Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium
Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium
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DOI：
10.1098/rspa.2015.0790
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发表时间：
2016-01-01
影响因子：
3.5
通讯作者：
Rizzi, N. L.
中科院分区：
文献类型：
--
作者：
dell'Isola, F.;Giorgio, I.;Rizzi, N. L.
本文的目的是找到一个计算效率和预测模型的类系统，我们称之为“缩放结构”。对这些材料的兴趣因三维打印技术的扩散而增加。一旦选择了合适的长度尺度，它们可以被视为通过枢轴相互连接并经历大位移和大变形的梁（也称为纤维）族。然而，在非线性梁理论的文献中，相对较少的“现成的”结果。在本文中，我们考虑一个离散弹簧模型的可扩展梁，并提出了一种启发式均匀化技术的皮奥拉第一次使用的连续完全非线性梁模型制定。均匀化的能量，我们得到了一些独特的和有趣的功能，我们开始描述通过数值求解一些示例性的变形问题。此外，我们考虑了缩放结构，找到了相应的均匀化第二梯度变形能，并研究了一些平面问题。这些二维问题的数值解通过能量最小化得到，并与一些实验测量，其中伸长现象不能忽略。
The aim of this paper is to find a computationally efficient and predictive model for the class of systems that we call 'pantographic structures'. The interest in these materials was increased by the possibilities opened by the diffusion of technology of three-dimensional printing. They can be regarded, once choosing a suitable length scale, as families of beams (also called fibres) interconnected to each other by pivots and undergoing large displacements and large deformations. There are, however, relatively few 'ready-to-use' results in the literature of nonlinear beam theory. In this paper, we consider a discrete spring model for extensible beams and propose a heuristic homogenization technique of the kind first used by Piola to formulate a continuum fully nonlinear beam model. The homogenized energy which we obtain has some peculiar and interesting features which we start to describe by solving numerically some exemplary deformation problems. Furthermore, we consider pantographic structures, find the corresponding homogenized second gradient deformation energies and study some planar problems. Numerical solutions for these two-dimensional problems are obtained via minimization of energy and are compared with some experimental measurements, in which elongation phenomena cannot be neglected.