An extended formulation of the macro-element (ME) based models, representing for both adherends and adhesive along the entire overlap in only one four-node element, is presented. Compared to earlier modelling, continuum ME (CME) and discrete ME (DME) based models, the adherend parts are also modelled as plane continuum media, for which high order displacement fields are freely supposed. Both extended CME (ECME) and extended DME (EDME) based modelling can have their displacement field orders of each continuum layer be set individually, and can be enriched using springs for interfaces or boundary conditions modelling, allowing the stresses to vanish at the free edges. The methodology and formulation of the stiffness matrix for both the adherend without adhesive and the bonded overlap is presented. The assessment is performed for a single-lap joint geometry by comparison results from a plane strain finite element (FE) model with extended ME-based models. Good agreements are shown for both thin and thick adhesive case studies.

中文翻译：

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基于宏观单元建模的扩展公式 – 应用于单搭接接合接头


提出了基于宏观单元 （ME） 的模型的扩展公式，该模型仅代表一个四节点单元中整个重叠的粘附物和粘合剂。与早期建模、基于连续体 ME （CME） 和离散 ME （DME） 的模型相比，粘附部分也被建模为平面连续介质，可以自由假设高阶位移场。基于扩展 CME （ECME） 和扩展 DME （EDME） 的建模都可以单独设置每个连续层的位移场阶次，并且可以使用弹簧进行界面或边界条件建模，从而允许应力在自由边缘消失。介绍了无胶粘剂和粘合重叠的刚度矩阵的方法和公式。通过将平面应变有限元 （FE） 模型的结果与基于 ME 的扩展模型进行比较，对单搭接关节几何形状进行评估。薄胶粘剂和厚胶粘剂案例研究都显示出良好的一致性。