Enhanced Cellular Materials through Multiscale, Variable-Section Inner Designs: Mechanical Attributes and Neural Network Modeling.

In the current work, the mechanical response of multiscale cellular materials with hollow variable-section inner elements is analyzed, combining experimental, numerical and machine learning techniques. At first, the effect of multiscale designs on the macroscale material attributes is quantified as a function of their inner structure. To that scope, analytical, closed-form expressions for the axial and bending inner element-scale stiffness are elaborated. The multiscale metamaterial performance is numerically probed for variable-section, multiscale honeycomb, square and re-entrant star-shaped lattice architectures. It is observed that a substantial normal, bulk and shear specific stiffness increase can be achieved, which differs depending on the upper-scale lattice pattern. Subsequently, extended mechanical datasets are created for the training of machine learning models of the metamaterial performance. Thereupon, neural network (NN) architectures and modeling parameters that can robustly capture the multiscale material response are identified. It is demonstrated that rather low-numerical-cost NN models can assess the complete set of elastic properties with substantial accuracy, providing a direct link between the underlying design parameters and the macroscale metamaterial performance. Moreover, inverse, multi-objective engineering tasks become feasible. It is shown that unified machine-learning-based representation allows for the inverse identification of the inner multiscale structural topology and base material parameters that optimally meet multiple macroscale performance objectives, coupling the NN metamaterial models with genetic algorithm-based optimization schemes.

Investigating the Effect of Aging on the Viscosity of Tendon Fascicles and Fibers.

In the current work, we investigate the effect of aging on the viscosity of tendon subunits. To that scope, we make use of experimental relaxation curves of healthy and aged tendon fascicles and fibers, upon which we identify the viscosity parameters characterizing the time-dependent behavior of each tendon subunit. We subsequently combine the obtained results with analytical viscoelastic homogenization analysis methods to extract information on the effective viscous contribution of the embedding matrix substance at the fiber scale. The results suggest that the matrix substance plays a significant role in the relaxation process of the upper tendon subunits both for aged and healthy specimens. What is more, the viscosity coefficients computed for the fibrillar components indicate that aging leads to a viscosity reduction that is statistically significant for both fascicles and fibers. Its impact is more prominent for the lower hierarchical scale of fibers. As such, the reduced stress relaxation capability at the tendon macroscale is to be primarily attributed to the modified viscosity of its inner fibrillar subunits rather than to the matrix substance.

Exploiting Viscoelastic Experimental Observations and Numerical Simulations to Infer Biomimetic Artificial Tendon Fiber Designs.

Designing biomimetic artificial tendons requires a thorough, data-based understanding of the tendon's inner material properties. The current work exploits viscoelastic experimental observations at the tendon fascicle scale, making use of mechanical and data analysis methods. More specifically, based on reported elastic, volumetric and relaxation fascicle scale properties, we infer most probable, mechanically compatible material attributes at the fiber scale. In particular, the work provides pairs of elastic and viscous fiber-scale moduli, which can reproduce the upper scale tendon mechanics. The computed range of values for the fiber-scale tendon viscosity attest to the substantial stress relaxation capabilities of tendons. More importantly, the reported mechanical parameters constitute a basis for the design of tendon-specific restoration materials, such as fiber-based, engineering scaffolds.

Unravelling the viscoelastic, buffer-like mechanical behavior of tendons: A numerical quantitative study at the fibril-fiber scale.

We investigate the capacity of tendons to bear substantial loads by exploiting their hierarchical structure and the viscous nature of their subunits. We model and analyze two successive tendon scales: the fibril and fiber subunits. We present a novel method for bridging intra-scale experimental observations by combining a homogenization analysis technique with a Bayesian inference method. This allows us to infer elastic and viscoelastic moduli at the embedded fibril scale that are mechanically compatible with the experimental data observed at the fiber scale. We identify the rather narrow range of moduli values at the fibrillar scale that can reproduce the mechanical behavior of the fiber, while we quantify the viscoelastic contribution of the embedding, non-collagenous matrix substance. The computed viscoelastic moduli suggest that a great part of the stress relaxation capacity of tendons needs to be attributed to the embedding matrix substance of its inner components, classifying it as a primal load relaxation constituent.