The computational framework for continuum-kinematics-inspired peridynamics
The computational framework for continuum-kinematics-inspired peridynamics
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DOI：
10.1007/s00466-020-01885-3
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发表时间：
2020-04
影响因子：
4.1
通讯作者：
A. Javili;S. Firooz;A. McBride;P. Steinmann
中科院分区：
文献类型：
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作者：
A. Javili;S. Firooz;A. McBride;P. Steinmann
周波理论（PD）是一种非局部连续介质形式。PD的原始版本仅限于基于键的相互作用。基于键的PD是几何精确的，其运动学类似于经典连续介质力学（CCM）。然而，它不能正确地捕捉泊松效应。这个缺点通过基于状态的PD解决，但是运动学没有被准确地保留。连续运动学启发的周期运动学（CPD）提供了一个几何上精确的框架，其基本的运动学与CCM相吻合，并正确地捕捉泊松效应。在CPD中，人们区分一个、两个和三个邻居的相互作用。单邻相互作用等价于原始PD形式主义的基于键的相互作用。然而，两个和三个邻居的相互作用是从根本上不同的状态为基础的相互作用的连续运动学的基本要素被精确地保存。这方面的贡献的目的是阐述计算方面的持续专业发展，并提出详细的推导，是必不可少的，其实施。通过一系列的数值例子阐明了计算CPD的主要特点。这些问题包括大变形的三维问题。所提出的策略是鲁棒的，并观察与牛顿-拉夫森计划的二次收敛率。
Peridynamics (PD) is a non-local continuum formulation. The original version of PD was restricted to bond-based interactions. Bond-based PD is geometrically exact and its kinematics are similar to classical continuum mechanics (CCM). However, it cannot capture the Poisson effect correctly. This shortcoming was addressed via state-based PD, but the kinematics are not accurately preserved. Continuum-kinematics-inspired peridynamics (CPD) provides a geometrically exact framework whose underlying kinematics coincide with that of CCM and captures the Poisson effect correctly. In CPD, one distinguishes between one-, two- and three-neighbour interactions. One-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism. However, two- and three-neighbour interactions are fundamentally different from state-based interactions as the basic elements of continuum kinematics are preserved precisely. The objective of this contribution is to elaborate on computational aspects of CPD and present detailed derivations that are essential for its implementation. Key features of the resulting computational CPD are elucidated via a series of numerical examples. These include three-dimensional problems at large deformations. The proposed strategy is robust and the quadratic rate of convergence associated with the Newton–Raphson scheme is observed.