Abstract A new multi-scale framework to numerically model the bridging effect in through-thickness reinforced (TTR) composite laminates with z-pins is presented. The framework first establishes a library of bridging maps, calculated by a micromechanical semi-analytical constitutive bridging model. For the macro-scale, a tri-linear cohesive law has been developed to model initiation and propagation of the interfacial damage in the presence of z-pins. The cohesive law takes into account the energy dissipated by delamination propagation through the matrix in the interlaminar region, plus the energy contributed by the z-pin bridging up to complete pull-out from the laminate or z-pin failure. The information regarding the failure mode and the consequent dissipated energy comes from the library of bridging maps. The tri-linear cohesive law has been implemented in a user material subroutine of a commercial finite element software. The framework has been validated against experimental data and an excellent correlation has been achieved.

中文翻译：

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用于模拟全厚度增强复合材料层压板分层的能量等效桥接图公式

摘要 提出了一种新的多尺度框架，用于对带 z 销的全厚度增强 (TTR) 复合材料层压板的桥接效应进行数值模拟。该框架首先建立了一个桥接图库，由微机械半解析本构桥接模型计算。对于宏观尺度，已经开发了三线性内聚定律来模拟在 z 销存在下界面损伤的引发和传播。内聚定律考虑了通过层间区域中通过基质的分层传播所耗散的能量，加上 z 引脚桥接以完全从层压板中拉出或 z 引脚失效所贡献的能量。有关故障模式和随之而来的耗散能量的信息来自桥接图库。三线性内聚定律已在商业有限元软件的用户材料子程序中实现。该框架已经根据实验数据进行了验证，并且已经实现了极好的相关性。