Modeling and algorithms for two-scale time homogenization of viscoelastic-viscoplastic solids under large numbers of cycles
Modeling and algorithms for two-scale time homogenization of viscoelastic-viscoplastic solids under large numbers of cycles
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DOI：
10.1016/j.ijplas.2015.03.005
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发表时间：
2015-07-01
影响因子：
9.8
通讯作者：
Doghri, I.
中科院分区：
文献类型：
--
作者：
Haouala, S.;Doghri, I.
提出了粘弹粘塑性（VE-VP）耦合均匀固体在大循环作用下的双尺度时间均质化公式和算法。主要目的是预测长时间响应，同时大大降低计算成本。该方法基于宏观和微观时间尺度的定义，以及未知变量的渐近展开式。首先，建立基于热力学框架的VE-VP本构模型。其次，将原VE-VP初边值问题分解为微观时间尺度（快时间尺度）和宏观时间尺度（慢时间尺度）耦合问题。前者是纯VE问题，每个宏时间步长求解一次；后者是非线性问题，采用全隐式时间积分迭代求解。对于微尺度时间平均，提出了单点积分和多点积分算法。对单轴和多轴循环载荷的数值模拟表明了所提方法的计算效率和准确性。(C) 2015 Elsevier Ltd.版权所有。
A two-scale time homogenization formulation and the corresponding algorithms are proposed for coupled viscoelastic viscoplastic (VE-VP) homogeneous solids subjected to large numbers of cycles. The main aim is to predict the long time response while reducing the computational cost considerably. The method is based on the definition of macro and micro-chronological time scales, and on asymptotic expansions of the unknown variables. First, the VE-VP constitutive model is formulated based on a thermodynamical framework. Next, the original VE-VP initial-boundary value problem is decomposed into coupled micro-chronological (fast time scale) and macro-chronological (slow time-scale) problems. The former is purely VE, and solved once for each macro time step, whereas the latter problem is nonlinear and solved iteratively using fully implicit time integration. For micro-scale time averaging, one-point and multi-point integration algorithms are developed. Several numerical simulations on uniaxial and multiaxial cyclic loadings illustrate the computational efficiency and the accuracy of the proposed methods. (C) 2015 Elsevier Ltd. All rights reserved.