3D Cellular Automata Finite Element Method with Explicit Microstructure: Modeling Quasi-brittle Fracture using Meshfree Damage Propagation
3D Cellular Automata Finite Element Method with Explicit Microstructure: Modeling Quasi-brittle Fracture using Meshfree Damage Propagation
复制标题
具有显式微观结构的 3D 元胞自动机有限元方法：使用无网格损伤传播模拟准脆性断裂
DOI：
10.1016/j.mspro.2014.06.186
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Saucedo-Mora L
中科院分区：
文献类型：
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作者：
Saucedo-Mora L
准脆性断裂是一种新出现的特征，基于宏观力学的数值方法不能很好地处理这一问题。由于其复杂的微观结构，连续介质方法对于这些材料来说可能过于简单，需要更精细的离散化才能获得令人满意的结果。在数值方面，这意味着高级方法的计算成本，如粘性单元或嵌入式裂纹，对于工程规模的问题来说往往太高。在本文中，我们使用元胞自动机与有限元方法相结合，以考虑在有限元模拟中的准脆性性能的微观结构的影响。这里的微观结构是明确的建模细分成小元素称为细胞的有限元。梯度微观结构，纹理和颗粒各向异性可以很容易地模拟在微观结构与多相和初始的有限元网格的影响是擦除在微观结构的发展。该方法提供了表示有限元模型和微观结构的两组单元。第一种方法用于将工程尺度问题与细观结构联系起来，得到宏观力学问题的应力场和应变场。有了这些，我们使用第二组元素计算微观力学场，它明确地描述了微观结构。我们使用无网格的方法通过微观结构的损伤发展。根据微观结构损伤重新计算有限元的材料属性，断裂路径相对于有限元网格是完全自由的。通过这种方法，准脆性断裂可以通过微观结构自由发展，提高了复杂微观结构中工程长度尺度计算的精度和计算成本。
Quasi-brittle fracture is an emergent characteristic, and this cannot be treated satisfactorily with the numerical methods based on macromechanics. Because of their complex microstructure, the continuum approach can be too simple for these materials, and needs a finer discretization to obtain satisfactory results. In numerical terms, this means that the computational cost of advanced methods, such as cohesive elements or embedded cracks, is often too high for engineering scale problems. In this paper we use the Cellular Automata integrated with Finite Element method to account for the effect of microstructure on quasi-brittle properties within the finite element simulation. Here the microstructure is modeled explicitly by subdividing a finite element into small elements called cells. Graded microstructures, textures and particle anisotropy can be readily simulated in microstructures with multiple phases and the influence of the initial finite element mesh is erased during the development of the microstructure. This method provides two sets of elements representing the finite element model and the microstructure. The first is used to link the engineering scale problem with the microstructure, obtaining the stress and strain fields of the macro-mechanical problem. With those, we compute the micro-mechanical fields using the second set of elements, which describes explicitly the microstructure. We use the Meshfree approach for the damage development through the microstructure. The material properties of the finite elements are recomputed according to the microstructure damage and the fracture path is completely free with respect to the finite element mesh. By this method quasi-brittle fracture can develop freely through the microstructure, improving the accuracy and computational cost of the calculations at engineering length-scales in complex microstructures.