The notion of dynamic inclusion can be utilized to represent phenomena in micromechanics of solids such as phase transformations, in particular when subjected to dynamic loading. If the size of a dynamic inclusion is comparable to the inherent length parameters of its constituent material, then the size effect manifests its significance. The present paper is, hence, dedicated to the employment of the complete form of Mindlin’s first strain gradient theory of elasticity to address a special class of dynamic inclusion problems. Specifically, in this paper, an analytical solution is obtained for the elastic displacement field developed in an infinitely extended isotropic medium due to a suddenly expanding spherical inclusion that undergoes a constant and uniform distribution of classical dilatational eigenstrains. The employment of such a theoretical framework results in eliminating the classical singularities of the strain and stress fields of the problem. The analysis presented in this paper can, moreover, account for the effect of microinertia on the response of the medium to the sudden expansion of the inclusion, by incorporating an additional characteristic length into the equation of motion of the medium. An extended version for Hadamard conditions associated with the adopted theory is also derived, and subsequently, it is shown that the obtained solution of the considered problem satisfies these conditions.

动态夹杂物的概念可用于表示固体微观力学中的现象，例如相变，特别是在受到动态载荷时。如果动态夹杂物的尺寸与其组成材料的固有长度参数相当，那么尺寸效应就体现了它的重要性。因此，本文致力于使用 Mindlin 的第一个弹性应变梯度理论的完整形式来解决一类特殊的动态包含问题。具体而言，在本文中，获得了在无限扩展的各向同性介质中由于突然膨胀的球形夹杂物经历经典膨胀特征应变的恒定且均匀分布的弹性位移场的解析解。采用这种理论框架可以消除问题的应变和应力场的经典奇异性。此外，本文提出的分析可以通过在介质的运动方程中加入额外的特征长度来解释微惯性对介质对夹杂物突然膨胀的响应的影响。还导出了与采用的理论相关的 Hadamard 条件的扩展版本，随后表明所考虑问题的获得的解决方案满足这些条件。通过在介质的运动方程中加入一个额外的特征长度来解释微惯性对介质对夹杂物突然膨胀的响应的影响。还导出了与采用的理论相关的 Hadamard 条件的扩展版本，随后表明所考虑问题的获得的解决方案满足这些条件。通过在介质的运动方程中加入一个额外的特征长度来解释微惯性对介质对夹杂物突然膨胀的响应的影响。还导出了与采用的理论相关的 Hadamard 条件的扩展版本，随后表明所考虑问题的获得的解决方案满足这些条件。