A nonlinear elastic model for nets made up of two families of curved fibers is proposed. The net is planar prior to the deformation, but the equilibrium configuration that minimizes the total potential energy can be a surface in the three-dimensional space. This elastic surface accounts for the stretching, bending, and torsion of the constituent fibers regarded as a continuous distribution of Kirchhoff rods. A specific example of fiber arrangement, namely a cycloidal orthogonal pattern, is examined to illustrate the predictive abilities of the model and assess the limit of applicability of it. A numerical micro–macro-identification is performed with a model adopting a standard continuum deformable body at the level of scale of the fibers. A few finite element simulations are carried out for comparison purposes in statics and dynamics, performing modal analysis. Finally, a topology optimization problem has been carried out to change the macroscopic shear stiffness to enlarge the elastic regime and reduce the risk of damage without excessively losing bearing capacity.

提出了由两类弯曲纤维组成的网的非线性弹性模型。网络在变形之前是平面的，但是使总势能最小化的平衡构型可以是三维空间中的表面。该弹性表面解释了被视为基尔霍夫棒的连续分布的组成纤维的拉伸，弯曲和扭曲。检查了纤维排列的一个特定示例，即摆线正交图案，以说明该模型的预测能力并评估其适用范围。使用在纤维尺度水平上采用标准连续体可变形体的模型对数值进行宏观识别。为了比较静态和动态，进行了一些有限元模拟，执行模态分析。最后，进行了拓扑优化问题，以改变宏观剪切刚度，以扩大弹性范围并降低损坏的风险，而不会过度损失承载能力。