The indentation of a microcapsule with a spherical indenter is an effective technique to evaluate the elastic properties of microcapsule shells. The spherical indentation of a microcapsule could be modelled as a microsphere with core–shell structure indented by a rigid sphere. Based on the assumption that the deformed pattern of microcapsule is axisymmetric at small indentation displacement, the deformed profile of shell was divided into five regions according to curvature change. The strain energy of shell was then obtained by adding the bending and membrane strain energy of each region together. The strain energy of core is mainly caused by the volume change of core. The microcapsule was treated as a system and its total potential energy is the sum of the strain energy of shell and core minus the work done by external load. Applying the minimum total potential principle, a spherical indentation model that establishes the relationship among the indentation load, the indentation displacement, and the elastic properties and geometric parameters of microcapsules was proposed. Experiments were carried out on PMMA microcapsules with different dimensions to validate the newly proposed spherical indentation model. The average value of elastic moduli obtained by conventional nanoindentation tests on bulk PMMA and the cross-section of PMMA shell was regarded as the nominal value. The average elastic modulus of PMMA shells determined by the proposed model shows a good agreement with the nominal value. Finally, finite element simulations combined with the proposed model were used to predict the indentation behaviors of microcapsules with different dimensions.

用球形压头压入微胶囊是一种评估微胶囊壳弹性性能的有效技术。微胶囊的球形压痕可以模拟为具有核壳结构的微球体，该微球体由刚性球体缩进。假设微囊变形模式在压痕位移较小时为轴对称，根据曲率变化将壳体变形轮廓分为五个区域。然后通过将每个区域的弯曲和膜应变能加在一起得到壳的应变能。核心的应变能主要是由核心的体积变化引起的。微胶囊被视为一个系统，其总势能是壳核应变能减去外载荷所做功的总和。应用最小总电位原理，提出了一种球形压痕模型，该模型建立了压痕载荷、压痕位移以及微胶囊的弹性特性和几何参数之间的关系。对不同尺寸的 PMMA 微胶囊进行了实验，以验证新提出的球形压痕模型。将通过常规纳米压痕测试在块状 PMMA 和 PMMA 壳截面上获得的弹性模量的平均值作为标称值。由所提出的模型确定的 PMMA 壳的平均弹性模量与标称值吻合良好。最后，结合所提出的模型的有限元模拟用于预测不同尺寸微胶囊的压痕行为。