In this paper, a new method, named the Fragile Points Method (FPM), is developed for computer modeling in engineering and sciences. In the FPM, simple, local, polynomial, discontinuous and Point-based trial and test functions are proposed based on randomly scattered points in the problem domain. The local discontinuous polynomial trial and test functions are postulated by using the Generalized Finite Difference method. These functions are only piece-wise continuous over the global domain. By implementing the Point-based trial and test functions into the Galerkin weak form, we define the concept of Point Stiffnesses as the contribution of each Point in the problem domain to the global stiffness matrix. However, due to the discontinuity of trial and test functions in the domain, directly using the Galerkin weak form leads to inconsistency. To resolve this, Numerical Flux Corrections, which are frequently used in Discontinuous Galerkin methods are further employed in the FPM. The resulting global stiffness matrix is symmetric and sparse, which is advantageous for large-scale engineering computations. Several numerical examples of 1D and 2D Poisson equations are given in this paper to demonstrate the high accuracy, robustness and convergence of the FPM. Because of the locality and discontinuity of the Point-basedtrial and test functions, this method can be easily extended to model extreme problems in mechanics, such as fragility, rupture, fracture, damage, and fragmentation. These 2 extreme problems will be discussed in our future studies.

In this study, the morphological evolution and sintering properties of the palygorskite nanofibers were studied along with the increase of temperature, using raw palygorskite as materials. The palygorskite powder was calcined at different temperatures in the range of 100°C‐1200°C, and the microstructural evolution of the palygorskite nanofibers was investigated by thermogravimetric and differential thermal analysis (TG‐DTA), X‐ray diffraction (XRD), scanning electron microscopy (SEM), and high‐resolution transmission electron microscope (HRTEM). Furthermore, the palygorskite powder was shaped to bars by dry pressing and sintered from 700°C to 1200°C. The properties of the sintered palygorskite were characterized by bending strength, mercury intrusion porosimeter (MIP), and stepwise isothermal dilatometry (SID). The results showed that the morphology of palygorskite nanofibers maintained unchanged till 1000°C. The palygorskite nanofibers molted to bind each other and formed a solid interwoven network structure at 1100°C. Correspondingly, it was shown from the sharply decrease of the sintered palygorskite porosity from 45.46% at 1000°C to 1.82% at 1100°C that the dense sintering of palygorskite started at 1100°C. With the sintering proceeding, some closed micropores fused each other to form bigger opening pores, resulting in a slight increase of porosity at 1200°C. However, the pore size distribution got more uniform and the density of the sintered body increased. So the bending strength of the sintered body reached the maximum of 176.67 Mpa and finally the main crystalline phases of the sintered sample changed to quartz, enstatite, and kyanite. The sintering activation energy of the palygorskite was measured by means of SID with a value of 906.46 kJ·mol−1.

In this paper, a new type of porous ceramics was prepared using the raw sepiolite mineral. The porous ceramics was shaped by the dry pressing method and sintered in the range of 700 ~ 1200 °C. The temperature-microstructure evolution and the properties of porous sepiolite ceramics were investigated by thermo gravimetric and differential thermal analyses (TG-DTA), X-ray diffraction (XRD), bending strength, compressive strength, scanning electron microscopy (SEM) and mercury intrusion porosimeter (MIP). The sintering kinetics of the porous ceramics from sepiolite was investigated by means of stepwise isothermal dilatometry (SID). The mechanical properties improved with the increasing sintering temperature, and the bending strength and compression strength reached a maximum of 52 MPa and 32 MPa respectively at 1200 °C. The porosity increased with the sintering temperature until 1100 °C attaining the value of 55.40% and then decreased to a value of 46.48% at 1200 °C. The main crystal phases of the porous ceramics were akermanite and diopside. At 1200 °C, the pores inside the ceramics basically follows a unimodal distribution, which was mainly located near 553 nm. The sintering activation energy of porous sepiolite ceramics was measured by step isothermal thermal expansion with a value of 791.42 kJ/mol in the range of 1000 °C to 1200 °C.

The sintering process of bone china bodies containing 0, 2, 4, and 6 wt % palygorskite was studied by X-ray diffraction (XRD), differential scanning calorimetry and thermogravimetry (DSC/TG), and dilatometric tests. According to the XRD and DSC/TG results, the increment of palygorskite increased the content of the amorphous phase and reduced the formation temperature of the early liquid phase in the bone china bodies. The shrinkage data showed that the starting sintering temperature and maximum shrinkage temperature of bone china bodies in the stage of liquid-phase sintering decreased by 20 and 15 °C via adding 6 wt % palygorskite, respectively. Also, the maximum shrinkage rose with increasing amount of palygorskite. Moreover, the kinetic analysis of shrinkage data was conducted by the Salem model. The value of the mechanismcharacteristic exponent, m, rose from 0.62 to 0.91 by adding 6 wt % palygorskite. In addition, with increasing palygorskite, the value of activation energy, E a , linearly reduced, and the value of rate constant A increased.

Notched components are commonly used in engineering structures, where stress concentration may easily lead to crack initiation and development. The main goal of this work is to develop a simple numerical method to predict the strength and crack‐growth‐path of U‐notched specimens made of brittle materials. For this purpose, the Fragile Points Method (FPM), as previously proposed by the authors, has been augmented by an interface debonding model at the interfaces of the FPM domains, to simulate crack initiation and development. The formulations of FPM are based on a discontinuous Galerkin weak form where point‐based piece‐wise‐continuous polynomial test and trial functions are used instead of element‐based basis functions. In this work, the numerical fluxes introduced across interior interfaces between subdomains are postulated as the tractions acting on the interface derived from an interface debonding model. The interface damage is triggered when the numerical flux reaches the interface strength, and the process of crack‐surface separation is governed by the fracture energy. In this way, arbitrary crack initiation and propagation can be naturally simulated without the need for knowing the fracture‐patch before‐hand. Additionally, a small penalty parameter is sufficient to enforce the weak‐form continuity condition before damage initiation, without causing problems such as artificial compliance and numerical ill‐conditioning. As validations, the proposed FPM method with the interface debonding model is used to predict fracture strength and crack‐growth trajectories of U‐notched structures made of brittle materials, which is useful but challenging in engineering structural design practices.

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Heavy metals can bring health risks through the enrichment of crops and food chain, but there are few reports on their impact on the nutritional quality of crops. In this paper, the hydroponic-culturedpea seedlings under lead and cadmium stress were used to evaluate the heavy metal effects on growth, safety and nutrients variation. Lead has little effect on the sprout growth, and it mainly concentrates in the roots and seldom can be transferred to the edible parts. It would not bring health and safety hazards to the edible parts of stems and leaves but decrease the mineral nutrientsin peasprout slightly. Cadmium significantlyaffectboth growth and nutrition value of pea sprout, not only the root is abundant, but also the transfer rate of root and stem, which is about 13%. The nutrient content of Ca and Zn in stem and leaf is decreased significantly under cadmium stress.