Recent advancements in Machine Learning approaches for solid body mechanics

Machine learning methods have attracted growing interest across many fields, including solid mechanics. Constitutive artificial neural networks (CANNs) have shown high efficiency and accuracy for modeling hyperelastic materials, while physics-informed neural networks (PINNs) provide a data-free alternative to conventional simulation techniques. However, standard PINNs often require large, complex networks and dense sampling in the simulation domain to achieve stable and accurate results. This presentation gives an overview of several current NN-based approaches for both constitutive modeling and simulation. It introduces extended ML-based constitutive models for cyclic plasticity, concrete damage plasticity, and magneto-active polymers. These approaches enable simplified and accelerated material characterization while maintaining high accuracy. An integrated framework for simulation and material characterization is also proposed. As an example, a coupled CANN–DEM approach is presented: the material behavior is first learned from a limited set of complex experiments, and the resulting model is then used to simulate new loading scenarios with promising accuracy and robustness. In addition, the quadrature-based Deep Energy Method (Q-DEM) is discussed, offering significant improvements in accuracy and stability. Finally, oscillatory PINNs (oPINNs) are introduced for combined transient and modal analysis. By circumventing Dahlquist’s barriers, oPINNs achieve substantial stability gains compared to traditional time-stepping schemes.

Speaker : Stefan Hildebrand

Biography:

Stefan Hildebrand is a doctoral researcher at the Department of Structural and Computational Mechanics at Technische Universität Berlin. His work focuses on combining data-driven and physics-informed methods in solid mechanics, with applications ranging from automated material characterization to digital twins. After studying Computational Engineering Sciences and working as a software engineer for the automotive multibody simulation software SIMDRIVE3D at CONTECS engineering services GmbH, he has held guest research positions at IIT Bombay and Georgia Tech, and received recognitions including a Junior-Fellowship by German Informatics Society and Forbes 30 Under 30.
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