Thermodynamics of galaxy clusters in modified Newtonian potential

We study the thermodynamics of galaxy clusters in a modified Newtonian potential motivated by a general solution to Newton’s “sphere-point” equivalence theorem. We obtain the N particle partition function by evaluating the configurational integral while accounting for the extended nature of galaxies (via the inclusion of the softening parameter ε into the potential energy function). This softening parameter takes care of the galaxy-halos whose effect on structuring the shape of the galactic disc has been found recently. The spatial distribution of the particles (galaxies) is also studied in this framework. A comparison of the new clustering parameter b + to the original clustering parameters is presented in order to visualize the effect of the modified gravity. We also discuss the possibility of system symmetry breaking via the behavior of the specific heat as a function of temperature.

Experimental and Numerical Investigation on the Perforation Resistance of Double-Layered Metal Shield under High-Velocity Impact of Armor-Piercing Projectiles

In the case of protection of transportation systems, the optimization of the shield is of practical interest to reduce the weight of such components and thus increase the payload or reduce the fuel consumption. As far as metal shields are concerned, some investigations based on numerical simulations showed that a multi-layered configuration made of layers of different metals could be a promising solution to reduce the weight of the shield. However, only a few experimental studies on this subject are available. The aim of this study is therefore to discuss whether or not a monolithic shield can be substituted by a double-layered configuration manufactured from two different metals and if such a configuration can guarantee the same perforation resistance at a lower weight. In order to answer this question, the performance of a ballistic shield constituted of a layer of high-strength steel and a layer of an aluminum alloy impacted by an armor piercing projectile was investigated in experimental tests. Furthermore, an axisymmetric finite element model was developed. The effect of the strain rate hardening parameter C and the thermal softening parameter m of the Johnson–Cook constitutive model was investigated. The numerical model was used to understand the perforation process and the energy dissipation mechanism inside the target. It was found that if the high-strength steel plate is used as a front layer, the specific ballistic energy increases by 54% with respect to the monolithic high-strength steel plate. On the other hand, the specific ballistic energy decreases if the aluminum plate is used as the front layer.

A Constitutive Model of High-Early-Strength Cement with Perlite Powder as a Thermal-Insulating Material Confined by Caron Fiber Reinforced Plastics at Elevated Temperatures

A parabolic stress–strain constitutive model for inorganic thermal-insulating material confined by carbon fiber-reinforced polymer (CFRP) exposed to a surrounding elevated temperature was proposed in this paper. The thermal-insulating material used in this study was composed of high-early-strength cement (HESC) and perlite powder. The compression strengths of four kinds of perlite powder composition ratios of thermal-insulating materials cylindrical specimens which were confined by one, two, and three-layer CFRP composite materials were acquired. The experimental results showed that the compression strength was enhanced as the amount of perlite substitute decreased or as the number of CFRP wrapping layers increased. The Mohr–Columb failure criteria were adopted to predict the maximum compressive strength of CFRP-confined inorganic thermal-insulating material. The strain at the maximum compressive strength was found from the experimental results, and the corresponding axial strain at the maximum compressive strength in the constitutive model was determined from the regression analysis. Furthermore, the compressive strengths of the four different perlite composites of thermal-insulating materials were obtained when heating the specimens from ambient temperature to 300 °C. The compressive strength decreased with an increase in temperature, and a thermal softening parameter model was proposed; the thermal softening parameter was determined from the experimental maximum compressive strength at an elevated temperature. Combining the above two models, the constitutive model of HESC with perlite powder additive as a thermal-insulating material confined by CFRP under elevated temperature was proposed.

Potential softening and eccentricity dynamics in razor-thin, nearly Keplerian discs

ABSTRACTIn many astrophysical problems involving discs (gaseous or particulate) orbiting a dominant central mass, gravitational potential of the disc plays an important dynamical role. Its impact on the motion of external objects, as well as on the dynamics of the disc itself, can usually be studied using secular approximation. This is often done using softened gravity to avoid singularities arising in calculation of the orbit-averaged potential – disturbing function – of a razor-thin disc using classical Laplace–Lagrange theory. We explore the performance of several softening formalisms proposed in the literature in reproducing the correct eccentricity dynamics in the disc potential. We identify softening models that, in the limit of zero softening, give results converging to the expected behaviour exactly, approximately or not converging at all. We also develop a general framework for computing secular disturbing function given an arbitrary softening prescription for a rather general form of the interaction potential. Our results demonstrate that numerical treatments of the secular disc dynamics, representing the disc as a collection of N gravitationally interacting annuli, are rather demanding: for a given value of the (dimensionless) softening parameter, ς ≪ 1, accurate representation of eccentricity dynamics requires N ∼ Cς−χ ≫ 1, with C ∼ O(10), 1.5 ≲ χ ≲ 2. In discs with sharp edges a very small value of the softening parameter ς (≲ 10−3) is required to correctly reproduce eccentricity dynamics near the disc boundaries; this finding is relevant for modelling planetary rings.

