Statistics for Spatial Data.

Freedom of design, mass customisation, waste minimisation and the ability to manufacture complex structures, as well as fast prototyping, are the main benefits of additive manufacturing (AM) or 3D printing. A comprehensive review of the main 3D printing methods, materials and their development in trending applications was carried out. In particular, the revolutionary applications of AM in biomedical, aerospace, buildings and protective structures were discussed. The current state of materials development, including metal alloys, polymer composites, ceramics and concrete, was presented. In addition, this paper discussed the main processing challenges with void formation, anisotropic behaviour, the limitation of computer design and layer-by-layer appearance. Overall, this paper gives an overview of 3D printing, including a survey on its benefits and drawbacks as a benchmark for future research and development.

Additive manufacturing (3D printing): A review of materials, methods, applications and challenges

In the paper, we present a new definition of fractional deriva tive with a smooth kernel which takes on two different representations for the temporal and spatial variable. The first works on the time variables; thus it is suitable to use th e Laplace transform. The second definition is related to the spatial va riables, by a non-local fractional derivative, for which it is more convenient to work with the Fourier transform. The interest for this new approach with a regular kernel was born from the prospect that there is a class of non-local systems, which have the ability to descri be the material heterogeneities and the fluctuations of diff erent scales, which cannot be well described by classical local theories or by fractional models with singular kernel.

http://www.naturalspublishing.com/files/published/0gb83k287mo759.pdf

A new Definition of Fractional Derivative without Singular Kernel

Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications

A mean-field phase diagram for conformationally symmetric diblock melts using the standard Gaussian polymer model is presented. Our calculation, which traverses the weak- to strong-segregation regimes, is free of traditional approximations. Regions of stability are determined for disordered (DIS) melts and for ordered structures including lamellae (L), hexagonally packed cylinders (H), body-centered cubic spheres (QIm3m), close-packed spheres (CPS), and the bicontinuous cubic network with Ia3d symmetry (QIa3d). The CPS phase exists in narrow regions along the order−disorder transition for χN ≥ 17.67. Results suggest that the QIa3d phase is not stable above χN ∼ 60. Along the L/QIa3d phase boundaries, a hexagonally perforated lamellar (HPL) phase is found to be nearly stable. Our results for the bicontinuous Pn3m cubic (QPn3m) phase, known as the OBDD, indicate that it is an unstable structure in diblock melts. Earlier approximation schemes used to examine mean-field behavior are reviewed, and compa...

Unifying Weak- and Strong-Segregation Block Copolymer Theories

The effect of lode parameter on the yield surface of Schoen's IWP triply periodic minimal surface lattice

We have developed a novel, facile and architecturally versatile fabrication method for specially designed cellular graphene lattices using additively manufactured polymer-based gyroidal triply periodic minimal surface (TPMS) as the initial sacrificial scaffold. Three-dimensional (3D)-printed templates of the polymeric gyroid lattices were coated with a mixture of graphene oxide (GO) and hydrazine solution via the hydrothermal process, followed by drying and thermal etching of the polymer scaffold, which resulted in a neat reduced GO (rGO) lattice of the gyroidal TPMS structure. Scanning electron microscopy and micro-computed tomography were used to evaluate the morphology and size of the 3D rGO architectures, while a Raman response at 1360[Formula: see text]cm[Formula: see text] (D peak), 1589[Formula: see text]cm[Formula: see text] (G peak) and 2696[Formula: see text]cm[Formula: see text] (2D peak) verified the presence of rGO. Thermo–electro–mechanical properties of rGO gyroid lattices of different densities were characterized where the highest Young’s modulus recorded was 351[Formula: see text]kPa for a sample with a density of 45.9[Formula: see text]mg[Formula: see text][Formula: see text][Formula: see text]cm[Formula: see text]. The rGO gyroid lattice exhibits an electrical conductivity of 1.07[Formula: see text]S[Formula: see text][Formula: see text][Formula: see text]m[Formula: see text] and high thermal insulation property with a thermal conductivity of 0.102[Formula: see text]W[Formula: see text][Formula: see text][Formula: see text]m[Formula: see text][Formula: see text]K[Formula: see text]. It is demonstrated that the hydrothermal-assisted fabrication process is adaptable for different lattice architectures based on 3D-printed scaffolds and thus has wide functional applications.

