Hardening and non-associated flow NURBS plasticity.

In numerical analysis the failure of engineering materials is controlled through specifying yield envelopes (or surfaces) that bound the allowable stress in the material. Simple examples include the prismatic von Mises (circle) and Tresca (hexagon) yield surfaces. However, each surface is distinct and requires a specific equation describing the shape of the surface to be formulated in each case. These equations impact on the numerical implementation (specifically relating to stress integration) of the models and therefore a separate algorithm must be constructed for each model. Recently a framework was proposed that allows any isotropic yield surface to be represented by a NURBS surface and the constitutive model formulated using the name numerical algorithm. This paper presents, for the first time, an extension to this framework to allow both hardening (expansion/contraction of the surfaces) and a non-associated plastic flow rule. As with previous work on NURBS plasticity, the constitutive framework is combined with an implicit backward-Euler-type stress integration algorithm. The numerical performance of the algorithm is demonstrated using both material point investigations and boundary value simulations

Constitutive modelling of Sandvik 1RK91

A physically based constitutive equation is being developed for the maraging\ud stainless steel Sandvik 1RK91. The steel is used to make precision parts. These parts are formed through multistage forming operations and heat treatments from cold rolled and annealed sheets. The specific alloy is designed to be thermodynamically unstable, so that deformation even at room temperatures can bring about a change in the phase of face centred cubic austenite to either hexagonal closed packed martensite and/or, body centred cubic martensite. This solid state phase change is a function of the strain path, strain, strain rate and temperature. Thus, the fraction of the new phase formed depends on the state of stress at a given location in the part being formed. Therefore a set of experiments is being conducted in order to quantify the stress-strain behavior of this steel under various stress states, strain, strain rate as well as temperature. A magnetic sensor records the fraction of ferromagnetic martensite formed from paramagnetic austenite. A thermocouple as well as an infra red thermometer is used to log the change in temperature of the steel during a mechanical test. The force-displacement data are converted to stress-strain data after correcting for the changes in strain rate and temperature. These data are then cast into a general form of constitutive equation and the transformation equations are derived from Olson-Cohen type functions

Characterisation and modelling of the plastic material behaviour and its application in sheet metal forming simulation

The application of simulation models in sheet metal forming in automotive industry has proven to be beneficial to reduce tool costs in the designing stage and for optimising current processes. Moreover, it is a promising tool for a material supplier to optimise material choice and development for both its final application and its forming capacity. The present practice requires a high predictive value of these simulations. The material models in these simulation models need to be developed sufficiently to meet the requirement of the predictions. For the determination of parameters for the material models, mechanical tests at different strain paths are necessary 1. Usually, the material models implemented in the simulation models are not able to describe the plastic material behaviour during monotonic strain paths sufficiently accurate 2. This is true for the strain hardening model, the influence of strain rate and the description of the yield locus in these models. A first stage is to implement the improved material models which describe this single strain path behaviour in a better way. In this work, different yield criteria, a hardening model and their comparison to experiments are described extensively. The improved material model has been validated initially on forming limit curves which are determined experimentally with Nakazima strips. These results will be compared with predictions using Marciniak-Kuczinsky-analysis with both the new material model and the conventional material model. Finally, the validation on real pressed products will be shown by comparing simulation results using different material models with the experimental data. The next challenge is the description of the material after a change of strain path. Experimental evidence given here shows that this behaviour cannot be treated using the classical approach of an equivalent strain as the only history variable

A generic contact detection framework for cylindrical particles in discrete element modelling

This paper aims to develop a generic framework for detecting contact between cylindrical particles in discrete element modelling based on a full exploitation of the axi-symmetrical property of cylinders. The main contributions include: (1) A four-parameter based local representative system is derived to describe the spatial relationship between two cylinders so that the 3D cylinder-cylinder intersection problem can be reduced to a series of 2D circle-ellipse intersections, which considerably simplifies the contact detection procedure. (2) A two-stage contact detection scheme is proposed in which no-overlap contact pairs are identified in the first overlap check stage, and then the actual overlap region is determined in the second resolution stage and represented by two schemes: the layered representation which is generic, and the edge representation which is numerically more efficient but less accurate. (3) The most significant contribution is the development of two theorems that establish a fundamental relationship between the contact point and contact normal of two contacting cylinders, offering a simple approach to determining the normal direction based on the contact point and vice versa. These theorems are valid not only for cylinders, but also for any axi-symmetrical shapes and their combinations. Some numerical issues are discussed. Numerical examples are presented to illustrate the capability and applicability of the proposed methodologies

Enhanced approach to consistency in gradient-dependent plasticity

This note proposes a modification of gradient-dependent plasticity to improve convergence. In gradient-dependent plasticity, the consistency condition, which results in a differential equation with respect to the plastic multiplier, is solved simultaneously with the equilibrium equation. In each iteration, the consistency condition is not really satisfied and the stress is generally not on the yield surface; this results in poor convergence. A modification is proposed, in which gradient-dependent plasticity is recast into the classical plasticity framework and a strict stress mapping strategy is established. Instead of solving a differential equation simultaneously with the equilibrium equation, the plastic multiplier is solved by minimizing a functional separately. The consistency condition can be satisfied and the stress is mapped back to the yield surface

Conmutación temporal entre técnicas numéricas implícita y explícita para simulación de estructuras no lineales inestables

AbstractSimulation problems involving non-linear materials imply in numerous cases divergence of the implicit method which use return mapping algorithms for modelling of the nonlinear response. A switching implicit-explicit numerical technique in the context of Finite Element Methods is presented in this paper. Implicit/explicit mesh partitions are not considered whatsoever. Formulation for application to nonlinear hyperelastic materials and nonlinear elastic-plastic materials is provided. Furthermore, the response of the solid subjected to large deformations is presented and is embedded in the proposed technique. Numerical tests for nonlinear problems (geometric and/or material) showed the accurateness of the technique