Bending analysis of sandwich panel composite with a re-entrant lattice core using zig-zag theory.

The sandwich panel structures have been widely used in many industrial applications because of their high mechanical properties. The middle layer of these structures is very important factor in controlling and enhancing their mechanical performance under various loading scenarios. The re-entrant lattice configurations, are prominent candidates that can be used as the middle layer in such sandwich structures because of several reasons namely the simplicity in tuning their elastic (e.g., values of Poisson's ratio and elastic stiffness) and plastic (e.g., high strength-to-weight ratio) properties by only adjusting the geometrical features of the constituting unit cells. Here, we investigated the response of a three-layered sandwich plate with a re-entrant core lattice under flexural bending using analytical (i.e., zig-zag theory), computational (i.e., finite element) and experimental tests. We also analyzed the effects of different geometrical parameters (e.g., angle, thicknesses, and length to the height ratio of unit cells) of re-entrant lattice structures on the overall mechanical behavior of sandwich structures. We found that the core structures with auxetic behavior (i.e., negative Poisson's ratio) resulted in a higher bending strength and a minimum out-of-plane shear stress as compared to those with conventional lattices. Our results can pave way in designing advanced engineered sandwich structures with architected core lattices for aerospace and biomedical applications.

The sensitivity of cartilage contact pressures in the knee joint to the size and shape of an anatomically shaped meniscal implant.

Since meniscal geometry affects the cartilage contact pressures, it is essential to carefully define the geometry of the synthetic meniscal implant that we developed. Recently, six independent modes of size- and shape-related geometry variation were identified through 3D statistical shape modeling (SSM) of the medial meniscus. However, this model did not provide information on the functional importance of these geometry characteristics. Therefore, in this study finite element simulations were performed to determine the influence of anatomically-based meniscal implant size and shape variations on knee cartilage contact pressures. Finite element simulations of the knee joint were performed for a total medial meniscectomy, an allograft, the average implant geometry, six implant sizes and ten shape variations. The geometries of the allograft and all implant variations were based on the meniscus SSM. Cartilage contact pressures and implant tensile strains were evaluated in full extension under 1200N of axial compression. The average implant induced cartilage peak pressures intermediate between the allograft and meniscectomy and also reduced the cartilage area subjected to pressures >5MPa compared to the meniscectomy. The smaller implant sizes resulted in lower cartilage peak pressures and compressive strains than the allograft, yet high implant tensile strains were observed. Shape modes 2, 3 and 6 affected the cartilage contact stresses but to a lesser extent than the size variations. Shape modes 4 and 5 did not result in changes of the cartilage stress levels. The present study indicates that cartilage contact mechanics are more sensitive to implant size than to implant shape. Down-sizing the implant resulted in more favorable contact mechanics, but caused excessive material strains. Further evaluations are necessary to balance cartilage contact pressures and material strains to ensure cartilage protection and longevity of the implant.

Direct noninvasive measurement and numerical modeling of depth-dependent strains in layered agarose constructs.

Biomechanical factors play an important role in the growth, regulation, and maintenance of engineered biomaterials and tissues. While physical factors (e.g. applied mechanical strain) can accelerate regeneration, and knowledge of tissue properties often guide the design of custom materials with tailored functionality, the distribution of mechanical quantities (e.g. strain) throughout native and repair tissues is largely unknown. Here, we directly quantify distributions of strain using noninvasive magnetic resonance imaging (MRI) throughout layered agarose constructs, a model system for articular cartilage regeneration. Bulk mechanical testing, giving both instantaneous and equilibrium moduli, was incapable of differentiating between the layered constructs with defined amounts of 2% and 4% agarose. In contrast, MRI revealed complex distributions of strain, with strain transfer to softer (2%) agarose regions, resulting in amplified magnitudes. Comparative studies using finite element simulations and mixture (biphasic) theory confirmed strain distributions in the layered agarose. The results indicate that strain transfer to soft regions is possible in vivo as the biomaterial and tissue changes during regeneration and maturity. It is also possible to modulate locally the strain field that is applied to construct-embedded cells (e.g. chondrocytes) using stratified agarose constructs.