Deep rock are often in a true triaxial stress state. Studying the impacts of varying unloading speeds on their strain energy (SE) density is highly significant for predicting rock stability. Through true triaxial unloading principal stress experiments and true triaxial stress equilibrium unloading experiments on sandstone, this paper proposes a method to compute the SE density in a true triaxial compressive unloading principal stress test. This method aims to analyze the SE variation in rocks under the action of true triaxial unloading principal stresses. Acoustic emission is used to verify the correctness of the SE density calculation method in this paper. This study found that: (1) Unloading in one principal stress direction causes the SE density to rise in the other principal stress directions. This rise in SE, depending on its reversibility, can be categorized into elastic and dissipated SE. (2)When unloading principal stresses, the released elastic SE density in the unloading direction is influence by the stress path and rate. (3) The higher the unloading speed will leads to greater increases in the input SE density, elastic SE density, and dissipative SE density in the other principal stress directions. (4) The dissipated SE generated under true triaxial compression by unloading the principal stress is positively correlated with the damage to the rock; with an increase in unloading rate, there is a corresponding increase in the formation of cracks after unloading. (5) Utilizing the stress balance unloading test, we propose a calculation method for SE density in true triaxial unloading principal stress tests.

Some previous researches have demonstrated that appropriate mechanical stimulation can enhance bone formation. However, most studies have employed the strain energy density (SED) method for predicting bone remodeling, with only a few considering the potential impact of wall fluid shear stress (FSS) on this process. To bridge this gap, the current study compared the prediction of bone formation and resorption via SED and wall FSS by using fluid-solid coupling numerical simulation. Specifically, 8-week-old female Sprague-Dawley rats were subjected to stretching of the eighth caudal vertebra using a custom-made device. Based on micro-computed tomography images, a three-dimensional model integrating fluid-solid coupling was created to represent compact bone, cancellous bone, and bone marrow. The animals were grouped into control, 1 Hz, and 10 Hz categories, wherein a tensile displacement load of 1000 με was applied to the loading end. The results revealed that SED values tended to increase with elevated porosity, whereas wall FSS values decreased it. Notably, wall FSS demonstrated the higher predictive accuracy for cancellous bone resorption than SED. These findings support the notion that fluid flow within cancellous bone spaces can significantly impact bone resorption. Therefore, the findings of this study contribute to a more comprehensive understanding of the role of wall FSS in bone remodeling, providing a theoretical support for the dynamic evolution of bone structures under mechanical stimulation.

To accurately evaluate the probabilistic characteristics of the fatigue properties of materials with small sample data under different stress ratios, a data fusion method for torsional fatigue life under different stress ratios is proposed based on the energy method. A finite element numerical modeling method is used to calculate the fatigue strain energy density during fatigue damage. Torsional fatigue tests under different stresses and stress ratios are carried out to obtain a database for research. Based on the test data, the Wt-Nf curves under a single stress ratio and different stress ratios are calculated. The reliability of the models is illustrated by the scatter band diagram. More than 85% of points are within ±2 scatter bands, indicating that the fatigue life under different stress ratios can be represented by the same Wt-Nf curve. Furthermore, P-Wt-Nf prediction models are established to consider the probability characteristics. According to the homogeneity of the Wt-Nf model under different stress ratios, we can fuse the fatigue life data under different stress ratios and different strain energy densities. This data fusion method can expand the small sample test data and reduce the dispersion of the test data between different stress ratios. Compared with the pre-fusion data, the standard deviations of the post-fusion data are reduced by a maximum of 21.5% for the smooth specimens and 38.5% for the notched specimens. And more accurate P-Wt-Nf curves can be obtained to respond to the probabilistic properties of the data.

