A non-smooth tension–compression asymmetric constitutive law has important applications in modelling of bio-composite structures with a unilateral contact behavior and no-tension/compression structures. Quadratic programming algorithms based on Parametric Variational Principle (PVP) have good numerical robustness on this kind of issue. However, the challenge of computational cost prevents its application into some practical engineering structures with a large-scale degree of freedoms (DOFs). The paper proposes an efficient model reduction method based on the Extended Multiscale FEM (EMsFEM) for mechanical analysis of composite structures with tension–compression asymmetric properties. At the macro-scale, a reduced-order model is constructed and solved to get the displacement field, while a complementarity finite element formulation is proposed to get the stress field at the micro-scale. A two-scale iterative scheme bridging upscale and downscale computations is developed to deal with material nonlinearity. Numerical simulations show satisfactory computational accuracy of the proposed model reduction method, which can find applications in nacre-like composites and membrane antennae. Compared with the previous FEM-PVP, the proposed EMsFEM-PVP method saves computer’s memory and CPU time greatly. The study provides a generalized numerical way to handle large-scale non-smooth mechanics.

非光滑的拉伸-压缩非对称本构律在具有单侧接触行为和无拉伸/压缩结构的生物复合结构建模中具有重要的应用。基于参数变分原理（PVP）的二次规划算法在此类问题上具有良好的数值鲁棒性。但是，计算成本的挑战阻止了其在具有大规模自由度（DOF）的某些实际工程结构中的应用。本文提出了一种基于扩展多尺度有限元法（EMsFEM）的有效模型简化方法，用于具有拉压不对称特性的复合结构的力学分析。在宏观尺度上，构造并求解降阶模型以获得位移场，提出了互补有限元公式来获得微观尺度的应力场。提出了一种将高阶和低阶计算相结合的两尺度迭代方案，以处理材料非线性问题。数值模拟表明，所提出的模型简化方法具有令人满意的计算精度，可以在珍珠质复合材料和膜天线中找到应用。与以前的FEM-PVP相比，提出的EMsFEM-PVP方法大大节省了计算机的内存和CPU时间。该研究提供了一种处理大型非光滑力学的通用数值方法。数值模拟表明，所提出的模型简化方法具有令人满意的计算精度，可以在珍珠质复合材料和膜天线中找到应用。与以前的FEM-PVP相比，提出的EMsFEM-PVP方法大大节省了计算机的内存和CPU时间。该研究提供了一种处理大型非光滑力学的通用数值方法。数值模拟表明，所提出的模型简化方法具有令人满意的计算精度，可以在珍珠质复合材料和膜天线中找到应用。与以前的FEM-PVP相比，提出的EMsFEM-PVP方法大大节省了计算机的内存和CPU时间。该研究提供了一种处理大型非光滑力学的通用数值方法。