Influence of manufacturing process-induced geometrical defects on the energy absorption capacity of polymer lattice structures

Modern additive manufacturing processes enable fabricating architected cellular materials of complex shape,which can be used for different purposes.Among them,lattice structures are increasingly used in applications requiring a compromise among lightness and suited mechanical properties,like improved energy absorption capacity and specific stiffness-to-weight and strength-to-weight ratios.A dedicated modeling strategy to assess the energy absorption capacity of lattice structures under uni-axial compression loading is presented in this work.The numerical model is developed in a non-linear framework accounting for the strain rate effect on the mechanical responses of the lattice structure.Four geometries,i.e.,cubic body centered cell,octet cell,rhombic-dodecahedron and truncated cuboctahedron 2+,are investigated.Specifically,the influence of the relative density of the representative volume element of each geometry,the strain-rate dependency of the bulk material and of the presence of the manufacturing process-induced geometrical imperfections on the energy absorption capacity of the lattice structure is investigated.The main outcome of this study points out the importance of correctly integrating geometrical imperfections into the modeling strategy when shock absorption applications are aimed for.

Geometric Accuracy and Energy Absorption Characteristics of 3D Printed Continuous Ramie Fiber Reinforced Thin-Walled Composite Structures

The application of continuous natural fibers as reinforcement in composite thin-walled structures offers a feasible approach to achieve light weight and high strength while remaining environmentally friendly.In addition,additive manufacturing technology provides a favorable process foundation for its realization.In this study,the printability and energy absorption properties of 3D printed continuous fiber reinforced thin-walled structures with different configurations were investigated.The results suggested that a low printing speed and a proper layer thickness would mitigate the printing defects within the structures.The printing geometry accuracy of the structures could be further improved by rounding the sharp corners with appropriate radii.This study successfully fabricated structures with vari-ous configurations characterized by high geometric accuracy through printing parameters optimization and path smoothing.Moreover,the compressive property and energy absorption characteristics of the structures under quasi-static axial compression were evaluated and compared.It was found that all studied thin-walled structures exhibited progressive folding deformation patterns during compression.In particular,energy absorption process was achieved through the combined damage modes of plastic deformation,fiber pullout and delamination.Furthermore,the com-parison results showed that the hexagonal structure exhibited the best energy absorption performance.The study revealed the structure-mechanical property relationship of 3D printed continuous fiber reinforced composite thin-walled structures through the analysis of multiscale failure characteristics and load response,which is valuable for broadening their applications.

An Original Didactic of the Standard Model “The Particle’s Geometric Model” (Nucleons and K-Mesons)

This paper shows a didactic model (PGM), and not only, but representative of the Hadrons described in the Standard Model (SM). In this model, particles are represented by structures corresponding to geometric shapes of coupled quantum oscillators (IQuO). By the properties of IQuO one can define the electric charge and that of color of quarks. Showing the “aurea” (golden) triangular shape of all quarks, we manage to represent the geometric combinations of the nucleons, light mesons, and K-mesons. By the geometric shape of W-bosons, we represent the weak decay of pions and charged Kaons and neutral, highlighting in geometric terms the possibilities of decay in two and three pions of neutral Kaon and the transition to anti-Kaon. In conclusion, from this didactic representation, an in-depth and exhaustive phenomenology of hadrons emerges, which even manages to resolve some problematic aspects of the SM.

An Original Didactic about Standard Model (Geometric Model of Particle: The Quarks)

This work shows a didactic model representative of the quarks described in the Standard Model (SM). In the model, particles are represented by structures corresponding to geometric shapes of coupled quantum oscillators (GMP). From these didactic hypotheses emerges an in-depth phenomenology of particles (quarks) fully compatible with that of SM, showing, besides, that the number of possible quarks is six.

