Stress relaxing granular bioprinting materials enable complex and uniform organoid self-organization

Summary. It is known that if M is a 3 × 3 magic matrix then every positive, odd power of M is a magic matrix, while an even power need not be. Given any n × n magic matrix M, we find all polynomials f such that f(M) is a magic matrix.

At present, the Sudoku matrix, turtle shell matrix, and octagonal matrix have been put forward according to the magic matrix-based data hiding methods. Moreover, the magic matrices to be designed depend on the size of the embedding capacity. In addition, by determining the classification of points of pixel pairs after applying a magic matrix and by determining the traversal area, the average peak signal-to-noise ratio (PSNR) can be improved. Therefore, this topic intends to propose a data hiding method based on a 16 × 16 Sudoku matrix by using the 16 × 16 Sudoku matrix and extending it to a double-layer magic matrix. Low-cost data embedding methods are also studied, in order to improve the PSNR and maintain good image quality with the same embedding capacity.

Viscoelastic properties of hydrogels such as stress relaxation or plasticity have been recognized as important mechanical cues that dictate the migration, proliferation, and differentiation of embedded cells. Stress relaxation rates in conventional hydrogels are usually much slower than cellular processes, which impedes rapid cellularization of these elastic networks. Colloidal hydrogels assembled from nanoscale building blocks may provide increased degrees of freedom in the design of viscoelastic hydrogels with accelerated stress relaxation rates due to their strain-sensitive rheology which can be tuned via interparticle interactions. Here, we investigate the stress relaxation of colloidal hydrogels from gelatin nanoparticles in comparison to physical gelatin hydrogels and explore the particle interactions that govern stress relaxation. Colloidal and physical gelatin hydrogels exhibit comparable rheology at small deformations, but colloidal hydrogels fluidize beyond a critical strain while physical gels remain primarily elastic independent of strain. This fluidization facilitates fast exponential stress relaxation in colloidal gels at strain levels that correspond to strains exerted by cells embedded in physiological extracellular matrices (10-50%). Increased attractive particle interactions result in a higher critical strain and slower stress relaxation in colloidal gels. In physical gels, stress relaxation is slower and mostly independent of strain. Hence, colloidal hydrogels offer the possibility to modulate viscoelasticity via interparticle interactions and obtain fast stress relaxation rates at strains relevant for cell activity. These beneficial features render colloidal hydrogels promising alternatives to conventional monolithic hydrogels for tissue engineering and regenerative medicine. Statement of significanceIn the endeavor to design biomaterials that favor cell activity, research has long focused on biochemical cues. Recently, the time-, stress-, and strain-dependent mechanical properties, i.e. viscoelasticity, of biomaterials has been recognized as important factor that dictates cell fate. We herein present the viscoelastic stress relaxation of colloidal hydrogels assembled from gelatin nanoparticles, which show a strain-dependent fluidization at strains relevant for cell activity, in contrast to many commonly used monolithic hydrogels with primarily elastic behavior.

Effect of grain size on high-temperature stress relaxation behavior of fine-grained TC4 titanium alloy

The action of water solutions of dimethyl formamide on Dinitrile A fibers was studied using the stress-relaxation technique. After prior conditioning and stress relaxation in water, the addition of dimethyl formamide-water solutions produced an exponential stress relaxation. It was found that the rate and extent of stress relaxation in dimethyl formamide-water solutions is dependent on the dimethyl formamide concentration. The rate of stress relaxation in dimethyl formamide-water solutions is also dependent on the cross-sectional area and the state of orientation of the fiber. These data can best be explained by postulating that the rate of diffusion of the dimethyl formamide-water solution into the fiber controls the rate of stress relaxation. The diffusion coefficient is found to be concentration dependent, and the diffusion process has an activation energy of 14 kcal.

A proper Euler’s magic matrix is an integer n×n matrix M∈Zn×n such that M⋅Mt=γ⋅I for some nonzero constant γ, the sum of the squares of the entries along each of the two main diagonals equals γ, and the squares of all entries in M are pairwise distinct. Euler constructed such matrices for n=4. In this work, we use multiplication matrices of the octonions to construct examples for n=8, and prove that no such matrix exists for n=3.

