Constructing continuum-like measures based on a nonlocal lattice particle model: Deformation gradient, strain and stress tensors
Constructing continuum-like measures based on a nonlocal lattice particle model: Deformation gradient, strain and stress tensors
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DOI：
10.1016/j.ijsolstr.2019.04.014
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发表时间：
2019-09-01
影响因子：
3.6
通讯作者：
Chen, Hailong
中科院分区：
文献类型：
--
作者：
Chen, Hailong
利用加权最小二乘法和能量共轭技术，构造了变形梯度、应变和应力张量的类连续测度的显式表达式。虽然提出了基于非局部格子粒子模型，这些措施的配方是一般性的，可以应用到其他数值模型。变形梯度是基于相邻材料点的变形状态而建立的。在小应变范围内，无穷小应变张量由连接材料兴趣点与其所有相邻点的键的法向应变导出。第二个Piola-Kirchhoff应力张量是利用Green-Lagrange应变张量的能量共轭概念构造的。第一Piola-Kirchhoff和Cauchy应力张量也制定了基于导出的第二Piola-Kirchhoff应力张量。对于均匀和非均匀变形的问题，所有三个构造的措施产生非常好的预测相比，当地连续介质力学的解决方案。然而，第二个Piola-Kirchhoff公式预测不太准确的结果，在表面区域，由于不完整的邻居列表的材料点与这些地区。(C)2019爱思唯尔有限公司版权所有。
Explicit expressions for continuum-like measures of deformation gradient, strain and stress tensors were constructed using the techniques of weighted least squares and energy conjugate. Although presented based on a nonlocal lattice particle model, the formulations of these measures are general in nature and can be applied to other numerical models. Deformation gradient was formulated based on the deformation states of neighboring material points. Within the small strain limit, the infinitesimal strain tensor was derived from normal strains of bonds connecting material point of interest with all its neighbors. The second Piola-Kirchhoff stress tensor was constructed using the energy conjugate concept with respect to Green-Lagrangian strain tensor. The first Piola-Kirchhoff and Cauchy stress tensors were also formulated based on the derived second Piola-Kirchhoff stress tensor. For problems of homogeneous and inhomogeneous deformations, all three constructed measures yield very good predictions comparing to local continuum mechanics solutions. However, the second Piola-Kirchhoff formulation predicts less accurate results in surface regions due to incomplete neighbor list of material points with these regions. (C) 2019 Elsevier Ltd. All rights reserved.