We propose a projection-based model order reduction procedure for the ageing of large prestressed concrete structures. Our work is motivated by applications in the nuclear industry, particularly in the simulation of containment buildings. Such numerical simulations involve a multi-modeling approach: a three-dimensional nonlinear thermo-hydro-visco-elastic rheological model is used for concrete; and prestressing cables are described by a one-dimensional linear thermo-elastic behavior. A kinematic linkage is performed in order to connect the concrete nodes and the steel nodes: coincident points in each material are assumed to have the same displacement. We develop an adaptive algorithm based on a Proper Orthogonal Decomposition (POD) in time and greedy in parameter to build a reduced order model (ROM). The nonlinearity of the operator entails that the computational cost of the ROM assembly scales with the size of the high-fidelity model. We develop an hyper-reduction strategy based on empirical quadrature to bypass this computational bottleneck: our approach relies on the construction of a reduced mesh to speed up online assembly costs of the ROM. We provide numerical results for a standard section of a double-walled containment building using a qualified and broadly-used industrial grade finite element solver for structural mechanics (code$\_$aster).

翻译：我们针对大型预应力混凝土结构的老化过程提出了一种基于投影的模型降阶方法。本研究源于核工业领域的应用需求，特别是安全壳建筑的数值模拟。此类数值模拟涉及多模型耦合方法：混凝土采用三维非线性热-湿-粘弹性流变模型，预应力钢束则通过一维线性热弹性行为描述。通过运动学耦合实现混凝土节点与钢节点的连接：假定两种材料中的重合点具有相同的位移。我们开发了一种自适应算法，该算法基于时间方向的本征正交分解与参数方向的贪婪策略来构建降阶模型。由于算子的非线性特性，降阶模型装配的计算成本与高保真模型的规模相关。我们提出了一种基于经验求积的超降阶策略以突破这一计算瓶颈：该方法通过构建简化网格来加速降阶模型的在线装配成本。我们采用经认证且广泛使用的工业级有限元结构力学求解器代码$\_$aster，针对双壁安全壳建筑的标准截面给出了数值结果。