Neural Networks for Constitutive Modeling -- From Universal Function Approximators to Advanced Models and the Integration of Physics

Analyzing and modeling the constitutive behavior of materials is a core area in materials sciences and a prerequisite for conducting numerical simulations in which the material behavior plays a central role. Constitutive models have been developed since the beginning of the 19th century and are still under constant development. Besides physics-motivated and phenomenological models, during the last decades, the field of constitutive modeling was enriched by the development of machine learning-based constitutive models, especially by using neural networks. The latter is the focus of the present review, which aims to give an overview of neural networks-based constitutive models from a methodical perspective. The review summarizes and compares numerous conceptually different neural networks-based approaches for constitutive modeling including neural networks used as universal function approximators, advanced neural network models and neural network approaches with integrated physical knowledge. The upcoming of these methods is in-turn closely related to advances in the area of computer sciences, what further adds a chronological aspect to this review. We conclude this review paper with important challenges in the field of learning constitutive relations that need to be tackled in the near future

A multi-task learning-based optimization approach for finding diverse sets of material microstructures with desired properties and its application to texture optimization

The optimization along the chain processing-structure-properties-performance is one of the core objectives in data-driven materials science. In this sense, processes are supposed to manufacture workpieces with targeted material microstructures. These microstructures are defined by the material properties of interest and identifying them is a question of materials design. In the present paper, we addresse this issue and introduce a generic multi-task learning-based optimization approach. The approach enables the identification of sets of highly diverse microstructures for given desired properties and corresponding tolerances. Basically, the approach consists of an optimization algorithm that interacts with a machine learning model that combines multi-task learning with siamese neural networks. The resulting model (1) relates microstructures and properties, (2) estimates the likelihood of a microstructure of being producible, and (3) performs a distance preserving microstructure feature extraction in order to generate a lower dimensional latent feature space to enable efficient optimization. The proposed approach is applied on a crystallographic texture optimization problem for rolled steel sheets given desired properties

Deep Reinforcement Learning Methods for Structure-Guided Processing Path Optimization

A major goal of materials design is to find material structures with desired properties and in a second step to find a processing path to reach one of these structures. In this paper, we propose and investigate a deep reinforcement learning approach for the optimization of processing paths. The goal is to find optimal processing paths in the material structure space that lead to target-structures, which have been identified beforehand to result in desired material properties. There exists a target set containing one or multiple different structures. Our proposed methods can find an optimal path from a start structure to a single target structure, or optimize the processing paths to one of the equivalent target-structures in the set. In the latter case, the algorithm learns during processing to simultaneously identify the best reachable target structure and the optimal path to it. The proposed methods belong to the family of model-free deep reinforcement learning algorithms. They are guided by structure representations as features of the process state and by a reward signal, which is formulated based on a distance function in the structure space. Model-free reinforcement learning algorithms learn through trial and error while interacting with the process. Thereby, they are not restricted to information from a priori sampled processing data and are able to adapt to the specific process. The optimization itself is model-free and does not require any prior knowledge about the process itself. We instantiate and evaluate the proposed methods by optimizing paths of a generic metal forming process. We show the ability of both methods to find processing paths leading close to target structures and the ability of the extended method to identify target-structures that can be reached effectively and efficiently and to focus on these targets for sample efficient processing path optimization

Polysaccharide capsule composition of pneumococcal serotype 19A subtypes: Unaltered among subtypes and independent of the nutritional environment

Serotype 19A strains have emerged as a cause of invasive pneumococcal disease after the introduction of the seven-valent pneumococcal conjugate vaccine (PCV7) and serotype 19A has now been included in the recent thirteen-valent vaccine (PCV13). Genetic analysis has revealed at least three different capsular serotype 19A subtypes and nutritional environment dependent variation of the 19A capsule structure has been reported. Pneumococcal vaccine effectiveness and serotyping accuracy might be impaired by structural differences in serotype 19A capsules. We therefore analyzed the distribution of 19A subtypes collected within a Swiss national surveillance program and determined capsule composition in different nutritional conditions with high-performance liquid chromatography (HPLC), gas chromatography – mass spectrometry (GC-MS) and nuclear magnetic resonance spectroscopy (NMR). After the introduction of PCV7 a significant relative increase of subtype 19A-II and decrease of 19A-I occurred. Chemical analyses showed no difference in the composition as well as the linkage of 19A subtype capsular saccharides grown in defined and undefined growth media being consistent with a trisaccharide repeat unit composed of rhamnose, N-acetyl-mannosamine and glucose. In summary, our study suggests that no structural variance dependent of the nutritional environment or the subtype exists. The serotype 19A subtype shift observed after the introduction of the PCV7 can therefore not be explained by selection of a capsule variant. However, capsule composition analysis of emerging 19A clones is recommended in cases where there is no other explanation for a selective advantage such as antibiotic resistance or loss or acquisition of other virulence factor

Crystallographic texture-property data set originating from a simulated multi-step metal forming process

This publication contains a set of 76980 samples of crystallographic textures (as lists of orientations) and corresponding properties (Youngs modulus E and an anisotropy measure R*, similar to the Lankford coefficients, in three room directions). The data originates from a simulated multi-step metal forming process. The simulation was constrained to perform seven successive process steps of 10% strain at the material point in different directions. In each step, the orientation of the tension operation is chosen randomly from a set of 25 uniformly distributed orientations in the orientation space SO(3)

Simulation of texture evolution for a multi-step metal forming process

The published code performs a metal forming process simulation. The process consists of subsequent steps of uniaxial tension and compression, arbitrarily oriented to a reference coordinate system. The simulation is based on a Taylor-type crystal plasticity model. To run the simulation, Intel Fortran libraries are needed

CupNet - Pruning a network for geometric data

Using data from a simulated cup drawing process, we demonstrate how the inherent geometrical structure of cup meshes can be used to effectively prune an artificial neural network in a straightforward way