Residual stress widely exists in soft materials. Besides growth, inhomogeneous thermal expansion is also a primary cause of residual stress. However, establishing a proper hyperelastic constitutive relation is a great challenge since the existing theories cannot capture the change of underlying mechanical responses triggered by temperature variations. In this paper, a general hyperelastic constitutive relation for soft elastomers with thermally-induced residual stress is developed. We first reveal the initial temperature dependence of conventional thermoelastic models. This property attributes the alteration of the underlying thermoelastic response to free thermal expansions. Then, a compatibility-broken curvature compensation (CBCC) framework is established based on finite thermoelasticity. It generates a free thermal expansion to eliminate the Riemannian curvatures of the virtual stress-free configuration derived from the isothermal stress release. Such a mechanism indicates the non-local effect of the residual stress, which fundamentally modifies the traditional view that invariant formulations cover all the possible functional dependence of residual stress. Also, the obtained governing equations are similar to Einstein field equations of the general theory of relativity. This similarity may deeply imply a standard mechanism concerning the curvature compensation leading to residual stress genesis. We finally conduct comparative analyses of the spherically symmetric and axisymmetric problems between the current constitutive relation and the existing models. The influences of adopting distinct residual stresses, the performance of the non-local effect, and the availability of the new constitutive relation are investigated in detail. This framework can shed some light on the constitutive modeling of soft materials.

残余应力广泛存在于软材料中。除了生长之外，不均匀的热膨胀也是残余应力的主要原因。然而，建立适当的超弹性本构关系是一个巨大的挑战，因为现有的理论无法捕捉温度变化引发的潜在机械响应的变化。在本文中，建立了具有热致残余应力的软弹性体的一般超弹性本构关系。我们首先揭示了传统热弹性模型的初始温度依赖性。该属性归因于自由热膨胀的潜在热弹性响应的改变。然后，建立了基于有限热弹性的相容性破坏曲率补偿（CBCC）框架。它产生自由热膨胀，以消除源自等温应力释放的虚拟无应力结构的黎曼曲率。这种机制表明残余应力的非局部效应，从根本上改变了传统观点，即不变公式涵盖了残余应力的所有可能的函数依赖性。此外，所获得的控制方程与广义相对论的爱因斯坦场方程相似。这种相似性可能深刻地暗示了关于曲率补偿导致残余应力产生的标准机制。最后对当前本构关系与现有模型的球对称和轴对称问题进行了比较分析。详细研究了采用不同残余应力的影响、非局部效应的表现以及新本构关系的可用性。该框架可以为软材料的本构建模提供一些启示。