In the present paper, we propose the Continuous Displacement for Fracture (CDF) method, a continuous energy-based numerical approach to find mechanisms and crack patterns exhibited by 2D masonry structures subjected to given loads and settlements. The structure is modelled through the normal, rigid, no-tension material, and the equilibrium problem is solved as the minimum of the total potential energy (TPE). With the CDF method the solution is sought in the space of continuous functions. The CDF performances are compared and illustrated against the PRD approach that finds the TPE minimum in the space of small, piecewise-rigid displacements.

The CDF method is displacement-based approach, allowing for a direct control of the effects of foundation settlements. Some problems are proposed to benchmark the methodology against both PRD and analytical solutions to also clearly illustrate its peculiarities. Finally, its use and potentials are benchmarked and compared on a case study. CDF provides results in good agreement with both the PRD approach and another more sophisticated model. The main outcome is that, although more computationally cumbersome, CDF is mesh independent and perfectly captures a clear subdivision of the structural domain into macro-regions behaving as rigid or quasi-rigid bodies.

在本论文中，我们提出了连续位移断裂 (CDF) 方法，这是一种基于连续能量的数值方法，用于查找受到给定载荷和沉降的 2D 砌体结构所表现出的机制和裂缝模式。该结构通过法向、刚性、无张力材料建模，平衡问题以总势能 (TPE) 的最小值求解。使用 CDF 方法在连续函数空间中寻求解决方案。将 CDF 性能与 PRD 方法进行比较和说明，该方法在小的分段刚性位移空间中找到 TPE 最小值。

CDF 方法是基于位移的方法，允许直接控制基础沉降的影响。提出了一些问题，以针对 PRD 和分析解决方案对方法进行基准测试，以清楚地说明其特性。最后，在案例研究中对它的用途和潜力进行了基准测试和比较。CDF 提供的结果与 PRD 方法和另一个更复杂的模型非常吻合。主要结果是，虽然计算上更繁琐，但 CDF 是独立于网格的，并且完美地将结构域清晰地细分为表现为刚体或准刚体的宏观区域。