Non-linear numerical modeling is increasingly used for the simulation of complex processes such as forming or machining. The constitutive laws necessary for these simulations are therefore becoming more and more complex regarding the increasingly precise consideration of physical phenomena (plasticity, thermal dependence, damage ...) and their implementation in numerical codes requires the identification of many parameters. The use of these constitutive laws for dynamic or quasi-static applications requires the identification of these parameters under conditions close to those encountered during the real process, mainly in terms of deformation, strain rates, and temperatures. The availability of a constitutive law in the finite element codes does not guarantee the success of a study to be carried out if it does not comply with the model development criteria. This is because the models integrated in the numerical codes are not developed based on forms that are adjustable to any type of study. In this study, a new form of non-linear constitutive flow law based on the Modified Zerilli-Armstrong model, which can answer the above problem, has been developed to apply it to the numerical simulation of two different tests (a quasi-static compression test, the necking of a circular bar). This flow law is based on the modified Zerilli-Armstrong model, which, together with the new modified Johnson-Cook model, has been compared to appreciate the relevance of the proposal. For that, an implementation of this new law via the VUHARD subroutine into the Abaqus/Explicit finite element code was made to model the two tests. The comparison of the results obtained (from identification) by our proposed law with those obtained using the NMJC shows that this new law better approaches the experiments than the other one. This is also showed through the numerical results using the Abaqus software. It can be said that this way of formulating a flow law allows to highlight the great performance of the proposed approach. Although this law has been only used for quasi-static tests, we can say that it can also be used in dynamic tests.

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Tize Mha, P, Tongne, A, & Pantalé, O. (2022). A generalized non-linear flow law based on Modified Zerilli–Armstrong model and its implementation into Abaqus/Explicit FEM code.