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A nonlocal lattice particle model for J2 plasticity
International Journal for Numerical Methods in Engineering ( IF 2.9 ) Pub Date : 2020-06-07 , DOI: 10.1002/nme.6446
Haoyang Wei 1 , Hailong Chen 2 , Yongming Liu 1
Affiliation  

In virtue of their intrinsic integro‐differential formulation of underlying physical behavior of materials, discontinuous computational methods are more beneficial over continuum‐mechanics‐based approaches for materials failure modeling and simulation. However, application of most discontinuous methods is limited to elastic/brittle materials, which is partially due to their formulations are based on force and displacement rather than stress and strain measures as are the cases for continuous approaches. In this article, we formulate a nonlocal maximum distortion energy criterion in the framework of a lattice particle model for modeling of elastoplastic materials. Similar to the maximum distortion energy criterion in continuum mechanics, the basic idea is to decompose the energy of a discrete material point into dilatational and distortional components, and plastic yielding of bonds associated with this material point is assumed to occur only when the distortional component reaches a critical value. However, the formulated yield criterion is nonlocal since the energy of a material point depends on the deformation of all the bonds associated with this material point. Formulation of equivalent strain hardening rules for the nonlocal yield model was also developed. Compared to theoretical and numerical solutions of several benchmark problems, the proposed formulation can accurately predict both the stress‐strain curves and the deformation fields under monotonic loading and cyclic loading with different strain hardening cases.

中文翻译:

J2可塑性的非局部晶格粒子模型

凭借其固有的材料基本物理行为的积分微分公式,与基于连续力学的材料失效建模和仿真方法相比,不连续的计算方法更具优势。但是,大多数不连续方法的应用仅限于弹性/脆性材料,这部分是由于其配方是基于力和位移,而不是连续方法的应力和应变测量。在本文中,我们在用于弹塑性材料建模的晶格粒子模型框架内制定了非局部最大变形能量准则。类似于连续力学中的最大畸变能准则,基本思想是将离散材料点的能量分解为膨胀和变形分量,并且假定仅在变形分量达到临界值时才会发生与该材料点关联的键的塑性屈服。但是,由于屈服点的能量取决于与该屈服点相关的所有键的变形,因此制定的屈服准则不是局部的。还开发了用于非局部屈服模型的等效应变硬化规则。与几个基准问题的理论和数值解决方案相比,所提出的公式可以准确地预测在不同应变硬化情况下单调载荷和循环载荷下的应力-应变曲线和变形场。假定只有当变形分量达到临界值时才会发生与该材料点相关的键的塑性屈服。但是,由于屈服点的能量取决于与该屈服点相关的所有键的变形,因此制定的屈服准则不是局部的。还开发了用于非局部屈服模型的等效应变硬化规则。与几个基准问题的理论和数值解决方案相比,所提出的公式可以准确地预测在不同应变硬化情况下单调载荷和循环载荷下的应力-应变曲线和变形场。假定只有当变形分量达到临界值时才会发生与该材料点相关的键的塑性屈服。但是,由于屈服点的能量取决于与该屈服点相关的所有键的变形,因此制定的屈服准则不是局部的。还开发了用于非局部屈服模型的等效应变硬化规则。与几个基准问题的理论和数值解决方案相比,所提出的公式可以准确地预测在不同应变硬化情况下单调载荷和循环载荷下的应力-应变曲线和变形场。公式化的屈服准则是非局部的,因为材料点的能量取决于与此材料点相关的所有键的变形。还开发了用于非局部屈服模型的等效应变硬化规则。与几个基准问题的理论和数值解决方案相比,所提出的公式可以准确地预测在不同应变硬化情况下单调载荷和循环载荷下的应力-应变曲线和变形场。公式化的屈服准则是非局部的,因为材料点的能量取决于与此材料点相关的所有键的变形。还开发了用于非局部屈服模型的等效应变硬化规则。与几个基准问题的理论和数值解决方案相比,所提出的公式可以准确地预测在不同应变硬化情况下单调载荷和循环载荷下的应力-应变曲线和变形场。
更新日期:2020-06-07
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