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This paper aims to focus on studying the influence of gradient parameters, namely, thickness coefficient, length coefficient and height ratio of auxetic structure on responses such as strength, stiffness and specific energy absorption (SEA) under compressive loading. Optimization of significant parameters is also performed to maximize responses. Further, efforts have also been made to develop regression models for strength, stiffness and SEA of auxetic structure.

Central composite design of response surface methodology is used for planning experiments. Auxetic structures of acrylonitrile butadiene styrene (ABS) and poly-lactic acid (PLA) materials are fabricated by the material extrusion (ME) technique of additive manufacturing. Fabricated structures are tested under in-plane uniaxial compressive loading. Grey relational analysis is used for the optimization of gradient parameters of the unit cell of auxetic structure to maximize responses and minimize weight and time of fabrication.

From the analysis of variance of experimental data, it is found that the compressive strength of auxetic structures increases with a decrease in length coefficient and height ratio. In the case of ABS structures, stiffness increases with a decrease in thickness coefficient and length coefficient, while in the case of PLA structures, stiffness increases with a decrease in length coefficient and height ratio. SEA is influenced by length coefficient and thickness coefficient in ABS and PLA structures, respectively. Based on the analysis, statistical non-linear quadratic models are developed to predict strength, stiffness and SEA. Optimal configuration of auxetic structure is determined to maximize strength, stiffness, SEA and minimize weight and time of fabrication.

The present study is limited to re-entrant type of auxetic structures made of ABS and PLA materials only under compressive loading. Also, results from the current study are valid within a selected range of gradient parameters. The findings of the present study are useful in the optimal selection of gradient parameters for the fabrication of auxetic structures of maximum strength, stiffness and SEA with minimum weight and time of fabrication. These outcomes have wide applications in domains such as automotive, aerospace, sports and marine sectors.

Limited literature is available on studying the influence of gradient parameters of ME manufactured auxetic structure of ABS and PLA materials on responses, namely, strength, stiffness and SEA under compressive loading. Also, no work has been reported on studying the influence of gradient parameters on mechanical properties, weight and time of fabrication of auxetic structures. The present study is an attempt to fulfil the above research gaps.

A delamination fracture analysis of two-dimensional functionally graded multilayered end-loaded split beam configuration with non-linear mechanical behaviour of material is conducted. The beam is made of an arbitrary number of longitudinal layers. Perfect adhesion between layers is assumed. The material is two-dimensional functionally graded in the cross-section of each layer. Also, each layer has individual thickness and material properties. A delamination crack is located arbitrary along the beam height. The paper aims to discuss these issues.

The delamination fracture behaviour is investigated analytically in terms of the strain energy release rate by analysing the balance of the energy. An additional analysis of the delamination fracture is performed by applying the J-integral approach for verification.

The solutions derived are used to evaluate the effects of crack location, material gradients and material non-linearity on the delamination fracture behaviour of end-loaded split beam. The effect of material gradient on the distribution of the J-integral value along the crack front is elucidated too.

Delamination in the multilayered functionally graded end-loaded split beam exhibiting non-linear mechanical behaviour of the material is analysed assuming that the material property is distributed non-linearly in both thickness and width directions in each layer.

The study aims to explore the composition and microstructure of clay functionally graded materials under the process of double-gradient direct ink writing (DIW).

The investigation focused specifically on the pore characteristics of barite-kaolin clay composite after three-dimensional (3D) printing and sintering as well as its bionic application in geophysical model.

The model with pore and material variations brought about spatial and nonlinear mechanical properties. Moreover, the vertical gradient and connected pores in the upper kaolin part simulated the natural phenomenon of the landslide model (take Chinese Majiagou landslides as an example). Both the thermal debinding behavior and the kaolin powder particles characteristics [large pore volume (0.019 cm³g^–1) and pore size (29.20 nm)] were attributed to the interconnection channels.

Hence, the macroscopic and microscopic pores achieved by dual-gradient DIW process make it possible to control the permeability and details of properties, precisely in the geological model.

