Starting from the seminal works of Toupin, Mindlin and Germain, a wide class of generalized elastic models have been proposed via the principle of virtual work, by postulating expressions of the elastic energy enriched by additional kinematic descriptors or by higher gradients of the placement. More recently, such models have been adopted to describe phenomena which are not consistent with the Cauchy-Born continuum, namely the size dependence of apparent elastic moduli observed for micro and nano-objects, wave dispersion, optical modes and band gaps in the dynamics of heterogeneous media. For those structures the mechanical response is affected by surface effects which are predominant with respect to the bulk, and the scale of the external actions interferes with the characteristic size of the heterogeneities. Generalized continua are very often referred to as media with microstructure although a rigorous deduction is lacking between the specific microstructural features and the constitutive equations. While in the forward modelling predictions of the observations are provided, the actual observations at multiple scales can be used inversely to integrate some lack of information about the model. In this review paper, generalized continua are investigated from the standpoint of inverse problems, focusing onto three topics, tightly connected and located at the border between multiscale modelling and the experimental assessment, namely: (i) parameter identification of generalized elastic models, including asymptotic methods and homogenization strategies; (ii) design of non-conventional tests, possibly integrated with full field measurements and advanced modelling; (iii) the synthesis of meta-materials, namely the identification of the microstructures which fit a target behaviour at the macroscale. The scientific literature on generalized elastic media, with the focus on the higher gradient models, is fathomed in search of questions and methods which are typical of inverse problems theory and issues related to parameter estimation, providing hints and perspectives for future research.

从 Toupin、Mindlin 和 Germain 的开创性工作开始，通过虚功原理，通过假设由额外的运动学描述符或更高的放置梯度丰富的弹性能量的表达式，提出了一类广泛的广义弹性模型。最近，此类模型已被用来描述与柯西玻恩连续体不一致的现象，即微观和纳米物体观察到的表观弹性模量的尺寸依赖性、波色散、光学模式和动力学中的带隙。异构媒体。对于这些结构，机械响应受到相对于体积而言占主导地位的表面效应的影响，并且外部作用的规模会干扰异质性的特征尺寸。尽管在特定的微观结构特征和本构方程之间缺乏严格的推导，但广义连续体通常被称为具有微观结构的介质。虽然在正演模型中提供了观测值的预测，但可以反向使用多个尺度的实际观测值来整合模型中一些缺乏的信息。 在这篇综述论文中，从反问题的角度研究了广义连续体，重点关注三个紧密相连且位于多尺度建模和实验评估之间边界的主题，即：（i）广义弹性模型的参数识别，包括渐近模型方法和同质化策略； (ii) 非常规测试的设计，可能与全场测量和高级建模相结合； （iii）超材料的合成，即识别符合宏观尺度目标行为的微观结构。深入研究广义弹性介质的科学文献，重点关注较高梯度模型，寻找逆问题理论和参数估计相关问题的典型问题和方法，为未来的研究提供提示和视角。