Research on M-Paul Dynamic Constitutive Relation of Q235B Steel

In recent years, terrorist attacks and regional conflicts have increased and research on the resistance of building structures has been more highlighted. Q235B is a commonly used steel type in building structures, and there is an urgent need for research on its dynamic material properties. In this paper, Paul constitutive model was calibrated based on the material properties of Q235B steel. Based on the obtained results, it was found that the original model was not able to take into account temperature-softening effect. Therefore, a temperature-softening parameter was added into the temperature term of the original Paul model, and the modified M-Paul constitutive model was developed. Then, numerical prediction results obtained from Q235B steel penetration experiments using J-C (Johnson–Cook) and M-Paul constitutive models were compared. It was observed that J-C constitutive model significantly overestimated ballistic limit while estimations obtained from M-Paul constitutive model were closer to experimental results. This observation verified the correctness and effectiveness of M-Paul model and established a solid foundation for relevant research works on the impact resistance of building structures.

Three-Dimensional Unit Cell Study of a Porous Bulk Metallic Glass Under Various Stress States

Porous bulk metallic glasses (BMGs) exhibit an excellent combination of superior mechanical properties such as high strength, high resilience, large malleability, and energy absorption capacity. However, a mechanistic understanding of their response under diverse states of stress encountered in practical load-bearing applications is lacking in the literature. In this work, this gap is addressed by performing three-dimensional finite element simulations of porous BMGs subjected to a wide range of tensile and compressive states of stress. A unit cell approach is adopted to investigate the mechanical behavior of a porous BMG having 3% porosity. A parametric study of the effect of stress triaxialities T = 0, ±1/3, ±1, ±2, ±3, and ±∞, which correspond to stress states ranging from pure deviatoric stress to pure hydrostatic stress under tension and compression, is conducted. Apart from the influence of T, the effects of friction parameter, strain-softening parameter and Poisson’s ratio on the mechanics of deformation of porous BMGs are also elucidated. The results are discussed in terms of the simulated stress-strain curves, pore volume fraction evolution, strain to failure, and development of plastic deformation near the pore. The present results have important implications for the design of porous BMG structures.

Boron Effect on the Softening Parameter (Ω) of Advanced Ultra-High Strength Steels (A-UHSS) under Uniaxial Hot-Compression Conditions

ABSTRACTAdvanced ultra-high strength steels (A-UHSS) are revolutionizing both the steel and automotive industries, therefore it is imperative to study their hot plastic deformation behavior and modeling. The flow characteristics of all hot forming processes consist basically of two competitive phenomena: strain hardening and softening due to dynamic mechanisms (recovery and/or recrystallization). In this research work, the softening parameter was determined in a low carbon A-UHSS microalloyed steel with different amounts of boron (0, 14 and 214 ppm). Experimental stress–strain data of uniaxial hot-compression tests at different temperatures (950, 1000, 1050 and 1100 °C) and strain rates (10–3, 10–2 and 10–1 s–1) were used. The stress–strain relationships as a function of temperature and strain rate were described on the basis of the Estrin, Mecking, and Bergström model. The experimental values of the softening parameter Ω were adjusted using the least-squares method. In general, the results reveal that the softening parameter increases with increasing boron content.

Study on Post-Failure Deformation and Residual Strength of Rock Mass Based on Hoek-Brown Criterion

In order to predict the stability of surrounding rock mass in geotechnical engineering, it is important to study the post-failure deformation property and residual strength of rock mass. Based on evolutional behavior of strength parameters, aiming at generalized Hoek-Brown strength criterion, selecting major principal strain as strain softening parameter, this paper presents the method of solving post-failure stress-strain curve . In numerical case, the effect of evolutional law of strength parameters ， and to deformation and residual strength is discussed and we can draw the following conclusions: the greater the residual values of ， are and the smaller the residual value of is, the post-failure strain softening curve falls more gently and the greater the residual strength is.

Study on Grouting Pressure of Splitting Grouting Based on Cylindrical Expansion Considering Large Strain

Anti-seepage reinforcement technology of splitting grouting to improve the stability of dam, has been an effective reinforcement method in the field of dam reinforcement. Based on the extended SMP criterion and stress-dilatancy relation considering large strain, the governing equations of axisymmetric problem in the plane strain condition and the partial differential equations for the boundary-value problem of cavity expansion in frictional cohesive soils were established. Then, the early phase of splitting grouting is regarded as the plane strain question of cylindrical expansion infinite soil. Under initial grouting pressure, the soil body was supposed as ideal elastic mass. However, the soil body was supposed to generate plastic damage considering large strain with the increase of grouting pressure and submit the extended spatial mobilization plane theory. Solutions of radial and hoop stresses and strains around the grouting cavity were obtained by recursive computations. Furthermore, the influence of damage softening parameter, cohesion and friction angle was examined by a parametric study.

Effect of Austenite Deformation on Recrystallisation Behaviour in an X-70 Microalloyed Steel

In the present study, the effect of austenite deformation on the recrystallisation behaviour in terms of recrystallisation-stop and recrystallisation-limit temperatures (T5% and T95%) of an X70 niobium microalloyed pipeline steel have been investigated by interrupted plane strain compression tests. The extents of recrystallisation are calculated using a modified fractional softening parameter. And the 20% and 60% of fractional softening were correlated to T5% and T95%. Quantitative optical metallography indicates that this method provides for a convenient and reliable experimental measurement of the critical temperatures associated with the recrystallisation of austenite. The recrystallisation kinetics and the precipitation kinetics of Nb(CN) were calculated using two widely applied models. The experimental results from this study suggest that the current model of precipitation kinetics might overestimate the precipitation start time.