## 1 Introduction  
Improving the energy efficiency and achieving new performance levels of vehicles, machines and facilities is a continuous challenge for engineering and science. As an indispensable instrument for this goal, a consistent implementation of lightweight construction principles has been widely recognised. Integral design with a reduced number of joints as well as hybrid materials combining polymers, ceramics, lightweight alloys and composites offer the possibility to develop components with material effort optimised for the distribution of the operational loads. Fibre-reinforced plastics with \"tailored\" reinforcement especially enable an application-dependent trade-off between stiffness and damping combined with a damage tolerant design of dynamically loaded components [1; 2; 3; 4]. An ultimately stiffness/strength-oriented design, however, often causes a problematic vibration susceptibility, especially of common thin-walled components and makes the application of additional damping measures necessary. A number of such measures are being fundamentally conceptualised, mathematically and numerically modelled, as well as experimentally validated in numerous scientific projects. Herein, some recent representative examples include:  
* special sandwich panel cores, for example, in form of truss structures combined with intermediate layers of damping materials [5] or filled with granular materials [6], including cores with voids of optimised geometries [7],
* locally acting dampers such as compact acoustic black holes [8; 9], structurally integrated resonant metamaterials [10] and joints with viscoelastic damping [11],
* active magneto-/electro- or photorheological layers with the damping and stiffness controlled by magnetic, electric field or light, respectively [12; 13; 14; 15; 16],
* extended concepts of shunted piezoelectric actuator systems [17; 18; 19; 20],
* distributed active damping systems that use numerous vibration sensors and actuators attached to complex shaped structures, driven by real-time controllers [21; 22]. Most of these damping approaches achieved very good results. However, the total implementation costs of semi-active and especially of active damping systems are still high; also the additional mass of the structure-integrated and peripheral hardware is an essential drawback for many applications. Modelling, design and manufacturing methods that address the principle of passive damping layers are being further developed. Especially treatments belonging to the family of Constrained Layer Damping (CLD) in which damping layers are forced to shear deformations while the base structure vibrates in bending modes are applied for structures with complex geometries [23; 24]. Partial coverage with CLD segments of optimised shape is a common measure enabling a reduction of the mass overhead caused by the damping treatment [25]. On the one hand, the material configuration of CLD has not essentially changed for a long time. Bitumen- and rubber-based viscoelastic materials with some modifications, for example, particle addition, are still used, sometimes in combination with piezoelectric materials allowing an active behaviour of the damping treatment [26]. A concept followed in this publication, namely the replacement of the an uncompressible damping layer with a compressible one was considered until now solely by the authors [27; 28]. The compressibility of the damping layer can be achieved by the application of open-cell foams. This requires, however, in addition to appropriate modelling, sufficient material data, in particular regarding shear behaviour under compression. The monoaxial compressional behaviour of polymer-based open-cell foams has been already investigated [29; 30; 31]. The shear behaviour of open cell foams has so far only been investigated by Reference [32] but without precompression of the foams.