In the event of a crash involving a car, its seats, together with their backrests and head supports, ensure the safety of the passengers. The filling material used for such a car seat is normally made of polyurethane foam. To simulate the behaviour of the seat assembly during a crash, the material characteristics of the seat-filling foam should be appropriately modelled. The purpose of this paper is to present a method, with which the proper parameter values of the selected material model for the seat-filling foam can be easily determined.

In the study, an experiment with the specimen from seat-filling foam was carried out. The results from this experiment were the basis for the determination of the parameter values of the low-density-foam material model, which is often used in crash-test simulations. Two different numerical optimisation algorithms – a genetic algorithm and a gradient-descent algorithm – were coupled with LS-DYNA explicit simulations to identify the material parameters.

The paper provides comparison of two optimisation algorithms and discusses the engineering applicability of the results.

This paper presents an approach for the identification of the missing parameter values of the highly non-linear material model, if these cannot be easily determined directly from experimental data.

The purpose of this paper is to investigate the effect of imposing linear and quadratic composition gradients on the steady state creep behavior of a rotating functionally graded Al‐SiC_P disc operating under a radial thermal gradient.

Mathematical model to describe steady state creep behavior in rotating discs made of isotropic aluminum composite containing linear and quadratic distributions of Silicon Carbide (SiC_P) in the radial direction has been formulated. The discs are assumed to operate under a radial thermal gradient originating due to braking action as estimated by FEM analysis. The steady state creep behavior of the discs under stresses developing due to rotation has been determined following Sherby's law. Based on the developed model, the distributions of stresses and strain rates have been obtained and compared for various functionally graded material (FGM) discs containing the same average amount (20 vol per cent) of dispersoid. The creep response of a composite disc with uniform SiC_P content of 20 vol per cent and operating under a radial thermal gradient has also been computed for comparison with the results obtained for FGM discs.

The study reveals that the distribution of stresses and strain rates in a rotating composite disc operating under a radial thermal gradient are significantly affected by different particle distributions with in the disc. The creep stresses and steady state creep rates in a rotating FGM disc can be significantly reduced by employing more SiC_P particles in the middle compared to the inner and the outer radii.

The study provides an understanding of the required tailoring of composition in order to control creep stresses and creep rates in a rotating FGM disc operating under a radial thermal gradient.

The purpose of this study is to develop a novel approach to designing locally programmed multi-material distribution in a three-dimensional (3D) model, with the goal of producing a biomimetic robot that could mimic the locomotion of living organisms.

A voxelized representation is used to design the multi-material digital model and the material distribution in the model is optimized with the aims of mimicking the deflection dynamics of a real-life biological structure (i.e. inchworms) during its locomotion and achieving smooth deflection between adjacent regions. The design is validated post-fabrication by comparing the bending profiles of the printed robot with the deflection reference images of the real-life organism.

The proposed design framework in this study provides a foundation for multi-material multi-functional design for biomimicry and a wide range of applications in the manufacturing field and many other fields such as robotics and biomedical fields. The final optimized material design was 3D printed using a novel multi-material additive manufacturing method, magnetic field-assisted projection stereolithography. From the experimental tests, it was observed that the deflection curve and the deflection gradient of the printed robot within the adjacent regions of the body agreed well with the profiles taken from the real-life inchworm.

This paper presents a voxelized digital representation of the material distribution in printed parts, allowing spatially varied programming of material properties. The incorporation of reference images from living organisms into the design approach is a novel approach to transform image domain knowledge into the domain of engineering mechanical and material properties. Furthermore, the novel multi-material distribution design approach was validated through designing, 3D printing and prototyping an inchworm-inspired soft robot, which showed superior locomotion capability by mimicking the observed locomotion of the real inchworm.

The purpose of this paper is to develop an analysis of longitudinal fracture behaviour of a functionally graded non-linear-elastic circular shaft loaded in torsion. It is assumed that the material is functionally graded in both radial and longitudinal directions of the shaft (i.e. the material is bi-directional functionally graded).

