论文标题
迈向薄结构的相位场模型：一种粗粒的本构定律，用于脆性骨折
Towards a phase-field model for thin structures: a coarse-grained constitutive law for brittle fracture of beams
论文作者
论文摘要
损伤梯度模型使用材料刚度的调节近似断裂力学。为此，单个标量场（损坏）用于整体弹性能量。如果应用于弹性能量的梁和壳的结构模型是拉伸和弯曲贡献的总和，则类似的方法无法捕获一些重要的特征。例如，完全错过了由裂纹诱导的裂纹诱导的轴向和弯曲菌株之间的耦合。在这一贡献中，我们推断出具有与中心线的裂纹非对称的光束的本构定律。为了实现这一目标，我们使用尖锐的界面模型从2D问题中执行了渐近的粗粒程序。我们推断出均质的1D弹性能，耦合轴向和弯曲菌株，其本构参数以不同的方式取决于裂纹深度，我们说明它们的精确程度。这应该为薄结构的相位场梯度模型的合理发展铺平道路。
Damage gradient models approximate fracture mechanics using a modulation of the material stiffness. To this aim a single scalar field, the damage, is used to degrade as a whole the elastic energy. If applied to the structural models of beams and shells, where the elastic energy is the sum of the stretching and bending contributions, a similar approach is not able to capture some important features. For instance, the coupling between axial and bending strains induced by cracks non-symmetric with respect to the center line is completely missed. In this contribution, we deduce a constitutive law for a beam having a crack non-symmetric with respect to the center line. To achieve this, we perform an asymptotic coarse-grained procedure from a 2D problem, using a sharp interface model. We deduce a homogenized 1D elastic energy, coupling the axial and bending strains, the constitutive parameters of which depend in a different way on the crack depth and we state how precisely they do. This should pave the way to a rational development of a phase-field gradient model for thin structures.
