Mechanical properties of aerogels are controlled by the connectivity of their network. In this paper, in order to study these properties, computational models of silica aerogels with different morphological entities have been generated by means of the diffusion-limited cluster–cluster aggregation (DLCA) algorithm. New insights into the influence of the model parameters on the generated aerogel structures and on the finite deformation under mechanical loads are provided. First, the structural and fractal properties of the modeled aerogels are investigated. The dependence of morphological properties such as the particle radius and density on these properties is studied. The results are correlated with experimental small-angle X-ray scattering (SAXS) data of a silica aerogel. The DLCA models of silica aerogels are analyzed for their mechanical properties with finite element simulations. There, the aerogel particles are modeled as nodes and the interparticle bonds as beam elements to account for bond stretching, bending, and torsion. The scaling relation between the elastic moduli E and relative density ρ, E ∝ ρ m , is investigated and the exponent m = 3.61 is determined. Backbone paths evidently appear in the 3-d network structure under deformation, while the majority of the bonds in the network do not bear loads. The sensitivity of particle neck-sizes on the mechanical properties is also studied. All the results are shown to be qualitatively as well as quantitatively in agreement with the experimental data or with the available literature.

The structural features in silica aerogels are known to be modelled effectively by the diffusion-limited cluster-cluster aggregation (DLCA) approach. In this paper, an artificial neural network (ANN) is developed for...

In this article, we present a new procedure to automatically generate interpretable hyperelastic material models. This approach is based on symbolic regression which represents an evolutionary algorithm searching for a mathematical model in the form of an algebraic expression. This results in a relatively simple model with good agreement to experimental data. By expressing the strain energy function in terms of its invariants or other parameters, it is possible to interpret the resulting algebraic formulation in a physical context. In addition, a direct implementation of the obtained algebraic equation for example into a finite element procedure is possible. For the validation of the proposed approach, benchmark tests on the basis of the generalized Mooney-Rivlin model are presented. In all these tests, the chosen ansatz can find the predefined models. Additionally, this method is applied to the multi-axial loading data set of vulcanized rubber. Finally, a data set for a temperature-dependent thermoplastic polyester elastomer is evaluated. In latter cases, good agreement with the experimental data is obtained.

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Non‐crimp fabrics (NCFs) are a type of textile characterized by straight and long fibers. Due to their lightweight structures, they are widely used for fiber‐reinforced composites in automotive, aerospace, and other fields. NCFs consist of several differently oriented layers of unidirectional fibers, stacked on top of each other, and stitched together by stitching yarns. Due to this structure, constitutive modeling of the anisotropic properties of NCFs is still challenging requiring an accurate description, especially for multi‐axial loading. In this work, a deep learning framework constructed by artificial neural networks (ANNs) is presented that describes the constitutive behavior of NCFs. Such a framework is able to learn not only from the provided load‐displacement relation by experimental data of existing materials, but also from additional relevant information, such as geometric characteristics. The framework allows predicting the constitutive behavior of new fabric materials, whose experimental data are unavailable yet. This contribution aims to establish a constitutive model of dry NCFs based on a deep learning framework trained from virtual experimental data provided by finite element simulations of representative volume elements (RVEs) at the mesoscale. NCFs with only two families of fibers perpendicular to each other and stitched together are considered. The proposed constitutive model is capable of predicting the in‐plane material response of NCFs under arbitrary multi‐axial loading conditions. To this end, a procedure of training ANN for reaction forces responding to displacements of RVEs is investigated. In order to guarantee the predictive capability for various NCFs under multi‐axial loading conditions, the artificial neural network is used to learn from simulations of the same RVE provided by changing its fiber bundle properties (tensile moduli and shear moduli) and loading directions at the mesoscale. Finally, the proposed constitutive model is verified by comparing the predictive results with reference data sets for various materials in arbitrary axial loading.

Recently, data-driven approaches in the field of material modeling have gained significant attention. A major advantage of these approaches is the direct integration of experimental results into the models. Nevertheless, artificial neural networks (ANNs) are especially challenging to interpret from a physical point of view, since internal processes of ANNs are difficult to understand.In this work a new automatic method for the generation of constitutive models for hyperelastic materials is introduced. The presented method is based on symbolic regression, which is a genetic algorithm. Thereby, a mathematical model in the form of an algebraic expression is found that fits the given data as accurately as possible and has a compact representation. The strain energy density function is determined directly as a function of the strain invariants. The proposed ansatz is embedded into a continuum mechanical framework combining the benefits of known physical relations with the unbiased optimization approach of symbolic regression. Benchmark tests for the generalized Mooney-Rivlin model for uniaxial, equibiaxial and pure shear tests are presented. Finally, the presented procedure is tested on a temperature-dependent dataset of a thermoplastic polyester elastomer. A good agreement between obtained material models and experimental data is demonstrated.

Silica aerogels are highly porous ultralight materials with extremely low density and thermal conductivity. These exceptional properties of silica aerogels are often accounted to microstructure morphology, thus making them of keen research interest for analysing their structure-property relationships. The classical approach for this involved the microstructure modelling of the silica aerogels with aggregation-based modelling algorithm viz., diffusion-limited cluster-cluster aggregation (DLCA) and then performing finite element method (FEM) on the generated representative volume element (RVEs). However, the process often requires large computation time and resources.The objective of this work was thus to introduce an artificial intelligence approach based on neural networks and reinforcement learning to eliminate the necessity of generating and simulating 3D silica aerogel models for predicting their structural and mechanical properties. To this end for the forward prediction of the elastic modulus and fractal dimension of the silica aerogels from DLCA parameters, an artificial neural network was developed. Furthermore, to reverse engineer the material and perform inverse material design, a reinforcement learning framework was developed, that is shown to have learned to determine appropriate DLCA model parameters as actions for a desired fractal dimension and elastic modulus.

Silica aerogels are highly porous solids with very low densities and thermal conductivities. Their high porosity results in a fractal morphology which has a strong influence on their mechanical properties. The geometric structure of silica aerogels can be described by diffusion-limited cluster-cluster aggregation (DLCA) models.In this work, the DLCA method is implemented to model silica aerogel networks and investigate the influence of different input parameters, as for example, varying particle sizes on their fractal properties. The resulting model networks are characterized for their fractal properties and compared with the small angle X-ray scattering (SAXS) results of silica aerogels. Furthermore, their mechanical properties are simulated using the finite element method. There, the effect of varying densities on their mechanical properties is examined. In addition, an artificial neural network (ANN) is trained based on the input parameters of the DLCA algorithm to predict the fractal properties of the silica aerogel model. By inverting the ANN it is possible to identify the necessary inputs to generate desired fractal morphologies with specific mechanical properties.