This paper introduces a homogenization-based constitutive model for the large-strain mechanical response of elastomeric syntactic foams subject to arbitrary quasistatic loading and unloading conditions. Based on direct observations from experiments, this class of emerging foams are considered to be made of a nonlinear elastic matrix filled with a random isotropic distribution of hollow thin-walled spherical shells – commonly termed microspheres or microballoons – each having the same mean diameter that are made of an elastic brittle material that is much stiffer than the elastomeric matrix, typically, either glass or a hard polymer. Accordingly, such underlying microballoons behave effectively as rigid particles initially. Along a given loading path, however, they may fracture (in the case of glass microballoons) or buckle (in the case of polymer microballoons) at which point they abruptly transition to behave effectively as vacuous pores. On that account, the proposed constitutive model corresponds to a homogenization solution for the nonlinear elastic response of particle-filled porous elastomers – precisely, elastomers embedding both rigid spherical particles and vacuous spherical pores of equal monodisperse size – wherein the volume fraction of pores corresponds to the volume fraction of fractured or buckled microballoons and hence is not a fixed parameter but rather an internal variable of state that evolves as a function of the loading history. After the general presentation of the model, where its theoretical and practical features are discussed, its descriptive and predictive capabilities are showcased via comparisons with experimental data for silicone syntactic foams filled with glass microballoons.

本文介绍了基于均质化的本构模型，用于弹性体复合泡沫在任意准静态加载和卸载条件下的大应变力学响应。根据对实验的直接观察，这类新兴泡沫被认为是由非线性弹性基质制成的，该基质填充有空心薄壁球形壳（通常称为微球或微气球）的随机各向同性分布，每个均具有相同的平均直径，由比弹性体基质硬得多的弹性脆性材料制成的材料，通常是玻璃或硬质聚合物。因此，这种下面的微气球最初有效地表现为刚性颗粒。但是，沿着给定的加载路径，它们可能会破裂（对于玻璃微气球而言）或发生弯曲（对于聚合物微气球而言），此时它们会突然转变以有效表现为空洞。因此，建议的本构模型对应于均质解决方案，用于填充颗粒的多孔弹性体的非线性弹性响应-精确地讲，弹性体既嵌入了刚性球形颗粒，又嵌入了具有相同单分散尺寸的空泡球形孔，其中孔的体积分数对应于破裂或弯曲的微气球的体积分数，因此不是固定的参数，而是状态的内部变量，其根据加载历史而变化。在对模型进行一般介绍之后，讨论了模型的理论和实践特征，