The paper deals with the isogeometric analysis (IGA) of active composite laminates with piezoelectric layers. IGA is a special formulation of the finite element method (FEM) that aims at seamless integration of geometric and finite element modelling....

Machine learning methods are progressively investigated for a large amount of applications. Recently, the solution of partial differential equations (PDE) describing problems in elastostatics came into focus. The current work investigates two neural network-based classes of methods for their solution, namely the neural finite element method (FEM) and neural operator methods. The analysis of these approaches is carried out by means of numerical experiments with linear and nonlinear material behavior where the conventional FEM serves as a benchmark. The formulation of neural FEM allows for elegant integration of finite deformation hyperelasticity at medium training effort. Here, training data are replaced by the evaluation of the equilibrium PDE at sample points. In contrast, most neural operator methods require expensive training with large data sets, but then allow for solving multiple boundary value problems with the same machine learning model. For the comparative analysis, the maximal relative error values over the whole domain and over all components of the strain tensor are evaluated as accuracy measure. The current state of research shows that none of the methods investigated reaches the accuracy and computational performance of the conventional FEM. In many standard applications, the FEM achieves an accuracy of $$10^{-6}$$10 - 6 , whereas the numerical tests in the present work report a relative error of order of magnitude of $$10^{-4}$$10 - 4 for the neural FEM and $$10^{-2}$$10 - 2 to $$10^{-3}$$10 - 3 for neural operator methods.

Flexoelectricity arises in materials under strain gradients, which can be particularly significant for situations in which the existence of other electromechanical properties is absent or generating large flexoelectric properties is achievable. This effect has also been observed in some biological materials, whose understanding can hugely help to further enhance our understanding of vital biological processes like mechanotransduction, as well as the development of applications in regenerative medicine and drug delivery. While the field of flexoelectricity as a relevant topic in biological materials is relatively new and still developing, the current study aims to review available results on flexoelectric effects in biological materials such as cells and cell membranes, hearing mechanisms, and bone, and their potential applications in biomedical research. Therefore, we first provide a brief background on two main electromechanical couplings (piezoelectricity and flexoelectricity) and further, how flexoelectricity has been experimentally and theoretically identified. We then review flexoelectricity in different biological materials as the main aim of the current study. Within that, we provide additional emphasis on the influence of this effect on bone and bone remodeling. In particular, the study outlines current limitations and provides potential directions for future work, emphasizing the crucial role in the development of next-generation electromechanical devices and optimizing their function in the area of biomedical research.

The interior of a eukaryotic cell is a highly complex composite material which consists of water, structural scaffoldings, organelles, and various biomolecular solutes. All these components serve as obstacles that impede the motion of vesicles. Hence, it is hypothesized that any alteration of the cytoskeletal network may directly impact or even disrupt the vesicle transport. A disruption of the vesicle-mediated cell transport is thought to contribute to several severe diseases and disorders, such as diabetes, Parkinson’s and Alzheimer’s disease, emphasizing the clinical relevance. To address the outlined objective, a multiscale finite element model of the diffusive vesicle transport is proposed on the basis of the concept of homogenization, owed to the complexity of the cytoskeletal network. In order to study the microscopic effects of specific nanoscopic actin filament network alterations onto the vesicle transport, a parametrized three-dimensional geometrical model of the actin filament network was generated on the basis of experimentally observed filament densities and network geometries in an adenocarcinomic human alveolar basal epithelial cell. Numerical analyzes of the obtained effective diffusion properties within two-dimensional sampling domains of the whole cell model revealed that the computed homogenized diffusion coefficients can be predicted statistically accurate by a simple two-parameter power law as soon as the inaccessible area fraction, due to the obstacle geometries and the finite size of the vesicles, is known. This relationship, in turn, leads to a massive reduction in computation time and allows to study the impact of a variety of different cytoskeletal alterations onto the vesicle transport. Hence, the numerical simulations predicted a 35% increase in transport time due to a uniformly distributed four-fold increase of the total filament amount. On the other hand, a hypothetically reduced expression of filament cross-linking proteins led to sparser filament networks and, thus, a speed up of the vesicle transport.