Pantographic fabrics are presented as a paradigmatic example to discuss the research perspective on multiphysics and multiscale materials. Reduced-order modeling, obtained by introducing higher-gradient or microstructured continua, shows much smaller computational needs than those required by full-scale 3D modeling calculations and by equivalent discrete spring systems. Researches already available in the literature compare theoretical predictions with results obtained in real experiments, analyzing both in-plane and out-of-plane deformations possibly induced by local buckling phenomena. The goal is to achieve three major objectives: (1) formulate coarse-scale nonlinear higher-gradient continuum models describing a more general class of pantographic metamaterials, based on finer-scale descriptions, through homogenization techniques; (2) implement finite element analyses with shape functions possessing higher regularity or employing mixed formulations to perform simulations with the above-formulated models; and (3) validate and verify the derived models through the acquisition and analysis of experimental data. These goals would likely push toward the improvement of 3D printing protocols to enhance the quality of the pantographic prototypes and DIC as experiments measurement technique. It can be also conjectured that many macroscopic deformation energies can be synthesized by using as elementary elements, inside periodicity cells, some pantographic modules.

中文翻译：

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多物理场和多尺度材料的研究视角：一个典型案例

弓形织物是一个典型的例子，讨论了多物理场和多尺度材料的研究前景。通过引入更高梯度或微观结构的连续体获得的降阶建模显示的计算需求比全尺寸3D建模计算和等效离散弹簧系统所需的计算需求小得多。文献中已有的研究将理论预测与实际实验中获得的结果进行了比较，同时分析了可能由局部屈曲现象引起的平面内和平面外变形。目的是实现三个主要目标：（1）通过均化技术，基于更细微的描述，制定描述更广义类别的多维超材料的粗尺度非线性高梯度连续谱模型；（2）利用规则性较高的形状函数进行有限元分析，或采用混合公式对上述模型进行仿真。（3）通过获取和分析实验数据来验证和验证衍生模型。这些目标可能会推动3D打印协议的改进，以提高全景图原型的质量以及作为实验测量技术的DIC。还可以推测，通过使用周期性单元内部的某些缩放模块作为基本元素，可以合成许多宏观变形能。（3）通过获取和分析实验数据来验证和验证衍生模型。这些目标可能会推动3D打印协议的改进，以提高全景图原型的质量以及作为实验测量技术的DIC。还可以推测，通过使用周期性单元内部的某些缩放模块作为基本元素，可以合成许多宏观变形能。（3）通过获取和分析实验数据来验证和验证衍生模型。这些目标可能会推动3D打印协议的改进，以提高全景图原型的质量以及作为实验测量技术的DIC。还可以推测，通过使用周期性单元内部的某些缩放模块作为基本元素，可以合成许多宏观变形能。