一种显式子步应力点积分算法及其在SMA数值模拟中的应用

形状记忆合金（shape memory alloys，简称SMA）具有复杂的热力本构关系，为了模拟SMA及其组合结构复杂的受力和变形行为，在数值模拟中需要采用可靠且高效的应力点积分算法．隐式应力点回映算法已经成功应用于形状记忆合金的数值模拟，但在复杂加载条件下,荷载增量较大时有可能导致整体非线性迭代求解不收敛．推广了局部误差控制的显式子步积分算法，首次将其应用于形状记忆合金及其组合结构这类热力相变问题的应力点积分，并通过数值算例对所提算法和隐式应力点回映算法进行了比较．数值结果表明:对于大规模数值模拟和计算，整体子步步数决定着总体计算时间；所提出的修正Euler自动子步方案可以有效减少整体子步步数，在保证相同计算精度的前提下能够大幅提高有限元计算效率，因而更适合大规模形状记忆合金智能结构的数值模拟.

An Explicit Sub-Stepping Stress Integration Method and Its Applications in Numerical Simulations of SMA

Shape memory alloy (SMA) has complex thermomechanical constitutive relation, thus its numerical simulations demand reliable and efficient stress integration algorithms. The implicit return mapping stress point algorithms, which have been successfully applied to such materials, may encounter convergence difficulties when loading conditions are complicated or load steps are large. Hence, an explicit sub stepping stress integration method with automatic local error control was proposed for the simulation of the thermomechanical constitutive relation of shape memory alloys. By investigating several numerical examples, the efficiency of the proposed method and the implicit return mapping stress point algorithm were evaluated and compared. Numerical results indicate that the number of global sub-steps dominates the entire analyzing time for large-scale computations.The proposed modified Euler automatic sub-stepping scheme leads to less global sub-steps so that the computing time is significantly reduced. Therefore, the explicit sub-stepping stress integration method has the potential for large-scale SMA simulations and computations.