Micromechanical Loading Studies in Ex Vivo Cultured Embryonic Rat Bones Enabled by a Newly Developed Portable Loading Device.

Mechanical loading has been described as having the potential to affect bone growth. In order to experimentally study the potential clinical applications of mechanical loading as a novel treatment to locally modulate bone growth, there is a need to develop a portable mechanical loading device enabling studies in small bones. Existing devices are bulky and challenging to transfer within and between laboratories and animal facilities, and they do not offer user-friendly mechanical testing across both ex vivo cultured small bones and in vivo animal models. To address this, we developed a portable loading device comprised of a linear actuator fixed within a stainless-steel frame equipped with suitable structures and interfaces. The actuator, along with the supplied control system, can achieve high-precision force control within the desired force and frequency range, allowing various load application scenarios. To validate the functionality of this new device, proof-of-concept studies were performed in ex vivo cultured rat bones of varying sizes. First, very small fetal metatarsal bones were microdissected and exposed to 0.4 N loading applied at 0.77 Hz for 30 s. When bone lengths were measured after 5 days in culture, loaded bones had grown less than unloaded controls (p < 0.05). Next, fetal rat femur bones were periodically exposed to 0.4 N loading at 0.77 Hz while being cultured ex vivo for 12 days. Interestingly, this loading regimen had the opposite effect on bone growth, i.e., loaded femur bones grew significantly more than unloaded controls (p < 0.001). These findings suggest that complex relationships between longitudinal bone growth and mechanical loading can be determined using this device. We conclude that our new portable mechanical loading device allows experimental studies in small bones of varying sizes, which may facilitate further preclinical studies exploring the potential clinical applications of mechanical loading.

The transverse and longitudinal elastic constants of pulp fibers in paper sheets.

Cellulose fibers are a major industrial input, but due to their irregular shape and anisotropic material response, accurate material characterization is difficult. Single fiber tensile testing is the most popular way to estimate the material properties of individual fibers. However, such tests can only be performed along the axis of the fiber and are associated with problems of enforcing restraints. Alternative indirect approaches, such as micro-mechanical modeling, can help but yield results that are not fully decoupled from the model assumptions. Here, we compare these methods with nanoindentation as a method to extract elastic material constants of the individual fibers. We show that both the longitudinal and the transverse elastic modulus can be determined, additionally enabling the measurement of fiber properties in-situ inside a sheet of paper such that the entire industrial process history is captured. The obtained longitudinal modulus is comparable to traditional methods for larger indents but with a strongly increased scatter as the size of the indentation is decreased further.

Stochastic Constitutive Model of Isotropic Thin Fiber Networks Based on Stochastic Volume Elements.

Thin fiber networks are widely represented in nature and can be found in man-made materials such as paper and packaging. The strength of such materials is an intricate subject due to inherited randomness and size-dependencies. Direct fiber-level numerical simulations can provide insights into the role of the constitutive components of such networks, their morphology, and arrangements on the strength of the products made of them. However, direct mechanical simulation of randomly generated large and thin fiber networks is characterized by overwhelming computational costs. Herein, a stochastic constitutive model for predicting the random mechanical response of isotropic thin fiber networks of arbitrary size is presented. The model is based on stochastic volume elements (SVEs) with SVE size-specific deterministic and stochastic constitutive law parameters. The randomness in the network is described by the spatial fields of the uniaxial strain and strength to failure, formulated using multivariate kernel functions and approximate univariate probability density functions. The proposed stochastic continuum approach shows good agreement when compared to direct numerical simulation with respect to mechanical response. Furthermore, strain localization patterns matched the one observed in direct simulations, which suggests an accurate prediction of the failure location. This work demonstrates that the proposed stochastic constitutive model can be used to predict the response of random isotropic fiber networks of arbitrary size.

Role of microstructures in the compression response of three-dimensional foam-formed wood fiber networks.

High-porosity, three-dimensional wood fiber networks made by foam forming present experimentally accessible instances of hierarchically structured, athermal fiber networks. We investigate the large deformation compression behavior of these networks using fiber-resolved finite element analyses to elucidate the role of microstructures in the mechanical response to compression. Three-dimensional network structures are acquired using micro-computed tomography and subsequent skeletonization into a Euclidean graph representation. By using a fitting procedure to the geometrical graph data, we are able to identify nine independent statistical parameters needed for the regeneration of artificial networks with the observed statistics. The compression response of these artificially generated networks and the physical network is then investigated using implicit finite element analysis. A direct comparison of the simulation results from the reconstructed and artificial network reveals remarkable differences already in the elastic region. These can neither be fully explained by density scaling, the size effect nor the boundary conditions. The only factor which provides the consistent explanation of the observed difference is the density and fiber orientation nonuniformities; these contribute to strain-localization so that the network becomes more compliant than expected for statistically uniform microstructures. We also demonstrate that the experimentally manifested strain-stiffening of such networks is due to development of new inter-fiber contacts during compression.

Biopolymer network geometries: characterization, regeneration, and elastic properties.

We study the geometry of biopolymer networks and effects of the geometry on bulk mechanical properties. It is shown numerically that the physical network geometry can be quantified statistically and regenerated from its statistical description, so that the regenerated network exhibits the same network mechanics as the physical network in the elastic regime. A collagen-I biopolymer network is used for validation. The method enables parametric studies of the network geometry, whose parameters are often difficult to vary independently in experiments.