation in order to affect the hydrostatic stress and deviatoric stress contributions, respectively. Both internal damage variables are independent and, as a consequence, they also require independent nucleation mechanisms for each one in order to trigger the growth contribution. These mechanisms require the determination of material parameters that are obtained through two calibration points: one for high and the other for low stress triaxiality. This is in contrast to other damage models that typically require one calibration point. In the first part of this paper, theoretical aspects of the constitutive formulation are presented and discussed. Then, an implicit numerical integration algorithm is derived, based on the operator split methodology, together with a methodology to perform the calibration of all material parameters. In order to assess the performance of the new model, the “butterfly” specimen was used and the 1045 steel was employed under a wide range of stress triaxiality. The results obtained from the numerical simulations are presented such as: the evolution of both damage parameters, the evolution of the equivalent plastic strain, the reaction versus displacement curve and the contour of the effective damage parameter. From the comparison of the numerical results with experimental evidence, it will be highlighted that the present formulation is able to predict accurately the location of fracture onset and the level of the associated equivalent plastic strain at fracture

Towards efficient modelling of macro and micro tool deformations in sheet metal forming

During forming, the deep drawing press and tools undergo large loads, and even though they are extremely sturdy structures, deformations occur. This causes changes in the geometry of the tool surface and the gap width between the tools. The deep drawing process can be very sensitive to these deformations. Tool and press deformations can be split into two categories. The deflection of the press bed-plate or slide and global deformation in the deep drawing tools are referred to as macro press deformation. Micro-deformation occurs directly at the surfaces of the forming tools and is one or two orders lower in magnitude. The goal is to include tool deformation in a FE forming simulation. This is not principally problematic, however, the FE meshes become very large, causing an extremely large increase in numerical effort. In this paper, various methods are discussed to include tool elasticity phenomena with acceptable cost. For macro deformation, modal methods or ’deformable rigid bodies’ provide interesting possibilities. Static condensation is also a well known method to reduce the number of DOFs, however the increasing bandwidth of the stiffness matrix limits this method severely, and decreased calculation times are not expected. At the moment, modeling Micro-deformation remains unfeasible. Theoretically, it can be taken into account, but the results may not be reliable due to the limited size of the tool meshes and due to approximations in the contact algorithms