Topology Optimization of Compliant Mechanisms with Geometrical Nonlinearities Using the Ground Structure Approach

The majority of topology optimization of compliant mechanisms uses linear finite element models to find the structure responses.Because the displacements of compliant mechanisms are intrinsically large,the topological design can not provide quantitatively accurate result.Thus,topological design of these mechanisms considering geometrical nonlinearities is essential.A new methodology for geometrical nonlinear topology optimization of compliant mechanisms under displacement loading is presented.Frame elements are chosen to represent the design domain because they are capable of capturing the bending modes.Geometrically nonlinear structural response is obtained by using the co-rotational total Lagrange finite element formulation,and the equilibrium is solved by using the incremental scheme combined with Newton-Raphson iteration.The multi-objective function is developed by the minimum strain energy and maximum geometric advantage to design the mechanism which meets both stiffness and flexibility requirements, respectively.The adjoint method and the direct differentiation method are applied to obtain the sensitivities of the objective functions. The method of moving asymptotes（MMA） is employed as optimizer.The numerical example is simulated to show that the optimal mechanism based on geometrically nonlinear formulation not only has more flexibility and stiffness than that based on linear formulation,but also has better stress distribution than the one.It is necessary to design compliant mechanisms using geometrically nonlinear topology optimization.Compared with linear formulation,the formulation for geometrically nonlinear topology optimization of compliant mechanisms can give the compliant mechanism that has better mechanical performance.A new method is provided for topological design of large displacement compliant mechanisms.

Geometric Structures of Stable Time-Variant State Feedback Systems

A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedback gains is given. Moreover, a diffeomorphic structure between the set of stabilizing time-variant state feedback gains and the Cartesian product of positive definite matrix and skew symmetric matrix satisfying certain algebraic conditions is constructed. Furthermore, an immersion and some results about the eigenvalue locations of stable state feedback systems are derived.

A Density Functional Theory Study of the Geometric and Electronic Structure of MgF_2 (110) Surface

Abstract＂ Ab initio density functional theory （DFT） was employed to study geometric and electronic structure of MgF2 （110） surface. Three different clean surface models have been considered. The results show that the surface terminated with one-layer F has the smallest relaxation and the lowest surface energy, which indicates this model is the most energetically favorable structure of MgF2（110） surface. Furthermore, the electronic properties are also discussed from the point of density of states and charge density. Analysis of electronic structure shows that the band gap of the surface is significantly narrowed with respect to the bulk. The electrons of the surface exhibit strong locality and larger effective mass.

An Initial Research on the Geometric Theory of Quasicrystal Structures

The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattice , and put them together to form the geometric lattices of quasicrystal structures . The general characteristics of quasicrystal geometric lattices , the relation between structural models and geometric lattices , and the relation formula (k=0 , 2 , 4 , 6 , 8, 10,12) of the symmetric axis between quasicrystal and crystal are discussed based on the quasicrystal space geometric lattices. This is of significant in quasicrystal research .

Information Geometric Structures for the Thermodynamic Manifold

In view of information geometry,the state space S of thermodynamic parameters is investigated.First a Riemannian metric for S is defined and then the α-geometric structures of S is given.Some of results obtained by other authors are extended.

Geometrical Structures of Certain Class of Statistical Manifolds

The geometrical structures of the certain class of statistical manifolds are investigated. The geometwhich includes the original geometrical metrics of S.Amari.

GEOMETRIC STRUCTURE OF ETHYLENOXIDE ADSORBED ON Cu(110) SURFACE

The binding energies of ethylene oxide (Et-O) adsorbed on Cu(110) surface for different adsorption sites and orientations are calculated with an atom superposition and electron delocalization molecular orbital (ASED-MO) using cluster models. It shows that the top site of Cu(110) surface is preferable for Et-O adsorption and the orientation of C-C bond of Et-O is parallel to the [110] direction of the substratc. The distance of an oxygen of Et-O to the Cu atom is approximately 1.5817(?). It is different from the supposition of C. Benndorf et al., in which the oxygen was proposed on the short bridge site with C-C bond orientating to [110] direction of Cu(110)

Geometric Structure and Tectonic Activities of Wanquan Fault,Hebei Province

Based on detailed investigations and prospecting,this paper describes the geometrical characteristics and tectonic activities of Wanquan fault in northwest of Beijing. This fault strikes mainly northeast or northeast to north,dipping southeast,and extends over a length of 15km. It is a major geological and geomorphological margin,controlling the neotectonic movement in this region. On the southeast side of Wanquan fault are the Late Quaternary unconsolidated deposits,forming a basin or deposition; but on the other side is Mesozoic volcano debris,forming lower-mountains and hills. Wanquan fault is a mid- to-high-angle normal fault dipping southeast. This fault was more active in the Quaternary. Since the middle-late part of the alate Pleistocene,the average rate with vertical slip of a single fault is over 0. 03 ～ 0. 3mm /a,but the fault has multiple slipping surfaces,and a total rate with vertical slip will be estimated.

