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首页> 外文期刊>International Journal of Solids and Structures >Discretized virtual internal bond model for nonlinear elasticity
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Discretized virtual internal bond model for nonlinear elasticity

机译：非线性弹性的离散虚拟内键模型

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摘要

The virtual internal bond (VIB) is a micro-macro constitutive model. Although this model is based on a postulated discrete microstructure, it ultimately returns to a continuum constitutive relation through a homogenization process. The homogenization process can reduce the internal degrees of freedom, but it omits the effect of the individual micro bond that may play an important role in the fracture process. The present research develops a discrete system to represent the nonlinear elasticity by discretizing the continuous VIB. This discrete system is composed of unit cells, which can adopt any geometry with any number of bonds. The system is characterized by the force-displacement, not the stress-strain constitutive relationship. The nonlinear properties of this discrete system are governed by the micro-bond potential. The micro bond properties are related to Young's modulus of the material, the volume and the bond number of the unit cell. For a given material, the unit cell has a certain topological structure and configuration. A discussion of two specific cases (the 2D triangular and 3D tetrahedral unit cells) suggests that the discrete system converges with decreasing unit cell size. In the unstructured unit cell scheme, the discrete system can almost precisely represent the initial Young's modulus and the Poisson ratio of a nonlinear continuum. A mixed fracture example demonstrates that the present method can efficiently simulate the fracture propagation. The present paper provides a theory for developing a lattice-type mechanical model for nonlinear elasticity and provides new method for the fracture simulation of a nonlinear elastic material.
机译：虚拟内部键（VIB）是微观宏本构模型。尽管此模型基于假定的离散微观结构，但最终通过均质化过程返回到连续的本构关系。均质化过程可以降低内部自由度，但忽略了可能在断裂过程中发挥重要作用的单个微键的作用。本研究开发了一种离散系统，通过离散化连续VIB来表示非线性弹性。这种离散的系统由晶胞组成，晶胞可以采用具有任意数量键的任何几何形状。该系统的特征是力-位移，而不是应力-应变本构关系。该离散系统的非线性特性受微键电势控制。微键性质与材料的杨氏模量，单位单元的体积和键数有关。对于给定的材料，晶胞具有某种拓扑结构和构造。对两种特定情况（2D三角形和3D四面体晶胞）的讨论表明，离散系统随着晶胞尺寸的减小而收敛。在非结构化晶胞方案中，离散系统几乎可以准确地表示初始杨氏模量和非线性连续体的泊松比。一个混合的裂缝实例表明，本方法可以有效地模拟裂缝的扩展。本文为非线性弹性材料的格构式力学模型的开发提供了理论基础，为非线性弹性材料的断裂模拟提供了新的方法。

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