Convergence analysis and validation of a discrete element model of the human lumbar spine

Degenerative diseases of the spine can lead to or hasten the onset of additional spinal problems that significantly reduce human mobility. The spine consists of vertebral bodies and intervertebral discs. The most degraded are intervertebral discs. The vertebral body consists of a shell (cortical bone tissue) and an internal content (cancellous bone tissue). The intervertebral disc is a complex structural element of the spine, consisting of the nucleus pulposus, annulus fibrosus, and cartilaginous plates. To develop numerical models for the vertebral body and intervertebral disc, first, it is necessary to verify and validate the models for the constituent elements of the lumbar spine. This paper, for the first time, presents discrete elements-based numerical models for the constituent parts of the lumbar spine, and their verification and validation. The models are validated using uniaxial compression experiments available in the literature. The model predictions are in good qualitative and quantitative agreement with the data of those experiments. The loading rate sensitivity analysis revealed that fluid-saturated porous materials are highly sensitive to loading rate: a 1000-fold increase in rate leads to the increase in effective stiffness of 130 % for the intervertebral disc, and a 250-fold increase in rate leads to the increase in effective stiffness of 50 % for the vertebral body. The developed model components can be used to create an L4-L5 segment model, which, in the future, will allow investigating the mechanical behavior of the spine under different types of loading.

Effective Stiffness of Fused Deposition Modeling Infill Lattice Patterns Made of PLA-Wood Material

Fused deposition modeling (FDM) uses lattice arrangements, known as infill, within the fabricated part. The mechanical properties of parts fabricated via FDM are dependent on these infill patterns, which make their study of great relevance. One of the advantages of FDM is the wide range of materials that can be employed using this technology. Among these, polylactic acid (PLA)-wood has been recently gaining attention as it has become commercially available. In this work, the stiffness of two different lattice structures fabricated from PLA-wood material using FDM are studied: hexagonal and star. Rectangular samples with four different infill densities made of PLA-wood material were fabricated via FDM. Samples were subjected to 3-point bending to characterize the effective stiffness and their sensitivity to shear deformation. Lattice beams proved to be more sensitive to shear deformations, as including the contribution of shear in the apparent stiffness of these arrangements leads to more accurate results. This was evaluated by comparing the effective Young’s modulus characterized from 3-point bending using equations with and without shear inclusion. A longer separation between supports yielded closer results between both models (~41% for the longest separation tested). The effective stiffness as a function of the infill density of both topologies showed similar trends. However, the maximum difference obtained at low densities was the hexagonal topology that was ~60% stiffer, while the lowest difference was obtained at higher densities (star topology being stiffer by ~20%). Results for stiffness of PLA-wood samples were scattered. This was attributed to the defects at the lattice element level inherent to the material employed in this study, confirmed via micro-characterization.

Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface

The main aim of this study is determination of the basic probabilistic characteristics of the effective stiffness for inelastic particulate composites with spherical reinforcement and an uncertain Gaussian volume fraction of the interphase defects. This is determined using a homogenization method with a cubic single-particle representative volume element (RVE) of such a composite and the finite element method solution. A reinforcing particle is spherical, located centrally in the RVE, surrounded by the thin interphase of constant thickness, and remains in an elastic reversible regime opposite to the matrix, which is hyper-elastic. The interphase defects are represented as semi-spherical voids, which are placed on the outer surface of this particle. The interphase is modeled as hyper-elastic and isotropic, whose effective stiffness is calculated by the spatial averaging of hyper-elastic parameters of the matrix and of the defects. A constitutive relation of the matrix is recovered experimentally by its uniaxial stretch. The 3D homogenization problem solution is based upon a numerical determination of strain energy density in the given RVE under specific uniaxial and biaxial stretches as well as under shear deformations. The analytical relation of the effective composite stiffness to the input uncertain parameter is recovered via the response function method, using a polynomial basis and an optimized order. Probabilistic calculations are completed using three concurrent approaches, namely the iterative stochastic finite element method (SFEM), Monte Carlo simulation and by the semi-analytical method. Previous papers consider the composite fully elastic, which limits the applicability of the resulting effective stiffness tensor computed therein. The current study voids this assumption and defines the composite as fully hyper-elastic, thus extending applicability of this tensor to strains up to 0.25. The most important research finding is that (1) the effective stiffness tensor is sensitive to random interface defects in its hyper-elastic range, (2) its resulting randomness is not close to Gaussian, (3) the semi-analytical method is not perfectly suited to stochastic calculations in this region of strains, as opposed to the linear elastic region, and (4) that the increase in random dispersion of defects volume fraction has a much higher effect on the stochastic characteristics of this stiffness tensor than fluctuation of the strain.

Substrate rigidity modulates traction forces and stoichiometry of cell matrix adhesions.

In cell matrix adhesions, integrin receptors and associated proteins provide a dynamic coupling of the extracellular matrix (ECM) to the cytoskeleton. This allows bidirectional transmission of forces between the ECM and the cytoskeleton, which tunes intracellular signaling cascades that control survival, proliferation, differentiation, and motility. The quantitative relationships between recruitment of distinct cell matrix adhesion proteins and local cellular traction forces are not known. Here, we applied quantitative superresolution microscopy to cell matrix adhesions formed on fibronectin-stamped elastomeric pillars and developed an approach to relate the number of talin, vinculin, paxillin, and focal adhesion kinase (FAK) molecules to the local cellular traction force. We find that FAK recruitment does not show an association with traction-force application whereas a ~60 pN force increase is associated with the recruitment of one talin, two vinculin, and two paxillin molecules on a substrate of effective stiffness of 47 kPa. On a substrate with a four-fold lower effective stiffness the stoichiometry of talin:vinculin:paxillin changes to 2:12:6 for the same ~60 pN traction force. The relative change in force-related vinculin recruitment indicates a stiffness-dependent switch in vinculin function in cell matrix adhesions. Our results reveal a substrate-stiffness-dependent modulation of the relation between cellular traction-force and the molecular stoichiometry of cell-matrix adhesions.

Investigation of moment-curvature and effective section stiffness of reinforced concrete columns

In determining the seismic performance of reinforced concrete (RC) structures in national and international seismic code, it is desired to use effective section stiffness of the cracked section in RC structural elements during the design phase. Although the effective stiffness of the cracked section is not constant, it depends on parameters such as the dimension of the cross-section, concrete strength and axial force acting on the section. In this study, RC column models with different axial load levels, concrete strength, longitudinal and transverse reinforcement ratios were designed to investigate effective stiffness. Analytically investigated parameters were calculated from TBEC (2018), ACI318 (2014), ASCE/SEI41 (2017), Eurocode 2 (2004) and Eurocode8 (2004, 2005) regulations and moment-curvature relationships. From the numerical analysis results, it is obtained that the axial load level, concrete strength, longitudinal and transverse reinforcement ratios have an influence on the effective stiffness factor of RC column sections. The calculated effective stiffness for RC columns increases with increasing transverse reinforcement ratio, longitudinal reinforcement ratio and concrete strength. Due to the increase of axial force, effective stiffness values of concrete have increased.