Identification of nonlinear kinematic hardening parameters for sheet metal from biaxial loading tests

In this work an anisotropic material model at finite strains with nonlinear mixed (isotropic and kinematic) hardening is used for the identification of the hardening parameters of sheet steel. The algorithmic system is thereby reduced to a single equation return mapping. For the identification, a cruciform specimen is loaded biaxially in an alternating shear test to provoke the kinematic hardening behavior and prevent the sheet from buckling. The material parameters are found through an optimization strategy by comparing the deformation field from the experiment to that from a finite element (FE) simulation. The resulting cost function is minimized by means of a gradient-based method

Topology Optimization of Elasto-Plastic Structures in Contact

This paper is concerned with the analysis as well as the numerical solution of the structural optimization problem for bilateral frictional contact problem where the static elasto-plastic material model with linear kinematic hardening rather than elastic material model is assumed. The displacement and stress of the bodies in elasto-plastic contact with a given friction are governed by the system of the coupled variational inequalities. In these problems usually very high stress appear along the surfaces in contact. It leads to wear or fatigue of the contacting surfaces. Therefore the aim of the topological optimization is to find such distribution of the material filling the body in contact to minimize the contact stress. Using von Mises yield function as well as the regularization and penalization techniques the original system of variational inequalities is transformed into the system of coupled nonlinear equations. The derivative of the cost functional with respect to the perturbation of the domain occupied by the body in contact is calculated using the material derivative method. Finite element method is used as the discretization method. In the numerical computations generalized Newton method is used to solve this contact problem. The level set method is used to describe and govern the evolution of the domain shape in the design space where the direction of the evolution is determined based on the calculated shape derivative. The results of computation are provided and discussed

Identification of plastic constitutive parameters at large deformations from three dimensional displacement fields

The aim of this paper is to provide a general procedure to extract the constitutive parameters of a plasticity model starting from displacement measurements and using the Virtual Fields Method. This is a classical inverse problem which has been already investigated in the literature, however several new features are developed here. First of all the procedure applies to a general three-dimensional displacement field which leads to large plastic deformations, no assumptions are made such as plane stress or plane strain although only pressure-independent plasticity is considered. Moreover the equilibrium equation is written in terms of the deviatoric stress tensor that can be directly computed from the strain field without iterations. Thanks to this, the identification routine is much faster compared to other inverse methods such as finite element updating. The proposed method can be a valid tool to study complex phenomena which involve severe plastic deformation and where the state of stress is completely triaxial, e.g. strain localization or necking occurrence. The procedure has been validated using a three dimensional displacement field obtained from a simulated experiment. The main potentialities as well as a first sensitivity study on the influence of measurement errors are illustrated

Implementation on a nonlinear concrete cracking algorithm in NASTRAN

A computer code for the analysis of reinforced concrete structures was developed using NASTRAN as a basis. Nonlinear iteration procedures were developed for obtaining solutions with a wide variety of loading sequences. A direct access file system was used to save results at each load step to restart within the solution module for further analysis. A multi-nested looping capability was implemented to control the iterations and change the loads. The basis for the analysis is a set of mutli-layer plate elements which allow local definition of materials and cracking properties

Numerical thermo-elasto-plastic analysis of residual stresses on different scales during cooling of hot forming parts

In current research, more and more attention is paid to the understanding of residual stress states as well as the application of targeted residual stresses to extend e.g. life time or stiffness of a part. In course of that, the numerical simulation and analysis of the forming process of components, which goes along with the evolution of residual stresses, play an important role. In this contribution, we focus on the residual stresses arising from the austenite-to-martensite transformation at microscopic and mesoscopic level of a Cr-alloyed steel. A combination of a Multi-Phase-Field model and a two-scale Finite Element simulation is utilized for numerical analysis. A first microscopic simulation considers the lattice change, such that the results can be homogenized and applied on the mesoscale. Based on this result, a polycrystal consisting of a certain number of austenitic grains is built and the phase transformation from austenite to martensite is described with respect to the mesoscale. Afterwards, in a two-scale Finite Element simulation the plastic effects are considered and resulting residual stress states are computed

Fast Determination of Soil Behavior in the Capillary Zone Using Simple Laboratory Tests

INE/AUTC 13.1

Thermo-micro-mechanical simulation of bulk metal forming processes

The newly proposed microstructural constitutive model for polycrystal viscoplasticity in cold and warm regimes (Motaman and Prahl, 2019), is implemented as a microstructural solver via user-defined material subroutine in a finite element (FE) software. Addition of the microstructural solver to the default thermal and mechanical solvers of a standard FE package enabled coupled thermo-micro-mechanical or thermal-microstructural-mechanical (TMM) simulation of cold and warm bulk metal forming processes. The microstructural solver, which incrementally calculates the evolution of microstructural state variables (MSVs) and their correlation to the thermal and mechanical variables, is implemented based on the constitutive theory of isotropic hypoelasto-viscoplastic (HEVP) finite (large) strain/deformation. The numerical integration and algorithmic procedure of the FE implementation are explained in detail. Then, the viability of this approach is shown for (TMM-) FE simulation of an industrial multistep warm forging

Shape optimization for elasto-plastic deformation under shakedown conditions

AbstractAn integrated approach for all necessary variations within direct analysis, variational design sensitivity analysis and shakedown analysis based on Melan’s static shakedown theorem for linear unlimited kinematic hardening material behavior is formulated. Using an adequate formulation of the optimization problem of shakedown analysis the necessary variations of residuals, objectives and constraints can be derived easily. Subsequent discretizations w.r.t. displacements and geometry using e.g. isoparametric finite elements yield the well known ‘tangent stiffness matrix’ and ‘tangent sensitivity matrix’, as well as the corresponding matrices for the variation of the Lagrangian-functional which are discussed in detail. Remarks on the computer implementation and numerical examples show the efficiency of the proposed formulation. Important effects of shakedown conditions in shape optimization with elasto-plastic deformations are highlighted in a comparison with elastic and elasto-plastic material behavior and the necessity of applying shakedown conditions when optimizing structures with elasto-plastic deformations is concluded