Pietro Carrara

Jonas Heinzmann, Francesco Vicentini, Pietro Carrara et al.

Phase-field models of fracture are widely used for simulating crack nucleation and propagation, yet the role of the phase-field regularization in the dynamic regime is not fully understood and depends critically on how the damage variable is coupled to the displacement field. In this paper, we analyze three alternative formulations: the brittle model with stiffness degradation, its variant with stiffness+density degradation, and our recently proposed phase-field regularization of cohesive fracture, which we extend to elastodynamics. By studying the interaction of a tensile and a compressive elastic wave with a phase-field crack in a one-dimensional bar, we determine for which models and under which conditions the phase-field regularization preserves the features of the wave-crack interaction expected for a sharp crack, and we theoretically explain which variables control the behavior. For the new cohesive model extended to dynamics, we further derive an analytical dynamic cohesive opening law. Finally, we study the dynamic behavior including branching of a two-dimensional notched plate at two loading intensities.

Jan Niklas Fuhg, Govinda Anantha Padmanabha, Nikolaos Bouklas et al.

This review article highlights state-of-the-art data-driven techniques to discover, encode, surrogate, or emulate constitutive laws that describe the path-independent and path-dependent response of solids. Our objective is to provide an organized taxonomy to a large spectrum of methodologies developed in the past decades and to discuss the benefits and drawbacks of the various techniques for interpreting and forecasting mechanics behavior across different scales. Distinguishing between machine-learning-based and model-free methods, we further categorize approaches based on their interpretability and on their learning process/type of required data, while discussing the key problems of generalization and trustworthiness. We attempt to provide a road map of how these can be reconciled in a data-availability-aware context. We also touch upon relevant aspects such as data sampling techniques, design of experiments, verification, and validation.