Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems

Identifying constitutive parameters for complex hyperelastic materials using physics-informed neural networks

Identifying constitutive parameters in engineering and biological materials, particularly those with intricate geometries and mechanical behaviors, remains a longstanding challenge. The recent advent of physics-informed neural networks (PINNs) offers promising solutions, but current frameworks are often limited to basic constitutive laws and encounter practical constraints when combined with experimental data. In this paper, we introduce a robust PINN-based framework designed to identify material parameters for soft materials, specifically those exhibiting complex constitutive behaviors, under large deformation in plane stress conditions. Distinctively, our model emphasizes training PINNs with multi-modal synthetic experimental datasets consisting of full-field deformation and loading history, ensuring algorithm robustness even with noisy data. Our results reveal that the PINNs framework can accurately identify constitutive parameters of the incompressible Arruda-Boyce model for samples with intricate geometries, maintaining an error below 5%, even with an experimental noise level of 5%. We believe our framework provides a robust modulus identification approach for complex solids, especially for those with geometrical and constitutive complexity.

Accelerated simulation methodologies for computational vascular flow modelling

Vascular flow modelling can improve our understanding of vascular pathologies and aid in developing safe and effective medical devices. Vascular flow models typically involve solving the nonlinear Navier-Stokes equations in complex anatomies and using physiological boundary conditions, often presenting a multi-physics and multi-scale computational problem to be solved. This leads to highly complex and expensive models that require excessive computational time. This review explores accelerated simulation methodologies, specifically focusing on computational vascular flow modelling. We review reduced order modelling (ROM) techniques like zero-/one-dimensional and modal decomposition-based ROMs and machine learning (ML) methods including ML-augmented ROMs, ML-based ROMs and physics-informed ML models. We discuss the applicability of each method to vascular flow acceleration and the effectiveness of the method in addressing domain-specific challenges. When available, we provide statistics on accuracy and speed-up factors for various applications related to vascular flow simulation acceleration. Our findings indicate that each type of model has strengths and limitations depending on the context. To accelerate real-world vascular flow problems, we propose future research on developing multi-scale acceleration methods capable of handling the significant geometric variability inherent to such problems.

Modified Taylor Impact Tests with Profiled Copper Cylinders: Experiment and Optimization of Dislocation Plasticity Model

Current progress in numerical simulations and machine learning allows one to apply complex loading conditions for the identification of parameters in plasticity models. This possibility expands the spectrum of examined deformed states and makes the identified model more consistent with engineering practice. A combined experimental-numerical approach to identify the model parameters and study the dynamic plasticity of metals is developed and applied to the case of cold-rolled OFHC copper. In the experimental part, profiled projectiles (reduced cylinders or cones in the head part) are proposed for the Taylor impact problem for the first time for material characterization. These projectiles allow us to reach large plastic deformations with true strains up to 1.3 at strain rates up to 105 s-1 at impact velocities below 130 m/s. The experimental results are used for the optimization of parameters of the dislocation plasticity model implemented in 3D with the numerical scheme of smoothed particle hydrodynamics (SPH). A Bayesian statistical method in combination with a trained artificial neural network as an SPH emulator is applied to optimize the parameters of the dislocation plasticity model. It is shown that classical Taylor cylinders are not enough for a univocal selection of the model parameters, while the profiled cylinders provide better optimization even if used separately. The combination of different shapes and an increase in the number of experiments increase the quality of optimization. The optimized numerical model is successfully validated by the experimental data about the shock wave profiles in flyer plate experiments from the literature. In total, a cheap, simple, but efficient route for optimizing a dynamic plasticity model is proposed. The dislocation plasticity model is extended to estimate grain refinement and volume fractions of weakened areas in comparison with experimental observations.

G2Φnet: Relating genotype and biomechanical phenotype of tissues with deep learning

Many genetic mutations adversely affect the structure and function of load-bearing soft tissues, with clinical sequelae often responsible for disability or death. Parallel advances in genetics and histomechanical characterization provide significant insight into these conditions, but there remains a pressing need to integrate such information. We present a novel genotype-to-biomechanical phenotype neural network (G2Φnet) for characterizing and classifying biomechanical properties of soft tissues, which serve as important functional readouts of tissue health or disease. We illustrate the utility of our approach by inferring the nonlinear, genotype-dependent constitutive behavior of the aorta for four mouse models involving defects or deficiencies in extracellular constituents. We show that G2Φnet can infer the biomechanical response while simultaneously ascribing the associated genotype by utilizing limited, noisy, and unstructured experimental data. More broadly, G2Φnet provides a powerful method and a paradigm shift for correlating genotype and biomechanical phenotype quantitatively, promising a better understanding of their interplay in biological tissues.

Machine Learning Methods for Multiscale Physics and Urban Engineering Problems

We present an overview of four challenging research areas in multiscale physics and engineering as well as four data science topics that may be developed for addressing these challenges. We focus on multiscale spatiotemporal problems in light of the importance of understanding the accompanying scientific processes and engineering ideas, where "multiscale" refers to concurrent, non-trivial and coupled models over scales separated by orders of magnitude in either space, time, energy, momenta, or any other relevant parameter. Specifically, we consider problems where the data may be obtained at various resolutions; analyzing such data and constructing coupled models led to open research questions in various applications of data science. Numeric studies are reported for one of the data science techniques discussed here for illustration, namely, on approximate Bayesian computations.