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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Three-dimensional explicit finite element formulation for shear localization with global tracking of embedded weak discontinuities
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Three-dimensional explicit finite element formulation for shear localization with global tracking of embedded weak discontinuities

机译：剪切定位三维明确有限元配方，嵌入式弱不连续性全局跟踪

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摘要

Shear localization is a damage mechanism characterized by the concentration of plastic deformation within thin bands of materials, often observed as a precursor to failure in metals. In this paper, we present a three-dimensional explicit finite element formulation with embedded weak discontinuities for the treatment of shear localization under dynamic loading conditions. In this formulation, the onset of localization is detected via a material stability analysis suitable for rate-sensitive materials, and the continuity of propagating shear bands is ensured using a global tracking strategy involving a heat-conduction type boundary value problem, solved for a scalar level set function over the global domain of the problem. In addition, we propose a modified quadrature rule that is used to compute the contribution of an individual element to the global finite element arrays, taking into account the position of the embedded shear band within that element. The mechanical threshold stress (MTS) model, modified to account for dynamic recrystallization, is adopted as the constitutive model for rate-and temperature-sensitive metallic materials, and the constitutive equations are formulated in a corotational setting. The algorithmic implementation of the integrated finite element framework, including the global tracking strategy, is described in detail. Subsequently, a simple example problem involving shear band formation under uni-axial tension is presented, to illustrate the advantages of the proposed computational framework over conventional finite element techniques, in terms of convergence and mesh insensitivity of their numerical results. In addition, to demonstrate the capabilities of the proposed computational framework in more realistic problems, numerical results are compared to data from split-Hopkinson pressure bar dynamic experiments, conducted on two stainless steel samples with different geometric designs. In each problem presented, we study the effect of the mesh size on the numerical solution, including global results such as the load-displacement response, and local quantities such as material state variables at individual quadrature points. These numerical studies show that the geometry and total volume of the fully-developed embedded shear band are independent of the mesh size. (C) 2019 Elsevier B.V. All rights reserved.
机译：剪切定位是一种损伤机构，其特征在于薄带内塑性变形的浓度，通常观察到金属失效的前体。在本文中，我们介绍了一种三维明确的有限元配方，具有嵌入式弱不连续性，用于在动态负载条件下治疗剪切定位。在该制剂中，通过适合于速率敏感材料的材料稳定性分析检测定位的发作，并且使用涉及传热型边值问题的全局跟踪策略来确保传播剪切带的连续性，为标量解决了标量级别在全局问题上的功能。另外，我们提出了一种修改的正交规则，用于计算单个元素对全局有限元阵列的贡献，考虑到该元件内的嵌入式剪切带的位置。修改为动态再结晶的机械阈值应力（MTS）模型被采用作为速率 - 和温度敏感金属材料的本构型模型，并且构成方程在蚀刻环境中配制。详细描述了包括全局跟踪策略的集成有限元框架的算法实现。随后，提出了一种涉及在单轴张力下剪切带形成的简单示例问题，以说明在其数值结果的收敛性和网眼不敏感性方面，所提出的计算框架在传统的有限元技术上的优点。此外，为了展示所提出的计算框架在更现实的问题中的能力，将数值结果与来自分流霍普金森压力条动态实验的数据进行比较，在具有不同几何设计的两个不锈钢样本上进行。在所呈现的每个问题中，我们研究网格尺寸对数值解决方案的影响，包括全局结果，例如负载 - 位移响应，以及各个正交点的局部数量，例如材料状态变量。这些数值研究表明，完全开发的嵌入式剪切带的几何和总体积与网格尺寸无关。 （c）2019 Elsevier B.v.保留所有权利。

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