A novel smooth discretization approach for elasto-plastic contact of bulky and thin structures

该项目的目的是介绍一种新的离散化方法，接触的庞大和薄壁结构，表现出明显的几何和材料的非线性。由此产生的光滑接触的方法将超越传统的平滑程序方面的一个健全的数学基础，但将在同一时间保留的低阶有限元离散化的简单性，在大部分的计算域。体积和接触面离散严格分离，但通过变分一致的耦合算子的基础上通用的双正交拉格朗日乘子基地互连。这种新的方法承诺提供最大的灵活性方面的光滑表面离散化（例如使用高阶FEM、Hermite插值、样条或NURBS）和完全独立的体积离散化（例如使用低阶非协调FEM、EAS或F-Bar技术）。此外，基于所谓的非线性互补函数和半线性互补函数的接触和摩擦以及有限应变塑性的综合处理，将开发光滑牛顿方法，与传统的径向返回映射方案相比，该方法可能提供上级鲁棒性。这两个建议的主题本身，特别是他们的组合数值处理，预计将允许在非线性固体和结构力学的复杂问题的情况下，真正可靠的模拟技术取得重大进展。

The project aims at introducing a new discretization method for contact of bulky and thin-walled structures exhibiting pronounced geometrical and material nonlinearities. The resulting smooth contact approach will go beyond traditional smoothing procedures with regard to a sound mathematical basis, but will at the same time retain the simplicity of low-order finite element discretizations in the bulk of the computational domain. Volume and contact surface discretizations are strictly separated, but interconnected via variationally consistent coupling operators based on generic biorthogonal Lagrange multiplier bases. This new approach promises to offer maximal flexibility with regard to a smooth surface discretization (e.g. using higher-order FEM, Hermite interpolation, splines or NURBS) and a completely independent volume discretization (e.g. using low-order non-conforming FEM, EAS or F-Bar techniques).In addition, an integrated treatment of contact and friction as well as finite strain plasticity based on so-called nonlinear complementarity functions and semi-smooth Newton methods will be developed, which possibly offers a superior robustness as compared with traditional radial return mapping schemes. Both proposed topics on their own, and especially their combined numerical treatment, are anticipated to allow for significant progress towards truly reliable simulation techniques for complex problem scenarios in nonlinear solid and structural mechanics.