Abstract Functional Graded Materials are widely developed in the past decades and graded foams are introduced recently because such graded foams can exhibit better energy absorption capacities than the uniform ones of the same weight. Meanwhile, very limited investigation on their constitutive model has been reported. Therefore, this study aims to investigate experimentally the quasi-static compressive behavior of graded foams and then establish a constitutive model based on the property of the homologous uniform foams. For this purpose, uniform foams with six different cell sizes and graded foams with twelve different gradient distributions are manufactured by using the additive manufacturing technique. Comparing with uniform foams, graded foams with similar relative density show a similar behavior in elastic and densification stages. The main difference lies in the fact that graded foams possess a hardening plateau stage rather than a constant one. Such hardening behavior is due to a successive collapse from the weakest region to the strongest region. In other words, graded foams exhibit successive plateau stresses of their component layers. Thus, the graded-foam property can be modeled using the mechanical properties of uniform-foam component layers. Indeed, we first determine the Gibson-Ashby relations for uniform foams from experimental data. Then, an elastic, plastic-hardening, locking model for graded foams is built from these uniform-foam Gibson-Ashby relations. This constitutive model can be used for predicting the quasi-static compressive responses of various graded foams, and verified by our experimental data and some published results. A finite element simulation is also conducted to verify the validity of this model. On the basis of this model, it is possible to tailor the mechanical properties of graded foams for various engineering applications without conducting experimental studies.

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分级泡沫的准静态压缩行为及本构模型

摘要 功能梯度材料在过去的几十年中得到了广泛的发展，最近引入了梯度泡沫，因为这种梯度泡沫比相同重量的均匀泡沫具有更好的能量吸收能力。同时，已经报道了对其本构模型的非常有限的研究。因此，本研究旨在通过实验研究分级泡沫的准静态压缩行为，然后基于同源均匀泡沫的性质建立本构模型。为此，使用增材制造技术制造了具有六种不同泡孔尺寸的均匀泡沫和具有十二种不同梯度分布的分级泡沫。与均匀泡沫相比，具有相似相对密度的分级泡沫在弹性和致密化阶段表现出相似的行为。主要区别在于分级泡沫具有硬化平台阶段而不是恒定阶段。这种硬化行为是由于从最弱区域到最强区域的连续坍塌。换句话说，分级泡沫表现出其组分层的连续平台应力。因此，梯度泡沫特性可以使用均匀泡沫组件层的机械特性进行建模。事实上，我们首先根据实验数据确定均匀泡沫的 Gibson-Ashby 关系。然后，根据这些均匀泡沫 Gibson-Ashby 关系建立了分级泡沫的弹性、塑性硬化、锁定模型。该本构模型可用于预测各种分级泡沫的准静态压缩响应，并通过我们的实验数据和一些已发表的结果进行验证。还进行了有限元仿真以验证该模型的有效性。在此模型的基础上，无需进行实验研究，就可以为各种工程应用定制分级泡沫的机械性能。