Structure-preserving geometric particle-in-cell methods for Vlasov-Maxwell systems

Recent development of structure-preserving geometric particle-in-cell （PIC） algorithms for Vlasov-Maxwell systems is summarized. With the arrival of 100 petaflop and exaflop computing power, it is now possible to carry out direct simulations of multi-scale plasma dynamics based on first-principles. However, standard algorithms currently adopted by the plasma physics community do not possess the long-term accuracy and fidelity required for these large-scale simulations. This is because conventional simulation algorithms are based on numerically solving the underpinning differential （or integro-differential） equations, and the algorithms used in general do not preserve the geometric and physical structures of the systems, such as the local energy-momentum conservation law, the symplectic structure, and the gauge symmetry. As a consequence, numerical errors accumulate coherently with time and long-term simulation results are not reliable. To overcome this difficulty and to harness the power of exascale computers, a new generation of structure-preserving geometric PIC algorithms have been developed. This new generation of algorithms utilizes modem mathematical techniques, such as discrete manifolds, interpolating differential forms, and non-canonical symplectic integrators, to ensure gauge symmetry, space-time symmetry and the conservation of charge, energy-momentum, and the symplectic structure. These highly desired properties are difficult to achieve using the conventional PIC algorithms. In addition to summarizing the recent development and demonstrating practical implementations, several new results are also presented, including a structure-preserving geometric relativistic PIC algorithm, the proof of the correspondence between discrete gauge symmetry and discrete charge conservation law, and a reformulation of the explicit non-canonical symplectic algorithm for the discrete Poisson bracket using the variational approach. Numerical examples are given to verify the advantages of the structure- preserving geometric PIC algorithms in comparison with the conventional PIC methods.

Resolving the geometric structure of trastuzumab by mobility capillary electrophoresis and native mass spectrometry

Available online Immunoglobulins G(IgGs)are Y-shaped globular proteins,however,their high flexibility and heterogeneity pose great challenges to their structure and conformation determinations.Geometric structure of IgG closely correlates to its biofunctions,such as the antibody escape of human immunodeficiency virus(HIV)could attribute to the distance mismatch between the ends of two Fab arms(antigen-binding sites)and envelope glycoprotein spikes on virion surface.Herein,we report the first use of mobility capillary electrophoresis(MCE)and native mass spectrometry(nMS)to resolve the internal geometric structure and conformation of an IgG(trastuzumab)in solution phase.After proteolysis,the ellipsoid dimensions of IgG and its subunits were measured by MCE-nMS experiments.IgG was then reconstructed,in which the sizes and relative positions of these three subunits in three-dimensional space were characterized.It was found that the two Fab arms have an angle of~102.1°and a distance of~11.0 nm between the two antigen-binding sites under native condition,and the Fc arm was tilted~16.0°towards one of the Fab arms.Fc was not on the plane of Fab-Fab,but has an angle of no larger than 103.1°.Under acidic environment(pH 3.0),each subunit of the IgG would unfold into larger dimensions,and the angles between these subunits also change.With great potential for tumor imaging and therapy,the structure of F(ab')_(2)fragments was also measured and validated by molecular dynamic simulation.It was found that the electrostatic force among these three subunits and steric hindrance stemming from Fc help maintaining the angle between two Fab arms.

