Abstract When manufacturing flexible devices, it is quite common that localized necking appears due to the low ductility of the metal sheets used. To delay the inception of such localized necking, several industrial companies have proposed a promising technical solution based on the bonding of elastomer substrates to the metal sheets used in the manufacturing processes. In this context, the comprehensive numerical understanding of the impact of such substrate coating on the improvement of the ductility of elastomer-supported metal layers still remains a challenging goal. To achieve this goal, the bifurcation approach as well as the Marciniak and Kuczynski model are used to predict the occurrence of localized necking. The mechanical behavior of the metal layer is modeled by a non-associated anisotropic plasticity model. The adoption of non-associated plastic flow rule allows separating the description of the plastic potential from that of the yield function, which is essential to accurately model strong plastic anisotropy characterizing cold-rolled sheets. As to the elastomer substrate, its mechanical behavior is described by a neo-Hookean law. The paper presents a variety of numerical results relating to the prediction of plastic strain localization in both freestanding and elastomer-coated metal layers. The effects of the non-associativity of the plastic flow rule for the metal layer and the addition of an elastomer substrate on the predictions of localized necking are especially underlined. It is shown that the ductility limits predicted by the non-associated elasto-plastic model are lower than their counterparts determined by an associated plasticity model. It is also proven that adhering an elastomer layer to the metal layer can substantially delay the initiation of plastic strain localization.

中文翻译：

---

使用非关联塑性流动规则预测衬底支撑金属层的成形性

摘要 在制造柔性设备时，由于所使用的金属板的延展性低而出现局部缩颈是很常见的。为了推迟这种局部颈缩的出现，几家工业公司提出了一种基于弹性体基材与制造过程中使用的金属板的粘合的有前途的技术解决方案。在这种情况下，对这种基材涂层对提高弹性体支撑金属层延展性的影响的全面数值理解仍然是一个具有挑战性的目标。为了实现这一目标，分岔方法以及 Marciniak 和 Kuczynski 模型用于预测局部颈缩的发生。金属层的机械行为由非关联的各向异性塑性模型建模。采用非关联塑性流动规则可以将塑性势的描述与屈服函数的描述分开，这对于准确模拟表征冷轧板的强塑性各向异性至关重要。对于弹性体基材，其力学行为由新胡克定律描述。本文介绍了与预测独立式和弹性体涂层金属层中塑性应变局部化相关的各种数值结果。特别强调了金属层塑性流动规则的非结合性和弹性体基材的添加对局部颈缩预测的影响。结果表明，非关联弹塑性模型预测的延展性极限低于关联塑性模型确定的对应物。