Wilfried Becker

In mechanical engineering, aerospace engineering and civil engineering, there are many situations where multi‐layer structures are applied. This can, for instance, be the overlap region of an adhesive joint, a local patch reinforcement on a substrate or a substrate with a protective layer. Under given mechanical or thermal loading, due to the dissimilar material properties, stress concentrations will typically arise at the ends of the involved layers, which might lead to the onset of debonding cracks and a subsequent debonding failure. In order to assess such situations in the framework of linear elasticity theory a closed‐form analytical approach is suggested based on layer‐wise displacement representations that take into account singular stress concentrations. From this, by means of the principle of minimum potential energy, an approximate closed‐form description of the resultant deformation and stress distribution can be derived and validated by accompanying finite element calculations. In order to assess potential failure in the framework of finite fracture mechanics, debonding cracks of finite length are introduced, and the corresponding incremental energy release is identified. Using the hybrid failure criterion suggested by Leguillon, it can be clearly concluded whether such debonding failure will happen in reality or not. By a corresponding optimization problem, the minimal critical loading leading to failure can also be determined. This is of high significance for the practical application.

Additive manufacturing (AM) offers new possibilities to fabricate and design lightweight lattice materials. Due to the superior mechanical properties of these lattice structures, they have the potential to replace honeycombs as cores in sandwich panels. In addition to the advantage of the integral fabrication thanks to AM, additively manufactured lattice core sandwich panels may be also used as heat exchangers, enabling a multifunctional use of the core. To ensure a reliable and safe structure, the mechanical response of lattice core sandwich panels under given load conditions must be predictable. In conventional sandwich panels subjected to compressive loads, the sandwich’s global buckling and the face sheets’ local buckling are the dominant failure modes. In constrast, core strut buckling may be the critical failure mode in lattice core sandwich panels. Therefore, an analytical 2D model to predict the local buckling of lattice core struts is considered in this study. Furthermore, the critical load for global buckling is obtained based on the first-order shear deformation theory. Thus, the transition from local buckling to global buckling depending on the length-to-thickness ratio is captured by the presented model. The comparison with finite element modeling of the sandwich model with truss cores has proved the accuracy of the derived model.

The design of graded and multifunctional lattice cores is driven by the increasing demand for high-performance components in lightweight engineering. This trend benefits from significant achievements in additive manufacturing, where the lattice core and the face sheets are fabricated simultaneously in a single print job. This work systematically compares the mechanical performance of sandwich panels comprising various graded lattice cores subjected to concentrated loads. In addition to graded lattice cores, uniform lattices and conventional honeycomb cores are analyzed. To obtain an optimized graded lattice core, a fully stressed design method is applied. Stresses and displacements are determined using a linear elastic analytical model that allows grading the core properties in a layerwise manner through the core thickness. The analysis indicates the superior performance of graded lattice cores compared to homogeneous lattice cores. However, conventional honeycombs outperform graded lattice cores in terms of load-to-weight ratio and stiffness-to-weight ratio. This study provides valuable insights for the design of lattice core sandwich panels and the advantages of several design approaches.

Additive manufacturing enables the fabrication of strut-based lattices that consist of periodic representative volume elements (RVE) and can be used as cores in sandwich panels. Due to the design freedom provided by additive manufacturing, the lattice strut diameter may vary through the lattice. Thus, the diameter distribution can be adapted to the stress variation in the sandwich core to achieve an efficient core design and avoid oversizing the core. Such grading approaches are required when the core is subjected to localized loads, e.g., near support points and load application areas. In this work, an analytical model is derived to determine stresses and deformations in lattice struts of RVE-based graded lattice cores in elastic sandwich panels using homogenization and dehomogenization methods. In contrast to already available models, the analytical model presented in this work allows grading the lattice strut diameter both along the sandwich length and through the core thickness. Furthermore, local stresses in the lattice struts caused by concentrated load application can be captured adequately by the present model. To highlight the benefits of graded cores, the strut stress distribution in graded cores is compared to the stress distribution in homogeneous cores.

Bolted joints are often used in thin parts such as plates or shell-like components in lightweight structures, e.g. air- and spacecraft. This is also motivated by an inexpensive manufacturing and the ability to disassemble. To make these joints, holes need to be drilled and stress concentrations arise. Leading to the instantaneous destruction of the connection, attention should be drawn to fatal tension failure. The efficient and precise prediction of the corresponding failure stresses using analytical methods is the focus of this paper. Usually, rows of bolts are placed. Then, the load is partly introduced into one bolt while the rest stays in the plate. This setting is also referred to as bolted joint under combined bearing-bypass load, which shall be idealised as a linear 2D plate problem. The corresponding characteristic stresses are discussed for orthotropic laminates showing good agreement to Finite Element values. Then, failure analysis is conducted using Finite Fracture Mechanics. This part is dedicated to quasi-isotropic laminates. The size effect and in this context the failure stress reduction with increasing bolt diameter is analysed. Primary physical effects due to finite dimensions and the ratio of bearing and total load are identified. The higher this ratio and the larger the bolt diameter, the lower the sustained failure stress. Failure envelopes for the graphical determination of the critical bearing and bypass stresses are provided. All in all, a comprehensive and efficient framework for tension failure assessment of composite bolted joints under bearing-bypass load interaction is developed.

In the present study, a two-dimensional stress-function method is applied to model the axial strain distribution in the tungsten disulfide (WS₂) flake embedded in an epoxy/polymethyl methacrylate nanocomposite structure subjected to an axial tension load. The analytical model strain distribution along the flake is calculated and compared with experimental and shear-lag model literature data for monolayer flake at an external strain of 0.35% and 0.55%, as well as with results for few-layer flakes at an external strain of 0.55%. The comparison shows good agreement and confirms the applicability of our model method for describing strains in nanocomposite layered structures in the elastic region of applied loads. The presented method is not appropriate for few layers flake at an external strain of 0.55% because of the appearance of relaxation zone and the formation of wrinkles in the flake.

The design and analysis of composite structures in the form of layered plates or shells is often driven by stress concentration phenomena that occur due to geometric or material discontinuities. One prominent example is the so-called free-edge effect that manifests itself in the form of significant localized interlaminar stress fields in the vicinity of free laminate edges and that is given rise to due to the mismatch of the elastic properties of the individual laminate layers. The free-edge effect has been under scientific investigation for more than five decades, and this paper aims at providing an overview of recent developments and scientific advances in this specific field wherein an emphasis is placed on investigations that were published in the time range between the years 2005 and 2020. This paper reviews closed-form analytical methods as well as semi-analytical and numerical analysis approaches and summarizes the recent state of the art concerning the investigation of stress singularities and experimental characterization of free-edge effects. This paper also reviews advanced problems such as free-edge effects in curved laminated structures and in piezoelectric laminates as well as in the vicinity of holes and other geometric discontinuities, and two new aspects in the field of free-edge effects, namely, the development and application of a new semi-analytical method (the so-called scaled boundary finite element method (SBFEM)) and the fracture mechanical strength assessment, also by novel approaches such as finite fracture mechanics, are also discussed. This paper closes with a summary and an outlook on future investigations.