The path-independent M-integral plays an important role in analysis of solids with inhomogeneities. However, the available applications are almost limited to linear-elastic or physically non-linear power law type materials under the assumption of infinitesimal strains. In this paper we formulate the M-integral for a class of hyperelastic solids undergoing finite anti-plane shear deformation. As an application we consider the problem of rigid inclusions embedded in a Mooney–Rivlin matrix material. With the derived M-integral we compute weighted averages of the shear stress acting on the inclusion surface. Furthermore, we prove that a system of rigid inclusions can be replaced by one effective inclusion.

路径无关的 M 积分在不均匀固体分析中发挥着重要作用。然而，可用的应用几乎仅限于无限小应变假设下的线弹性或物理非线性幂律类型材料。在本文中，我们为一类经历有限反平面剪切变形的超弹性固体制定了 M 积分。作为一个应用，我们考虑嵌入 Mooney-Rivlin 基体材料中的刚性夹杂物的问题。利用导出的 M 积分，我们计算作用在夹杂物表面上的剪切应力的加权平均值。此外，我们证明了刚性夹杂物系统可以被一种有效的夹杂物取代。