Abstract Fused deposition modeling (FDM) is a commonly used three-dimensional (3D) printing technology that can program shape memory polymers (SMPs) with performance-driven self-deforming functions. Deformation programming of four-dimensional (4D) printed models is particularly important for many applications. The purpose of this study was to develop an accurate simulation method for FDM-printed monolayer SMP models based on the secondary development of ABAQUS software, which could accurately and simply simulate the deformation processes of various pre-programmed structures. The constitutive function of SMPs used in engineering applications was developed to describe their thermo-mechanical parameters. Based on the constitutive model, the degree and mode of model deformation due to external temperature were simulated by configuring the anisotropic pre-strain stored in the printed model. As a result, the deformation of the SMP models controlled by structural parameters was consistent with the simulation results. The self-folding origami structures controlled by structural factors were designed by the proposed simulation method. The origami structures folded according to the predicted deformation angle and direction under thermal stimulation. Verifiably, this method was able to accurately simulate the deformations of complex 3D models with different structural parameters. This work can advance the development of FDM printed pre-programmed self-deformed SMP structure.

中文翻译：

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一种精确的有限元方法，用于对由熔融沉积建模产生的 4D 打印自变形结构进行编程

摘要 熔融沉积建模 (FDM) 是一种常用的三维 (3D) 打印技术，可以对形状记忆聚合物 (SMP) 进行编程，使其具有性能驱动的自变形功能。四维 (4D) 打印模型的变形编程对于许多应用来说尤其重要。本研究的目的是在ABAQUS软件二次开发的基础上，开发一种FDM打印单层SMP模型的精确模拟方法，可以准确、简单地模拟各种预编程结构的变形过程。开发了工程应用中使用的 SMP 的本构函数来描述它们的热机械参数。基于本构模型，通过配置存储在打印模型中的各向异性预应变来模拟由于外部温度引起的模型变形的程度和模式。因此，由结构参数控制的 SMP 模型的变形与模拟结果一致。通过所提出的模拟方法设计了受结构因素控制的自折叠折纸结构。折纸结构在热刺激下根据预测的变形角度和方向折叠。可验证的是，该方法能够准确模拟具有不同结构参数的复杂 3D 模型的变形。这项工作可以推进 FDM 印刷预编程自变形 SMP 结构的发展。结构参数控制的SMP模型变形与模拟结果一致。通过所提出的模拟方法设计了受结构因素控制的自折叠折纸结构。折纸结构在热刺激下根据预测的变形角度和方向折叠。可验证的是，该方法能够准确模拟具有不同结构参数的复杂 3D 模型的变形。这项工作可以推进 FDM 印刷预编程自变形 SMP 结构的发展。结构参数控制的SMP模型变形与模拟结果一致。通过所提出的模拟方法设计了受结构因素控制的自折叠折纸结构。折纸结构在热刺激下根据预测的变形角度和方向折叠。可验证的是，该方法能够准确模拟具有不同结构参数的复杂 3D 模型的变形。这项工作可以推进 FDM 印刷预编程自变形 SMP 结构的发展。折纸结构在热刺激下根据预测的变形角度和方向折叠。可验证的是，该方法能够准确模拟具有不同结构参数的复杂 3D 模型的变形。这项工作可以推进 FDM 印刷预编程自变形 SMP 结构的发展。折纸结构在热刺激下根据预测的变形角度和方向折叠。可验证的是，该方法能够准确模拟具有不同结构参数的复杂 3D 模型的变形。这项工作可以促进 FDM 印刷预编程自变形 SMP 结构的发展。