Contrasting bending energies from bulk elastic theories.

The choice of elastic energies for thin plates and shells is an unsettled issue with consequences for much recent modeling of soft matter. Through consideration of simple deformations of a thin body in the plane, we demonstrate that four bulk isotropic quadratic elastic theories have fundamentally different predictions with regard to bending behavior. At finite thickness, these qualitative effects persist near the limit of mid-surface isometry, and not all theories predict an isometric ground state. We discuss how certain kinematic measures that arose in early studies of rod mechanics lead to coherent definitions of stretching and bending, and promote the adoption of these quantities in the development of a covariant theory based on stretches rather than metrics.

选择薄板和壳的弹性能量是一个未安排的问题，对软物质的许多最新建模产生了影响。通过考虑平面中薄体的简单变形，我们证明了四个散装各向同性二次弹性理论在弯曲行为方面具有根本不同的预测。在有限的厚度下，这些定性效应持续到中表面等轴测图的极限附近，并且并非所有理论都可以预测等轴测基态。我们讨论在杆力学的早期研究中产生的某些运动学测量如何导致伸展和弯曲的连贯定义，并在基于拉伸而非度量的协变理论发展中促进这些数量的采用。