In this work, an extension of the strain energy for fibrous metamaterials composed of two families of parallel fibers lying on parallel planes and joined by connective elements is proposed. The suggested extension concerns the possibility that the constituent fibers come into contact and eventually scroll one with respect to the other with consequent dissipation due to friction. The fibers interact with each other in at least three different ways: indirectly, through microstructural connections that could allow a relative sliding between the two families of fibers; directly, as the fibers of a family can touch each other and can scroll introducing dissipation. From a mathematical point of view, these effects are modeled first by introducing two placement fields for the two fiber families and adding a coupling term to the strain energy and secondly by adding two other terms that take into account the interdistance between the parallel fibers and the Rayleigh dissipation potential (to account for friction).

在这项工作中，提出了对纤维超材料的应变能的扩展，该超材料由位于平行平面上并由连接元素连接的两个平行纤维家族组成。建议的扩展涉及组成纤维接触并最终使其中一个相对于另一根滚动并因此由于摩擦而耗散的可能性。纤维以至少三种不同的方式彼此相互作用：通过微观结构连接间接地进行，该微观结构连接可以允许两个纤维家族之间的相对滑动。直接作用，因为一个家庭的纤维可以相互接触并滚动滚动，从而导致耗散。从数学的角度来看，