 The natural extracellular matrix (ECM) exhibits remarkable viscoelasticity and stress relaxation. Constructing viscoelastic scaffolds that can precisely control the stress relaxation rate and possess good biocompatibility is a key challenge in the design of tissue engineering scaffolds. Understanding the factors influencing the viscoelasticity of scaffolds and their mechanisms, as well as implementing comprehensive regulatory strategies based on this understanding, are effective methods for precisely controlling the stress relaxation rate. Current research on viscoelastic scaffolds mainly focuses on the regulation of bulk hydrogel viscoelasticity, while the impact of 3D printing parameters on stress relaxation time remains underexplored. In this study, we controlled the structure and morphology of silk fibroin to obtain a crystalline silk fibroin fiber (SL) solution, which was then mixed with gelatin solution to achieve high-precision printing of low-concentration (<2%) silk fibroin. Based on this, we explored the effects of printing angle, fiber diameter, and porosity on the stress relaxation rate and elastic modulus of the scaffold. Specifically, as porosity increases, the relaxation rate tends to rise, while the elastic modulus decreases. Conversely, as the printing angle and fiber diameter increase, the relaxation rate significantly decreases, and the elastic modulus correspondingly increases. We verified these effects using alginate-based bioink, demonstrating the universality of the influence of printing parameters on scaffold viscoelasticity. Additionally, we constructed scaffolds with similar elastic moduli but different stress relaxation rates and investigated their effects on cell growth, thereby confirming the good biocompatibility of viscoelastic scaffolds. This study not only provides a theoretical basis for precisely controlling the stress relaxation rate of 3D-printed viscoelastic scaffolds but also offers new insights for the design and optimization of tissue engineering scaffolds.

Hydrogels with hierarchical hydrogen bonds enable tunable stress relaxation to direct macrophage-driven immunoregulation.

ABSTRACTHydrogel has been extensively studied for use as articular cartilage. The static and dynamic viscoelasticity behaviors of hydrogel grafted with ultra-high-molecular-weight polyethylene (UHMWPE) were studied by finite-element method (FEM) and dynamic mechanical analysis in this article. The results show that creep deformation presents an exponential function with the pore fluid velocity of hydrogel material. During the first period of stress relaxation, the internal fluid pore pressure of hydrogel material is less than partial pressure, which leads to the increasing fluid exudation, and the stress relaxation rate changes quickly. With the loss of fluid, the pore pressure and partial pressure achieve balance. Then, finally, stress relaxation reaches relative equilibrium. The storage modulus of hydrogel material increases with the increasing frequency, and there is a logarithmic regression between them. With the decrease in liquid–solid ratio, the storage modulus declines, while the loss modulus first increases and then decreases. When the strain increases, both storage modulus and loss modulus show an upward trend.

Rapid stretching of smooth muscle induces a large increase in stress (resistance to stretch), and stress gradually decreases to intermediate values (stress relaxation). This study elucidated whether [Ca2+]-dependent crossbridge activation or passive mechanical structures were responsible for resistance to stretch and stress relaxation in swine carotid media, a tissue that does not exhibit a myogenic response. Tissues were equilibrated at the optimal length for stress development (L0) and loaded with aequorin to estimate myoplasmic [Ca2+]. In tissues activated with contractile agonists, both resistance to stretch and the rate of stress relaxation appeared to correlate best with the stress present before stretch. Stretch-induced [Ca2+] transients had no major role in determining resistance to stretch or stress relaxation. In the unstimulated swine carotid, resistance to stretch was only slightly reduced and stress relaxation not affected by removal of extracellular Ca2+, suggesting that resistance to stretch and the rate of stress relaxation in unstimulated tissues was predominantly dependent on the passive components of smooth muscle rather than attached, Ca(2+)-dependent crossbridges. Incubation of tissues with tetraethylammonium ion had no measurable effect on stretch-induced [Ca2+] transients but increased resistance to stretch, suggesting that stretch-induced myogenic contractions may be mediated by an increase in the sensitivity of the contractile apparatus to [Ca2+]. Despite the ability of stretch to produce substantial increases in myoplasmic [Ca2+], the contractile apparatus of swine carotid is quite insensitive to the stretch-induced [Ca2+] elevations.

The stress relaxation (SR) process in zirconium-based alloys is intimately related to creep behavior as stress is diminished with time by creep. Open literature data show a complex and not fully understood relation between the primary and quasi-steady-state creep rates and the corresponding SR rates; in particular, it was observed that higher primary SR rates occur under irradiation. To further investigate this topic, in-reactor SR experiments were conducted on pre-irradiated zirconium alloy specimens. A unique four-point bend (4PB) technique was applied to measure SR of pre-irradiated and unirradiated rectangular specimens (35 by 6.5 by 0.8 mm in size) at regular intervals during their irradiation in the RBT-6 research reactor and a sibling out-reactor rig. The 4PB method had never been applied previously to highly pre-irradiated (up to 34 dpa) and prehydrided (up to 339 ppm) small specimens of zirconium alloys. The measured SR behavior can be analyzed with various creep behavior models. In addition, the alloy variants tested in this study were also a subset of those from a previous study on irradiation growth behavior. The unique loading fixture utilized can simultaneously apply 4PB loads on up to six specimens, without need for removing the specimens from the fixture to record SR versus time data. Additional fast fluence accrued during SR testing in RBT-6 was minimal. Post-test examinations on selected specimens were performed by metallography and transmission electron microscopy. This paper describes (i) the design of the loading fixture, (ii) in-reactor and out-reactor SR data, (iii) the SR data trends, especially the lack of any significant dependence of SR with c-component loop density and hydrogen, (iv) some observations on the effects of alloying additions on SR, (v) application of a simple phenomenological creep model to the SR data, and (vi) the post-test characterizations of SR test samples.

