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Item type:Publication, Access status: with files , Physics‐informed recurrent neural networks for predicting elasto‐plastic behavior in hierarchical finite element modelingNanoporous gold, with its hierarchical structure comprising interconnected networks on multiple length scales, poses significant computational challenges for traditional modeling methods. To solve this challenge, this study introduces a physics‐informed recurrent neural network (RNN) to model the homogenized material response of a diamond beam‐based representative volume element representing the lower level of hierarchy (LL), which was integrated as a material subroutine within an upper level (UL) finite element simulation. The RNN predicts the tangent stiffness matrix as a primary output from given strain trajectories. Secondary outputs such as stress, plastic strain, and plastic energy increments are derived through embedded physical relationships, ensuring physical consistency across the outputs. The RNN architecture enforces positive energy dissipation inherently through positive eigenvalues of the tangent stiffness matrix and further through penalization of negative energy increments, promoting thermodynamically consistent predictions. A two‐level hierarchical approach is employed, where the 2D UL model is subjected to uniaxial strain, while multiaxial strain conditions naturally arise locally within the structure. The inclusion of the LL significantly modifies the strain trajectories observed at the UL, while stress trajectories, although maintaining their general trend, experience considerable changes in magnitude. This approach demonstrates the capability to efficiently simulate hierarchical materials, capturing the influence of LL porosity on the UL material behavior while maintaining physical consistency. Additionally, the model allows for straightforward integration into finite element frameworks like Abaqus, offering a computationally efficient method for studying complex hierarchical materials.Publicationtype: Journal Article7 2 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Data-driven modelling of the multiaxial yield behaviour of nanoporous metalsNanoporous metals, built out of complex ligament networks, can be produced with an additional level of hierarchy. The resulting complexity of the structure makes modelling of the mechanical behaviour computationally expensive and time consuming. In addition, multiaxial stresses occur in the higher hierarchy ligaments. Therefore, knowledge of the multiaxial material behaviour, including the 6D yield surface, is required. Surrogate models, predicting the mechanical behaviour of the lower level of hierarchy, represented by finite element beam models, are a promising approach to overcome such challenges, when existing analytical models are not able to describe the material behaviour. Therefore, as a first step, we studied the elastic behaviour and the yield surfaces of representative volume elements with idealised diamond and Kelvin structure in finite element simulations. The yield surfaces showed pronounced anisotropy and could not be described by the Deshpande-Fleck model for isotropic solid foams. Instead, we used data-driven and hybrid artificial neural networks, as well as data-driven support vector machines and compared them regarding their potential for the prediction of yield surfaces. All considered methods were well suited and resulted in relative errors <4.5%. Support vector machines showed the best generalisation and accuracy in 6D stress space and are suitable for extrapolation outside the range of training data.Publicationtype: Journal ArticleScopus© Citations 5 57 81 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Simulated annealing framework for generating representative volume elements of materials with complex ligamentous microstructuresAt the microscale, various materials from biological tissues to nanoporous metals are formed by networks of ligaments. Here we propose a highly efficient simulated annealing (SA) framework for generating synthetic representative volume elements (RVE) of such materials. It can produce RVE where the microstructural characteristics both on the network level (e.g., node valency and ligament length) and on the level of individual ligaments (e.g., curvature) can be predefined by the user via probability distributions. As an application example of our framework, we generate a large variety of RVEs, analyze their mechanical properties by the finite element method, and establish through this approach links between microstructural descriptors and macromechanical properties of materials with ligamentous microstructures.Publicationtype: Journal Article47