局部损伤格点网络的自适应变分拟连续体方法
An adaptive variational Quasicontinuum methodology for lattice networks with localized damage
摘要：
具有耗散相互作用的晶格网络可用于描述材料的离散细观结构的力学，例如3D打印结构和泡沫。这种贡献涉及在这种材料中的裂纹萌生和传播，并侧重于自适应多尺度方法，捕捉空间演变的断裂。晶格网络自然包含非局部性，大变形和耗散机制发生在断裂带内。由于物理相关的长度尺度明显大于个体相互作用的长度尺度，离散模型在计算上是昂贵的。准连续体（QC）方法是一种专门为离散模型构建的多尺度方法。该方法通过仅在感兴趣的区域中完全解析底层晶格而在其他地方粗化来降低计算成本。在这方面的贡献，（变分）QC适用于工程规模的预测损坏晶格。为了处理空间演化的断裂带，提出了一种自适应方案。从能量一致性的角度讨论了自适应过程引起的影响，并在两个例子上证明了理论上的考虑。第一个作为一个概念的证明，说明了自适应方案的一致性，并提出了能量的错误。第二个演示了一个更复杂的问题的自适应QC计划的性能。
英文摘要：
Lattice networks with dissipative interactions can be used to describe the mechanics of discrete meso-structures of materials such as 3D-printed structures and foams. This contribution deals with the crack initiation and propagation in such materials and focuses on an adaptive multiscale approach that captures the spatially evolving fracture. Lattice networks naturally incorporate non-locality, large deformations, and dissipative mechanisms taking place inside fracture zones. Because the physically relevant length scales are significantly larger than those of individual interactions, discrete models are computationally expensive. The Quasicontinuum (QC) method is a multiscale approach specifically constructed for discrete models. This method reduces the computational cost by fully resolving the underlying lattice only in regions of interest, while coarsening elsewhere. In this contribution, the (variational) QC is applied to damageable lattices for engineering-scale predictions. To deal with the spatially evolving fracture zone, an adaptive scheme is proposed. Implications induced by the adaptive procedure are discussed from the energy-consistency point of view, and theoretical considerations are demonstrated on two examples. The first one serves as a proof of concept, illustrates the consistency of the adaptive schemes, and presents errors in energies. The second one demonstrates the performance of the adaptive QC scheme for a more complex problem.
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