Both cell migration and osteogenic differentiation are critical for successful bone regeneration. Therefore, understanding the mechanobiological aspects that govern these two processes is essential in designing effective scaffolds that promote faster bone regeneration. Studying these two factors at different locations is necessary to manage bone regeneration in various sections of a scaffold. Hence, a multiscale computational model was used to observe the mechanical responses of osteoblasts placed in different positions of the trabecular bone and gyroid scaffold. Fluid shear stresses in scaffolds at cell seeded locations (representing osteogenic differentiation) and strain energy densities in cells at cell substrate interface (representing cell migration) were observed as mechanical response parameters in this study. Comparison of these responses, as two critical factors for bone regeneration, between the trabecular bone and gyroid scaffold at different locations, is the overall goal of the study. This study reveals that the gyroid scaffold exhibits higher osteogenic differentiation and cell migration potential compared to the trabecular bone. However, the responses in the gyroid only mimic the trabecular bone in two out of nine positions. These findings can guide us in predicting the ideal cell seeded sites within a scaffold for better bone regeneration and in replicating a replaced bone condition by altering the physical parameters of a scaffold.

Cork composites are byproducts from wine stopper production, resulting from the agglomeration of cork granules with a thermoset resin. The resulting compound is a versatile and durable material with numerous industrial applications. Due to its unique properties, such as low-density, high-strength, excellent energy absorption, and good thermal and acoustic insulators, cork composites find room for application in demanding industries such as automotive, construction, and aerospace. However, agglomerated cork typically has a polyurethane matrix derived from petrochemical sources. This study focuses on developing eco-friendly porous polyurethane biocomposites manufactured with the used cooking oil polyol modified with cork. Since cork and polyurethane foam are typically used for impact shock absorption, the manufactured samples were subjected to impact loading. The assessment of crashworthiness is performed through 100 J impact tests. A finite element numerical model was developed to simulate the compression of these new composites under impact, and the model validation was performed. The highest specific absorbed energy was obtained for petrochemical polyol composites with the 3% addition of natural or modified cork. The research conducted in this study showcased the feasibility of substituting certain petrochemical components used for the synthesis of the polyurethane matrix with ecological waste vegetable oil components.

Polyetheretherketone (PEEK) has been proposed as alternative material for total knee arthroplasty implants due to its low stiffness, which may reduce stress-shielding. In cementless fixation, a proper primary fixation is required for long-term fixation. Previous research showed that the lower stiffness of a cementless PEEK femoral component results in larger micromotions at the implant-bone interface compared to a cobalt-chrome femoral component. A titanium inlay on the PEEK implant surface may improve the primary fixation while maintaining the favourable stiffness properties. Therefore, the effect of thickness and stiffness of a titanium inlay on the primary fixation and stress-shielding was investigated. A finite element model of the femur and femoral component was created with five titanium inlay variants. The micromotions and strain energy density (SED) were quantified as outcome measures. The distal thin - proximal thick variant showed the largest resulting micromotions (51.2 µm). Relative to the all-PEEK femoral component, the addition of a titanium inlay reduced the micromotions with 30 % to 40 % without considerably affecting the stress-shielding capacity (strain energy difference of 6 % to 10 %). Differences in micromotions (43.0-51.2 µm) and SED between the variants were relatively small. In conclusion, the addition of a titanium inlay could lead to a reduction of the micromotions without substantially affecting the SED distribution.

Improvement of cell migration by the nano-topographical modification of implant surface can directly or indirectly accelerate wound healing and osseointegration between bone and implant. Therefore, modification of the implant surface was done with TiO2 nanorod (NR) arrays to develop a more osseointegration-friendly implant in this study. Modulating the migration of a cell, adhered to a scaffold, by the variations of NR diameter, density and tip diameter in vitro is the primary objective of the study. The fluid structure interaction method was used, followed by the submodelling technique in this multiscale analysis. After completing a simulation over a global model, fluid structure interaction data was applied to the sub-scaffold finite element model to predict the mechanical response over cells at the cell-substrate interface. Special focus was given to strain energy density at the cell interface as a response parameter due to its direct correlation with the migration of an adherent cell. The results showed a huge rise in strain energy density after the addition of NRs on the scaffold surface. It also highlighted that variation in NR density plays a more effective role than the variation in NR diameter to control cell migration over a substrate. However, the effect of NR diameter becomes insignificant when the NR tip was considered. The findings of this study could be used to determine the best nanostructure parameters for better osseointegration.

