This paper presents a methodology where a macroscopic linear material response incorporates microscopic variations, such as transient interactions and micro-inertia effects. This is achieved by implementing the temporal coupling between macro and microstructures, along with the spatial coupling, within a dynamic computational homogenisation framework. In the context of dynamic multiscale modelling, the temporal coupling method offers significant advantages by effectively reducing deviations emerging from micro-inertia effects and transient phenomena. The effectiveness of the developed procedure is validated by a comparison of the macroscopic results with the solutions of direct numerical simulation for a one-dimensional periodic laminate bar with different contrast levels. The homogenised results obtained using the developed procedure indicate that a better prediction of the macroscopic requires a larger Representative Volume Element (RVE) which improves the estimation of multiscale strain energy and a larger time window which improves the estimation of multiscale kinetic energy. The simultaneous increase in the RVE size and the time averaging window yields the best results in predicting the macroscopic response.

本文提出了一种方法，其中宏观线性材料响应包含微观变化，例如瞬态相互作用和微惯性效应。这是通过在动态计算均质化框架内实现宏观和微观结构之间的时间耦合以及空间耦合来实现的。在动态多尺度建模的背景下，时间耦合方法通过有效减少微惯性效应和瞬态现象产生的偏差而具有显着的优势。通过将宏观结果与具有不同对比度的一维周期性层压板的直接数值模拟的解决方案进行比较，验证了所开发程序的有效性。使用开发的程序获得的均质化结果表明，更好的宏观预测需要更大的代表体积元（RVE）和更大的时间窗，以改善多尺度应变能的估计，从而改善多尺度动能的估计。 RVE 大小和时间平均窗口的同时增加在预测宏观响应方面产生了最佳结果。