The classical continuum mechanics faces difficulties in solving problems involving highly inhomogeneous deformations. The proposed theory investigates the impact of higher-order microscopic deformation on modeling of material behaviors and provides a refined interpretation of strain gradients through the homogenized strain energy density. Only one scale parameter, i.e., the size of the Representative Volume Element (RVE), is required by the proposed theory. By employing the variational approach and the Augmented Lagrangian Method (ALM), the governing equations for deformation as well as the numerical solution procedure are derived. It is demonstrated that the homogenized energy theory offers plausible explanations and reasonable predictions for the problems yet unsolved by the classical theory such as the size effect of deformation. The concept of homogenized strain energy proves to be more suitable for describing the intricate mechanical behavior of materials. And higher order partial differential equations can be effectively solved by the ALM by introducing supplementary variables to lower the highest order of the equations.

经典连续介质力学在解决涉及高度不均匀变形的问题时面临困难。所提出的理论研究了高阶微观变形对材料行为建模的影响，并通过均匀化应变能密度提供了对应变梯度的精细解释。该理论只需要一个尺度参数，即代表体积单元（RVE）的大小。通过采用变分法和增广拉格朗日法（ALM），推导了变形控制方程以及数值求解过程。事实证明，均质能量理论对变形尺寸效应等经典理论尚未解决的问题提供了合理的解释和合理的预测。事实证明，均匀应变能的概念更适合描述材料复杂的机械行为。而ALM可以通过引入补充变量降低方程的最高阶来有效求解高阶偏微分方程。