Cauchy-elastic solids include hyper-elasticity and a subset of elastic materials for which the stress does not follow from a scalar strain potential. More in general, hypo-elastic materials are only defined incrementally and comprise Cauchy-elasticity. Infringement of the hyper-elastic ‘dogma’ is so far unattempted and normally believed to be impossible, as it apparently violates thermodynamics, because energy may be produced in closed strain cycles. Contrary to this belief, we show that non-hyper-elastic behavior is possible and we indicate the way to a practical realization of this new concept. In particular, a design paradigm is established for artificial materials where follower forces, so far ignored in homogenization schemes, are introduced as loads prestressing an elastic two-dimensional grid made up of linear elastic rods (reacting to elongation, flexure and shear). A rigorous application of Floquet–Bloch wave asymptotics yields an unsymmetric acoustic tensor governing the incremental dynamics of the effective material. The latter is therefore the incremental response of a hypo-elastic solid, which does not follow from a strain potential and thus does not belong to hyper-elasticity. Through the externally applied follower forces (which could be originated via interaction with a fluid, or a gas, or by application of Coulomb friction, or non-holonomic constraints), the artificial material may adsorb/release energy from/to the environment, and therefore produce energy in a closed strain loop, without violating any rule of thermodynamics. The solid is also shown to display flutter, a material instability corresponding to a Hopf bifurcation, which was advocated as possible in plastic solids, but never experimentally found and so far believed to be impossible in elasticity. The discovery of elastic materials capable of sucking up or delivering energy in closed strain cycles through interaction with the environment paves the way to realizations involving micro and nano technologies and finds definite applications in the field of energy harvesting.

柯西弹性固体包括超弹性和弹性材料的子集，其应力不遵循标量应变势。更一般地，低弹性材料仅被增量定义并且包括柯西弹性。到目前为止，违反超弹性“教条”是无人尝试的，通常认为是不可能的，因为它显然违反了热力学，因为能量可能会在封闭的应变循环中产生。与这种信念相反，我们表明非超弹性行为是可能的，我们指出了这一新概念的实际实现方式。特别是，为人造材料建立了一种设计范式，其中跟随力，迄今为止在均质化方案中被忽略，引入预应力由线性弹性杆组成的弹性二维网格（对伸长、弯曲和剪切作出反应）。Floquet-Bloch 波渐近的严格应用产生了一个不对称的声学张量，它控制着有效材料的增量动力学。因此后者是的防弹性固体，其不增量响应不从应变势追随，因此不会不属于超弹性. 通过外部施加的跟随力（可以通过与流体或气体的相互作用产生，或通过应用库仑摩擦或非完整约束产生），人造材料可以从环境中吸收/释放能量，并且因此在闭合应变回路中产生能量，而不会违反任何热力学规则。固体还显示出颤振，这是一种与 Hopf 分叉相对应的材料不稳定性，这在塑性固体中被提倡尽可能多，但从未在实验中发现，迄今为止认为在弹性方面是不可能的。