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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 experiment, verification, and validation. 

Collagen scaffolds seeded with human chondrocytes have shown great potential for cartilage repair and regeneration. However, these porous scaffolds buckle under low compressive forces, creating regions of highly localized deformations that can cause cell death and deteriorate the integrity of the engineered tissue. We perform three-dimensional (3D) tomography-based characterization to track the evolution of collagen scaffolds’ microstructure under large deformation. The results illustrate how instabilities produce a spatially varying compaction across the specimens, with more pronounced collapse near the free boundaries. We discover that, independent of differences in pore-size distributions, all collagen scaffolds examined displayed strong auxetic behavior i.e., their transverse area contracts under compression, as a result of the instability cascade. This feature, typically characteristic of engineered metamaterials, is of critical importance for the performance of collagen scaffolds in tissue engineering, especially regarding the persistent challenge of lateral integration in cartilage constructs. 

Bacteria experience substantial physical forces in their natural environment including forces caused by osmotic pressure, growth in constrained spaces, and fluid shear. The cell envelope is the primary load-carrying structure of bacteria, but the mechanical properties of the cell envelope are poorly understood; reports of Young’s modulus of the cell envelope of E. coli are widely range from 2 MPa to 18 MPa. We have developed a microfluidic system to apply mechanical loads to hundreds of bacteria at once and demonstrated the utility of the approach for evaluating whole-cell stiffness. Here we extend this technique to determine Young’s modulus of the cell envelope of E. coli and of the pathogens V. cholerae and S. aureus. An optimization-based inverse finite element analysis was used to determine the cell envelope Young’s modulus from observed deformations. The Young’s modulus of the cell envelope was 2.06±0.04 MPa for E. coli, 0.84±0.02 MPa for E. coli treated with a chemical known to reduce cell stiffness, 0.12±0.03 MPa for V. cholerae, and 1.52±0.06 MPa for S. aureus (mean ± SD). The microfluidic approach allows examining hundreds of cells at once and is readily applied to Gram-negative and Gram-positive organisms as well as rod-shaped and cocci cells, allowing further examination of the structural causes of differences in cell envelope Young's modulus among bacteria species and strains.