A new orthogonal split of strain tensor into compressive and tensile parts is implemented within the phase field model to mimic unilateral contact condition with which any existing cracks and any crack propagation have to comply. The resulting phase field model offers several advantages as compared to other available schemes. First, it involves rigorous orthogonality between traction and compression parts. Second, it yields remarkably simple, new analytical expressions of the projectors which provide computational saving during the crack propagation simulation. Finally, it can be applied to arbitrary initial elastic anisotropic media, which is not the case of other available strain tensor split operators. A detailed comparison of the fracture responses predicted by the present model and other approaches is provided. It is shown that the present orthogonal decomposition is able to accurately predict experimental results and removes spurious effects found in other schemes for specific loads like compression.

中文翻译：

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在相场方法中实现新的应变分裂以模拟单边接触

在相场模型中实现了应变张量的新正交分裂成压缩和拉伸部分，以模拟任何现有裂纹和任何裂纹扩展都必须遵守的单边接触条件。与其他可用方案相比，由此产生的相场模型提供了几个优点。首先，它涉及牵引和压缩部分之间的严格正交性。其次，它产生了非常简单、新的投影仪分析表达式，在裂纹扩展模拟过程中提供了计算节省。最后，它可以应用于任意初始弹性各向异性介质，而其他可用的应变张量分裂算子则不然。提供了由本模型和其他方法预测的裂缝响应的详细比较。