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Simulation of the bending process of hardening metallic sheets using damage model. Part I: Theoretical development and numerical implementation

机译：使用损伤模型模拟硬化金属板的弯曲过程。第一部分：理论发展与数值实现

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This paper deals with the pure bending of thin and thick metallic sheets under plane strain condition. Its main objective is to construct an efficient, robust, incremental numerical tool that can be used to simulate the bending process and predict the sheets' bendability. In this investigation, the material constitutive law describing the mechanical behavior of the sheet is defined by an extended Gurson model. This model generalizes Gurson's original one to account for both plastic anisotropy and mixed (isotropic and kinematic) hardening of the matrix. In this model, only the growth phase of voids was considered (without taking into account nucleation). Here, the extended model was coupled with the kinematics of the pure bending process and with the equilibrium equations, and then implemented in an incremental numerical tool in order to predict the bendability of the sheets studied. This bendability was then verified using two different criteria. Part I of this paper focuses on the constitutive law, fulfillment of the force equilibrium, the thickness evolution and the shift of the neutral fiber, together with a comparison and discussion of the choices made by other authors regarding these parameters. The validation of the model developed in this paper will be carried out in Part II through simulations of the pure bending process.
机译：本文研究了平面应变条件下薄金属板和厚金属板的纯弯曲。它的主要目的是构建一个有效，健壮的增量数值工具，该工具可用于模拟弯曲过程并预测板材的可弯曲性。在这项研究中，通过扩展的Gurson模型定义了描述板材机械性能的材料本构定律。该模型概括了Gurson的原始模型，以说明塑性各向异性和基体的混合（各向同性和运动学）硬化。在此模型中，仅考虑空隙的生长阶段（不考虑成核作用）。在此，扩展模型与纯弯曲过程的运动学和平衡方程式耦合，然后在增量数值工具中实施，以预测所研究板材的可弯曲性。然后使用两个不同的标准验证了该可弯曲性。本文的第一部分着重于本构定律，力平衡的实现，中性纤维的厚度演变和位移，以及其他作者针对这些参数所作选择的比较和讨论。本文开发的模型的验证将在第二部分中通过模拟纯弯曲过程进行。

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