Development of a mixed displacement-stress formulation for the analysis of elastoplastic structures under small strains: Application to a locking-free, NURBS-based solid-shell element
Development of a mixed displacement-stress formulation for the analysis of elastoplastic structures under small strains: Application to a locking-free, NURBS-based solid-shell element
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DOI：
10.1016/j.cma.2015.07.012
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发表时间：
2015-10
影响因子：
7.2
通讯作者：
R. Bouclier;T. Elguedj;A. Combescure
中科院分区：
文献类型：
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作者：
R. Bouclier;T. Elguedj;A. Combescure
在本文中，我们开发了一个通用的框架扩展的混合位移-应力类型的配方弹塑性问题下的小应变。这种公式的困难在于，与用于不可压缩材料的更常见的混合方法相反，塑性（包括应力的偏量部分）受到静态未知量的影响。因此，塑性流动不仅仅由位移引起的应变控制。本文采用的方法是选择总弹性应力作为混合方程的静态未知量。然后，确定用作塑性投影的输入的应变场。我们应用这种形式主义的混合BMBS为基础的固体壳元Bouclier等人。(2013，2015年），这导致了一个有效的扩展到弹塑性域的元素。我们能够验证这个元素的能力，以克服壳锁定问题，通过几个测试案例，涉及线性各向同性应变硬化的塑性流动规则。
In this paper, we develop a general framework for the extension of mixed displacement-stress types of formulations to elastoplastic problems under small strains. The difficulty with such formulations is that, contrary to the more usual mixed methods used for incompressible materials, plasticity (which involves the deviatoric part of the stress) is affected by the static unknown. Thus, the plastic flow is not governed by displacement-induced strains alone. The approach followed in this paper consists in choosing the total elastic stress as the static unknown of the mixed formulation. Then, one determines a strain field which is used as input for the plastic projection. We applied this formalism to the mixed NURBS-based solid-shell element of Bouclier et al. (2013, 2015), which led to an efficient extension of the element into the elastoplastic domain. We were able to verify the ability of this element to overcome shell locking problems through several test cases involving a plastic flow rule with linear isotropic strain hardening.