The Ramberg–Osgood stress-strain relation is used to describe the non-linear mechanical behaviour of the functionally graded material. The fracture is studied in terms of the strain energy release rate by analysing the balance of the energy. The strain energy release rate is obtained also by differentiating of the complementary strain energy with respect to the crack area for verification.

Parametric studies are carried out in order to evaluate the influence of material gradients in radial and longitudinal directions, the crack location in radial direction and the crack length on the fracture behaviour of the shaft. It is found that by using appropriate gradients in radial and longitudinal directions, one can tailor the variations of material properties in order to improve the fracture performance of the non-linear-elastic circular shafts to the externally applied torsion moments.

A longitudinal cylindrical crack in a bi-directional functionally graded non-linear-elastic circular shaft loaded in torsion is analysed by using the Ramberg–Osgood stress-strain relation.

This paper aims to analyze the elastic-plastic delamination fracture behaviour of multilayered functionally graded four-point bending beam configuration.

The mechanical response of beam is described by a power-law stress-strain relation. The fracture is studied analytically in terms of the strain energy release rate by considering the beam complimentary strain energy. The beam can have an arbitrary number of layers. Besides, each layer may have different thickness and material properties. Also, in each layer, the material is functionally graded along the beam width. A delamination crack is located arbitrary between layers. Thus, the crack arms have different thickness.

The analysis developed is used to elucidate the effects of crack location, material gradient and non-linear behaviour of material on the delamination fracture. It is found that the material non-linearity leads to increase in the strain energy release rate. Therefore, the non-linear behaviour of material should be taken into account in fracture mechanics-based safety design of structural members and components made of multilayered functionally graded materials. The analysis revealed that the strain energy release rate can be effectively regulated by using appropriate material gradients in the design stage of multilayered functionally graded constructions.

Delamination fracture behaviour of multilayered functionally graded four-point bending beam configuration is studied in terms of the strain energy release rate by taking into account the material non-linearity.

Fabricating functionally graded scaffolds to mimic the complex spatial distributions of the composition, micro-structure and functionality of native tissues will be one of the key objectives for future tissue engineering research. This study aims to create a scaffold to mimic functionally-graded tissue using a hybrid process, which incorporated electrospun polycaprolactone (PCL) and electrosprayed hydroxyapatite (HA) in a simple pathway.

The PCL and HA were dispensed simultaneously from different positions to form a layer on a rotational mandrel, and a gradient construct was achieved by adjusting dispensing rates of both materials.

The morphology of scaffolds changed gradually from one layer to another layer with the change of the dispensing conditions of the two materials. The elemental distribution analysis revealed that C/Ca ratio linearly increased with certain dispensing rate ratio of PCL:HA. In addition, the thickness, mechanical properties (i.e. ultimate tensile stress and Young’s modulus), surface roughness and water contact angle of each layer changed accordingly with the variation of dispensing rate of PCL and HA, and the diameter distributions of PCL fibres and HA particles did not vary significantly.

This study showed the hybrid process has the potential to be used in fabrication of scaffold with functionally graded structure for tissue engineering applications, especially for mimicking the nature of the native 3D tendon–bone interface.

The representation of Heterogeneous Object (HO) is divided into two categories: Data model (DM) and material evaluation paradigm (MEP). A hybrid methodology with geometry model and volumetric dataset to represent heterogeneous properties is proposed in this paper. Geometry model of an object can guarantee the accuracy of the final HO slices; and volumetric dataset lends the flexible manipulability and other advantages to HO representation. Two MEPs, namely distance field (DF) based and Fixed Reference Features & Active Grading Source(s) (FRF&AGS) are presented to facilitate the process of HO representation according to the designer)s input parameters. The DM can be modified interactively with users until the final satisfactory result is obtained. In this paper, a scheme of HO slicing is described. In this method, we utilize the slices contour of geometrical model as constraint to reconstruct the HO slices, which can theoretically achieve the same accuracy with the geometrical shape. Some examples of Heterogeneous object represented with our scheme are provided.