Comparative Study of 3D-Printed Porous Titanium Alloy with Rod Designs of Three Different Geometric Structures for Orthopaedic Implantation

Porous titanium alloy is currently widely used in clinical treatment of orthopaedic diseases for its lower elastic modulus and ability to integrate with bone tissue.At the micro-level,cells can respond to different geometries,and at the macro-level,the geometric design of implants will also affect the biological function of cells.In this study,three kinds of porous scaffolds with square,triangular and circle rod shapes were designed and 3D printed.This study observed the proliferation and differentiation of MC3T3-E1 cells during surface culture of the three types of scaffolds.It also evaluated the characteristics of the three scaffolds by means of compression tests and scanning electron microscopy to provide a reference for the design of porous titanium alloy implants for clinical applications.The trends of cell proliferation and gene expression between the three types of scaffolds were observed after treatment with two inhibitors.The results show that the square rod porous scaffolds have the best proliferative and osteogenic activities,and these findings may be due to differences in piezo-type mechanosensitive ion channel component 1(Piezo1)and Yes-associated protein(YAP)expression caused by the macro-geometric topography.

GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION

Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.

Analysis of Machinable Structures and Their Wettability of Rotary Ultrasonic Texturing Method

Tailored surface textures at the micro- or nanoscale dimensions are widely used to get required functional performances. Rotary ultrasonic texturing （RUT） technique has been proved to be capable of fabricating periodic micro- and nanostructures. In the present study, diamond tools with geometrically defined cutting edges were designed for fabricating different types of tailored surface textures using the RUT method. Surface generation mechanisms and machinable structures of the RUT process are analyzed and simulated with a 3D-CAD program. Textured surfaces generated by using a triangular pyramid cutting tip are constructed. Different textural patterns from several micrometers to several tens of micrometers with few burrs were successfully fabricated, which proved that tools with a proper two-rake-face design are capable of removing cutting chips efficiently along a sinusoidal cutting locus in the RUT process. Technical applications of the textured surfaces are also discussed. Wetting properties of textured aluminum surfaces were evaluated by combining the test of surface roughness features. The results show that the real surface area of the textured aluminum surfaces almost doubled by comparing with that of a flat surface, and anisotropic wetting properties were obtained due to the obvious directional textural features.

Three-dimensional spatial structure of the macro-pores and flow simulation in anthracite coal based on X-ray μ-CT scanning data

The three-dimensional(3 D) structures of pores directly affect the CH4 flow.Therefore,it is very important to analyze the3 D spatial structure of pores and to simulate the CH4 flow with the connected pores as the carrier.The result shows that the equivalent radius of pores and throats are 1-16 μm and 1.03-8.9 μm,respectively,and the throat length is 3.28-231.25 μm.The coordination number of pores concentrates around three,and the intersection point between the connectivity function and the X-axis is 3-4 μm,which indicate the macro-pores have good connectivity.During the single-channel flow,the pressure decreases along the direction of CH4 flow,and the flow velocity of CH4 decreases from the pore center to the wall.Under the dual-channel and the multi-channel flows,the pressure also decreases along the CH4 flow direction,while the velocity increases.The mean flow pressure gradually decreases with the increase of the distance from the inlet slice.The change of mean flow pressure is relatively stable in the direction horizontal to the bedding plane,while it is relatively large in the direction perpendicular to the bedding plane.The mean flow velocity in the direction horizontal to the bedding plane(Y-axis) is the largest,followed by that in the direction horizontal to the bedding plane(X-axis),and the mean flow velocity in the direction perpendicular to the bedding plane is the smallest.

The Bare and Dressed Masses of Quarks in Pions via the of Quarks’ Geometric Model

In previous articles (Guido) we demonstrated that Quarks (u, d) are represented by golden geometric structures of coupled quantum oscillators. In this article we show the geometric structure of the pion triplet and, in particular, via the structure equation of neutral pion, we identify its decays and we solve the spin question in hadrons thanks also to introduction of algebraic operations [?, ⊕] on geometric structure. Moreover by means of the golden ratio between (u, d), we determine the values of bare masses of quarks (3.51 MeV for u-quark and 5.67 MeV for d-quark) and those ones bounded in a pion (53.31 MeV for u-quark and 85.26 MeV for d-quark). Finally, using algebraic operations [?, ⊕] we point out a new way to represent the processes of pions’ decay.

The Theoretical Value of Mass of the Light <i>η</i>-Meson via the Quarks’ Geometric Model

Highlighting a golden triangular form in u and d quarks (Quark Geometric Model), we build the geometric structures of light meson η and individualize its decays and spin. By the structure equations describing mesons, we determine a mathematic procedure to calculate the theoretical value of the mass of light mesons η.