Multi-scale modelling and canonical dual finite element method in phase transitions of solids
Multi-scale modelling and canonical dual finite element method in phase transitions of solids
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DOI：
10.1016/j.ijsolstr.2007.08.027
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发表时间：
2008-06
影响因子：
3.6
通讯作者：
D. Gao;Haofeng Yu
中科院分区：
文献类型：
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作者：
D. Gao;Haofeng Yu
本文提出了一个具有宏观和微观效应的固体材料相变的多尺度模型。该模型由一个半线性非凸偏微分方程化成一个耦合的二次混合变分问题，用正则对偶变换方法可将其转化为耦合的二次混合变分问题。这个变分问题的极值条件由一个三重性理论控制，它揭示了相变中的多尺度效应。为此，首次提出了求解固体多尺度相变中非凸变分问题的正则对偶有限元方法。文中给出了应用实例。结果表明，第一作者在非凸力学中发展的正则对偶理论可以用来模拟复杂的物理现象，并可以很容易地解决某些困难的非凸变分问题。正则对偶有限元方法给计算力学带来了一些新的见解。
This paper presents a multi-scale model in phase transitions of solid materials with both macro and micro effects. This model is governed by a semi-linear nonconvex partial differential equation which can be converted into a coupled quadratic mixed variational problem by the canonical dual transformation method. The extremality conditions of this variational problem are controlled by a triality theory, which reveals the multi-scale effects in phase transitions. Therefore, a potentially useful canonical dual finite element method is proposed for the first time to solve the nonconvex variational problems in multi-scale phase transitions of solids. Applications are illustrated. Results shown that the canonical duality theory developed by the first author in nonconvex mechanics can be used to model complicated physical phenomena and to solve certain difficult nonconvex variational problems in an easy way. The canonical dual finite element method brings some new insights into computational mechanics.