Strain Gradient Continuum Models for Linear Pantographic Structures: A Classification Based on Material Symmetries

Abstract

We analyze the mechanics of planar networks of extensible fibers, for which we derive the general form of the mechanical energy. We consider especially networks made of two sets of non orthogonal and non equivalent fibers, called the parallelogram structure, with variants obtained as specific patterns called the square, rectangular, and rhombic structures. The fibers of the network are assumed to obey Bernoulli kinematics. A second order gradient continuum is obtained. The arguments of the energy of these four patterns are obtained based on the material symmetry group of the considered structures.