Effect of surface area of grain boundaries on stress relaxation behavior in pure copper over wide range of grain sizes

Objective To explore the possible influences of intraoral environment on stress relaxation of thermoplastic materials, and compare the stress relaxation rates within different materials.Methods Five kinds of thermoplastic materials were tested in the air under room temperature and in the simulated intraoral environment.The stress relaxation rates were compared.Results The stress relaxation rates of all materials in the simulated intraoral environment were significantly greater than those obtained in the air under room temperature (P＜0.01).Conclusions Stress relaxation of thermoplastic materials could be significantly accelerated in the simulated intraoral environment. Key words: Thermoplastic material; Simulated intraoral environment; Stress relaxation; Invisible aligners

Some experimental measurements are described of stress relaxation and creep at room temperatures in vulcanizates of natural rubber, butyl, and SBR. In an unfilled natural rubber vulcanizate the rate of stress relaxation is found to rise sharply for extensions of more than about 200%. Reasons are given for attributing this to the growth of a crystalline phase. Similar rates are observed at all extensions for a carbon black filled natural rubber vulcanizate. This is shown to be in satisfactory accord with the Mullins-Tobin model structure for filled vulcanizates, when the whole of the observed relaxation occurs in “softened” regions at rates appropriate to the high local deformations. The failure of rubber-carbon black associations with time does not appear to constitute a major relaxation process. In noncrystallizing unfilled vulcanizates the rate of relaxation is found to decrease somewhat with extension, possibly due to finite-extensibility effects. Preliminary measurements on a filled SBR vulcanizate suggest that a significant contribution to the observed relaxation arises from progressive failure of rubber-filler associations in this case. The relation derived previously between the rates of creep and stress relaxation at equivalent deformations is confirmed in all cases, within experimental error. Its validity in highly-irreversible systems is thus established experimentally.

The article studied the following fundamental problems on the degradation of elastomers by heat and/or radiation by using the measurement of chemical stress relaxation. (1) The efficiency of scission and crosslinking of elastomers by radiation. (2) The continuous and intermittent chemical stress relaxation of tetrafluoroethylene-propylene elastomer was measured at 100°C under the irradiation of 60Co γ rays. The G value of crosslinking (Gc) was found to be 0.88 and the G value of scission (Gs) was 1.89 by this method. On the other hand, Gc and Gs values of the polymer, as obtained from a Charlesby-Pinner plot (sol fraction method) were 1.22 and 2.54, respectively. (3) The method how to express the magnitude of synergism between heat and radiation: The rate of continuous chemical stress relaxation under heat and radiation Kh+r is expressed as Kh+r = Kh + Cc Iα exp(–E'/RT), where Kh is the rate of stress relaxation by heat alone, I is dose rate, E' is the coefficient of synergism, R is the gas constant, T is the temperature (in K), and Cc is the constant which refers to the sensitivity for radiation. The exponent α shows the dose rate dependence. (4) The difference between heat aging and radiation induced degradation of elastomers: Pure vulcanized ethylene-propylene copolymer was irradiated with 60Co γ rays in air at room temperature. The rate of chain scission of irradiated samples by heat was independent from the dose and was found to be ten times higher than that of non-irradiated samples. The results suggest that irradiation consumes the antioxidant agents added during the polymer production process by the energy transfer from polymer to antioxidant agents. On the other hand, the rate of stress decay of non-irradiated samples increased with the heat aging time at all temperatures. In this case, heat degrades polymer and antioxidant agent simultaneously. (5) Pure vulcanized tetrafluoroethylene-propylene elastomer was irradiated by 60Co γ rays in air at room temperature. The chemical stress relaxation of the samples was measured at various temperatures ranging from 100°C to 200°C. The rate of scission increased with increasing dose, but the rate leveled off at about 100 kGy. The increase in scission by irradiation might be due to the initiation of autoxidation by thermal decomposition of hydroperoxide accumulated during irradiation.