We present a Finite Element model, which is devoted to describing the failure mechanics of quasi-brittle materials (e.g. concrete), such as the stiffness recovery effect at the transition from tension to compression, and the cyclic behavior with a low number of cycles. The material is studied at the meso-scale, and thus considered as a heterogeneous medium. The model is formulated within the framework of the strong discontinuity analysis and implemented using the Enhanced Finite Element Method (E-FEM). The key point is to locally embed the discontinuities inside the finite elements. Here, we take advantage of this strategy for two kinds of discontinuities. On the one hand, strong discontinuities aim to model cracks, at fine scale, that can open along mode-I. On the other hand, weak discontinuities are used to describe the elastic heterogeneity. In addition to the initiation and propagation of cracks, our main contribution is to add a closure mechanism. We show the ability of the model to simulate some of the well-known characteristics of such materials at macroscale, such as the unsymmetrical tension/compression behavior, the stiffness recovery effect, and hysterical load/displacement curve.

我们提出了一个有限元模型，该模型专门用于描述准脆性材料（例如混凝土）的破坏机理，例如从拉伸到压缩的过渡过程中的刚度恢复效果，以及循环次数少的循环行为。该材料是在介观尺度上研究的，因此被视为异质介质。该模型是在强不连续性分析的框架内制定的，并使用增强有限元方法（E-FEM）实施。关键是将不连续性局部嵌入到有限元内部。在这里，我们将这种策略用于两种不连续点。一方面，强烈的不连续性旨在模拟可以沿着模式I开裂的细小裂纹。另一方面，弱不连续性用于描述弹性异质性。除了引发和扩展裂纹，我们的主要贡献是增加了闭合机制。我们展示了该模型在宏观上模拟此类材料的一些众所周知的特性的能力，例如不对称的拉伸/压缩行为，刚度恢复效果和滞后载荷/位移曲线。