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Finite elastoplastic deformation of membrane shells

机译：膜壳的有限弹塑性变形

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Under restriction of an isotropic elastic response of deformed lattice, develops a covariant theory of finite elastoplasticity in principal axes of a pair of deformation tensors. In material description, the tensor pair consists of the plastic deformation tensor and the total deformation Cauchy-Green tensor. Applies the proposed theory to elastoplastic membrane shells, whose references and current configurations can be arbitrary space-curved surfaces. Pressure-insensitive von Mises yield criterion with isotropic hardening and a quadratic form of the strain energy function given in terms of elastic principal stretches are considered as a model problem. Through an explicit enforcement of the plane stress condition we arrive at a reduced two-dimensional problem representation, which is set in the membrane tangent plane. Numerical implementation of the presented theory relies crucially on the operator split methodology to simplify the state update computation. Presents a set of numerical examples in order to illustrate the performance of the presented methodology and indicate possible applications in the area of sheet metal forming.
机译：在变形晶格的各向同性弹性响应的约束下，发展了一对变形张量主轴上有限弹塑性的协变理论。在材料描述中，张量对由塑性变形张量和总变形柯西-格林张量组成。将所提出的理论应用于弹塑性膜壳，其参考和当前配置可以是任意空间弯曲的表面。具有各向同性硬化的压敏冯·米塞斯屈服准则和根据弹性主拉伸给出的应变能函数的二次形式被视为模型问题。通过显式实施平面应力条件，我们得到了减少的二维问题表示形式，该二维表示形式设置在膜切线平面中。提出的理论的数值实现至关重要地依赖于运算符拆分方法来简化状态更新计算。提出了一组数值示例，以说明所提出方法的性能并指出在钣金成形领域的可能应用。

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