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为有效模拟形状记忆合金增强聚合物基复合材料(SMA/PMCs)有效时变和伪弹性响应,基于变分渐近理论框架构建增量型细观力学模型。首先分别导出聚合物和形状记忆合金增量本构方程,建立统一的本构方程;以此为基础推导出能量泛函的变分表达式。考虑材料的时变和非线性特征,建立与求解切向瞬时有效矩阵有关的增量过程,并通过有限元数值实现。通过数值算例表明:构建的模型可用于模拟SMA/PMCs在不同加载率和温度下的有效时变、伪弹性响应,准确捕捉聚合物基体黏弹性诱发的复合材料率相关、滞回行为等。
In order to effectively simulate the effective time-varying and pseudo-elastic responses of shape memory alloy (SMA) reinforced polymer matrix composites (SMA / PMCs), an incremental meso-mechanics model was constructed based on the variational asymptotic theory. Firstly, the incremental constitutive equations of polymer and shape memory alloy are deduced respectively and a unified constitutive equation is established. Based on this, the variational expressions of energy functional are deduced. Considering the time-varying and nonlinear characteristics of the material, an incremental process related to the solution of the tangential instantaneous effective matrix is established and implemented by finite element numerical method. Numerical examples show that the model can be used to simulate the effective time-varying and pseudo-elastic response of SMA / PMCs under different loading rates and temperatures, and accurately capture the viscoelasticity-induced rate-dependent and hysteretic behavior of composite matrix.