论文标题
部分可观测时空混沌系统的无模型预测
Fragmentation analysis of a bar with the Lip-field approach
论文作者
论文摘要
唇段方法是使软化材料模型正常的新方法。它已经在1D准和2D准静脉液中进行了测试：本文将其扩展到1D动力学，这是动态碎片的具有挑战性的问题。唇段方法提出了要解决的机械问题，其中要最小化的是非规范化的问题。通过对损坏场的限制施加Lipschitz来阻止虚假定位。每个时间步骤的位移和损坏场是通过交错算法获得的，即为固定损伤场计算位移场，然后为固定位移场计算损伤场。确实，这两个问题是凸，这不是同时寻求位移和损害场的全球问题。增量电势是通过与粘性区模型的等效性获得的，这使材料参数校准变得简单。还提出了相当于凝聚区模型的非验证局部损害。它被用作唇段方法的参考，而无需实现位移跳跃。 这些方法应用于具有随机扰动材料特性的1D棒的脆性碎片，以加速空间收敛。比较了显式和隐式动态实现。与几种分析，数值和实验参考的有利比较旨在验证建模方法。
The Lip-field approach is a new way to regularize softening material models. It has already been tested in 1D quasistatic and 2D quasistatic: this paper extends it to 1D dynamics, on the challenging problem of dynamic fragmentation. The Lip-field approach formulates the mechanical problem to be solved as an optimization problem, where the incremental potential to be minimized is the non-regularized one. Spurious localization is prevented by imposing a Lipschitz constraint on the damage field. The displacement and damage field at each time step are obtained by a staggered algorithm, that is the displacement field is computed for a fixed damage field, then the damage field is computed for a fixed displacement field. Indeed, these two problems are convex, which is not the case of the global problem where the displacement and damage fields are sought at the same time. The incremental potential is obtained by equivalence with a cohesive zone model, which makes material parameters calibration simple. A non-regularized local damage equivalent to a cohesive zone model is also proposed. It is used as a reference for the Lip-field approach, without the need to implement displacement jumps. These approaches are applied to the brittle fragmentation of a 1D bar with randomly perturbed material properties to accelerate spatial convergence. Both explicit and implicit dynamic implementations are compared. Favorable comparison to several analytical, numerical and experimental references serves to validate the modeling approach.