Analysis of the dependency of the trabecular structure on loading conditions is essential for understanding and predicting bone structure formation. Although previous studies have investigated the relationship between loads and structural adaptations, there is a need for an in-depth analysis of this relationship based on the bone region and load specifics. In this study, the load dependency of the trabecular bone microstructure for twelve regions of interest (ROIs) in the synthetic proximal femur was quantitatively analyzed to understand the spatial characteristics under seven different loading conditions. To investigate the load dependency, a quantitative measure, called the load dependency score (LDS), was established based on the statistics of the strain energy density (SED) distribution. The results showed that for the global model and epiphysis ROIs, bone microstructures relied on the multiple-loading condition, whereas the structures in the metaphysis depended on single or double loads. These results demonstrate that a given ROI is predominantly dependent on a particular loading condition. The results confirm that the dependency analysis of the load effects for ROIs should be performed both qualitatively and quantitatively.

Cells mechanically interact with their environment to sense, for example, topography, elasticity and mechanical cues from other cells. Mechano-sensing has profound effects on cellular behaviour, including motility. The current study aims to develop a mathematical model of cellular mechano-sensing on planar elastic substrates and demonstrate the model\'s predictive capabilities for the motility of individual cells in a colony. In the model, a cell is assumed to transmit an adhesion force, derived from a dynamic focal adhesion integrin density, that locally deforms a substrate, and to sense substrate deformation originating from neighbouring cells. The substrate deformation from multiple cells is expressed as total strain energy density with a spatially varying gradient. The magnitude and direction of the gradient at the cell location define the cell motion. Cell-substrate friction, partial motion randomness, and cell death and division are included. The substrate deformation by a single cell and the motility of two cells are presented for several substrate elasticities and thicknesses. The collective motility of 25 cells on a uniform substrate mimicking the closure of a circular wound of 200 µm is predicted for deterministic and random motion. Cell motility on substrates with varying elasticity and thickness is explored for four cells and 15 cells, the latter again mimicking wound closure. Wound closure by 45 cells is used to demonstrate the simulation of cell death and division during migration. The mathematical model can adequately simulate the mechanically induced collective cell motility on planar elastic substrates. The model is suitable for extension to other cell and substrates shapes and the inclusion of chemotactic cues, offering the potential to complement in vitro and in vivo studies.

In vitro experiments in which tumour cells are seeded in a gelatinous medium, or hydrogel, show how mechanical interactions between tumour cells and the tissue in which they are embedded, together with local levels of an externally-supplied, diffusible nutrient (e.g., oxygen), affect the tumour\'s growth dynamics. In this article, we present a mathematical model that describes these in vitro experiments. We use the model to understand how tumour growth generates mechanical deformations in the hydrogel and how these deformations in turn influence the tumour\'s growth. The hydrogel is viewed as a nonlinear hyperelastic material and the tumour is modelled as a two-phase mixture, comprising a viscous tumour cell phase and an isotropic, inviscid interstitial fluid phase. Using a combination of numerical and analytical techniques, we show how the tumour\'s growth dynamics change as the mechanical properties of the hydrogel vary. When the hydrogel is soft, nutrient availability dominates the dynamics: the tumour evolves to a large equilibrium configuration where the proliferation rate of nutrient-rich cells on the tumour boundary balances the death rate of nutrient-starved cells in the central, necrotic core. As the hydrogel stiffness increases, mechanical resistance to growth increases and the tumour\'s equilibrium size decreases. Indeed, for small tumours embedded in stiff hydrogels, the inhibitory force experienced by the tumour cells may be so large that the tumour is eliminated. Analysis of the model identifies parameter regimes in which the presence of the hydrogel drives tumour elimination.