Scalable synthesis, characterization and testing of 3D architected gyroid graphene lattices from additively manufactured templates

Due to the lack of the classical local continuum formulation to produce physically meaningful and numerically converging results within large deformation and strain localization computations, a thermodynamically motivated micro-damage formulation is proposed for highrate and temperature dependent materials. This model uses a combined viscosity and nonlocal gradient localization limiters in order to regularize the dynamic strain localization problems. The enhanced nonlocal gradient-dependent theory formulates a constitutive framework on the continuum level that is used to bridge the gap between the micromechanical theories and the classical (local) continuum theories. They are successful in explaining the size effects encountered at the micron scale and in preserving the well-posedeness of the initial boundary value problem governing the solution of material instability triggering strain localization. Moreover, viscosity (rate dependency) allows the spatial difference operator in the governing equations to retain its hyperbolicity and the initial boundary value problem is well-posed. This is due to the incorporation of either explicit (via nonlocal theory) or implicit (via viscosity) intrinsic material length scale parameter in the constitutive description. Model capabilities are preliminarily illustrated for the dynamic localization of inelastic flow in adiabatic shear bands and the perforation of Weldox 460E steel plates with different thicknesses by deformable blunt projectiles at various impact speeds. The simulated shear band results well illustrated the potential of the proposed model in dealing with the well-known mesh sensitivity problem. Consequently the introduced implicit and explicit length scale measures are able to predict size effects in localization failures. The micro-damage model used to predict material behavior under dynamic loading conditions was earlier presented in Refs. 1 and 2. Thus, only the main equations will be given in the following. The model is based on the nonlocal gradient-dependent theory. It includes the von Mises yield criterion, the non-associated flow rules, isotropic and anisotropic strain hardening, strain rate hardening, softening due to adiabatic heating and anisotropic damage evolution, and finally a path dependent equation of state. The stress-strain rate relationship in the spatial and damaged configuration is given by

Modeling and Simulation of Perforation of Steel Plates by Blunt Projectiles

During highly dynamic and ballistic loading processes, large inelastic deformation associated with high strain rates leads, for a broad class of heterogeneous materials, to degradation and failure by localized damage and fracture. However, as soon as material failure dominates a deformation process, the material increasingly displays strain softening and the finite element predictions of ballistic response are considerably affected by the mesh size. This gives rise to non-physical description of the ballistic behavior and mesh-dependent ballistic limit velocities that may mislead the design of ballistic-resistant materials. This study is concerned with the development and numerical implementation of a novel coupled thermo-hypoelasto-viscoplastic and thermoviscodamage constitutive model within the laws of thermodynamics in which an intrinsic material length scale parameter is incorporated through the nonlocal gradient-dependent damage approach. It is shown through simulating plugging failure in ballistic penetration of high-strength steel targets by blunt projectiles that the length scale parameter plays the role of a localization limiter allowing one to obtain meaningful values for the ballistic limit velocity independent of the finite element mesh density. Therefore, the proposed nonlocal damage model leads to an improvement in the modeling and numerical simulation of high velocity impact related problems.

Rashid K. Abu Al-Rub

Papers

The effect of lode parameter on the yield surface of Schoen's IWP triply periodic minimal surface lattice

Scalable synthesis, characterization and testing of 3D architected gyroid graphene lattices from additively manufactured templates

Modeling and Simulation of Perforation of Steel Plates by Blunt Projectiles

Nonlocal Microdamage Constitutive Model for High Energy Impacts

A Gradient-Dependent Constitutive Model to Simulate Impact Damage Problem