Computational Investigation of the Effective Mechanical Behavior for 3D Pre-Buckled Auxetic Lattices

Negative Poisson’s ratio materials, or auxetics, have drawn attention for the past 30 years. The auxetic effect could lead to improved mechanical properties such as acoustic damping, indentation resistance, or crashworthiness. In this work, two 3D auxetic lattices are introduced. Auxeticity is achieved by design through pre-buckling of the lattice struts. The influence of geometrical parameters on the effective elastic properties is investigated using computational homogenization method with periodic boundary conditions. Effective Young’s modulus is 3D mapped to reveal anisotropy and identify spatial orientations of interest. The effective Poisson ratio is computed for various geometric configurations to characterize auxeticity. Finally, the influence of effective elastic properties on energy dissipation under compression is explored for elastoplastic lattices with different loading directions, using finite element simulations. Results suggest that loading 3D auxetic lattices along their stiffest direction maximizes their crashworthiness.ANR-16-CE08-000

Size and strain gradient effects in dislocation based constitutive modelling

The global trend to miniaturization of engineering structures across different industries, notably information, communication and biomedical industries, presents significant challenges to scientists and engineers. Due to the occurrence of specific effects and new features unknown in conventional metal forming, common forming operations cannot be simply replicated at micro scale. The new challenges cannot be addressed by experimentation alone. Neither are classical plasticity model adequate for accounting for the observed size effects that are critical for materials and process design. New constitutive models guided by microstructure considerations, and combining elements of dislocation theory and gradient plasticity in a physically sound and computationally economical way, are a promising answer to the demands of the nascent microforming industry. In this thesis, physically-based constitutive models described in terms of microstructural evolution have been developed. They account for the effect of the critical dimension of a work-piece on its mechanical response and provide information about the material behaviour required for design of microforming processes and equipment. The models presented utilise an approach in which the material is partitioned in two ’phases’: the dislocation cell walls and the cell interior. Several modifications of the model are proposed in order to account for two particular size effects associated with miniaturization. These can be expressed by two contradictory maxims: "smaller is weaker" and "smaller is stronger". Whereas the former applies when the dimensions of the specimen are decreased with respect to the pertinent microstructural length scale, such as the grain size, the latter holds when non-homogeneity of deformation at microscale becomes significant. The first effect is captured by a model that takes into account the geometrical dimensions of the specimen and also accounts for the microstructural features of the material, notably the average grain size. The second effect is represented by strain gradient models. In this thesis, two types of physically-based strain gradient models arising from two distinct physical mechanisms have been proposed. One originates from the occurrence of geometrically necessary dislocations and the other is associated with the reaction stresses due to plastic strain incompatibilities between neighbouring grains. The constitutive models developed have been implemented in the broadly used commercial finite element software ABAQUS via a specific user subroutine and additionally, a new type of user element has been proposed. A selection of case studies has demonstrated that the models are capable of describing the experimentally observed trends associated with miniaturization and possess a very good predictive capability. A significant advantage of this modelling approach is a relatively small number of adjustable parameters involved. Furthermore, these parameters have a clear physical meaning and can be identified in simple standardized tests. In summary, a physically sound, yet robust and user-friendly constitutive modelling frame has been developed, which can readily be used for simulations of microforming operations and the properties of the resulting parts and miniaturized structural members

Size and strain gradient effects in dislocation based constitutive modelling

The global trend to miniaturization of engineering structures across different industries, notably information, communication and biomedical industries, presents significant challenges to scientists and engineers. Due to the occurrence of specific effects and new features unknown in conventional metal forming, common forming operations cannot be simply replicated at micro scale. The new challenges cannot be addressed by experimentation alone. Neither are classical plasticity model adequate for accounting for the observed size effects that are critical for materials and process design. New constitutive models guided by microstructure considerations, and combining elements of dislocation theory and gradient plasticity in a physically sound and computationally economical way, are a promising answer to the demands of the nascent microforming industry. In this thesis, physically-based constitutive models described in terms of microstructural evolution have been developed. They account for the effect of the critical dimension of a work-piece on its mechanical response and provide information about the material behaviour required for design of microforming processes and equipment. The models presented utilise an approach in which the material is partitioned in two ’phases’: the dislocation cell walls and the cell interior. Several modifications of the model are proposed in order to account for two particular size effects associated with miniaturization. These can be expressed by two contradictory maxims: "smaller is weaker" and "smaller is stronger". Whereas the former applies when the dimensions of the specimen are decreased with respect to the pertinent microstructural length scale, such as the grain size, the latter holds when non-homogeneity of deformation at microscale becomes significant. The first effect is captured by a model that takes into account the geometrical dimensions of the specimen and also accounts for the microstructural features of the material, notably the average grain size. The second effect is represented by strain gradient models. In this thesis, two types of physically-based strain gradient models arising from two distinct physical mechanisms have been proposed. One originates from the occurrence of geometrically necessary dislocations and the other is associated with the reaction stresses due to plastic strain incompatibilities between neighbouring grains. The constitutive models developed have been implemented in the broadly used commercial finite element software ABAQUS via a specific user subroutine and additionally, a new type of user element has been proposed. A selection of case studies has demonstrated that the models are capable of describing the experimentally observed trends associated with miniaturization and possess a very good predictive capability. A significant advantage of this modelling approach is a relatively small number of adjustable parameters involved. Furthermore, these parameters have a clear physical meaning and can be identified in simple standardized tests. In summary, a physically sound, yet robust and user-friendly constitutive modelling frame has been developed, which can readily be used for simulations of microforming operations and the properties of the resulting parts and miniaturized structural members

Comparison of different extrusion methods for compaction of powders

Densification of metallic powders by means of extrusion is regarded as a very attractive processing technique that allows obtaining a high level of relative density of the compact. However, the uniformity of the relative density depends on that of strain distribution and on the processing parameters. Several variants of extrusion can be used for compaction of metal particulates, including the conventional extrusion (CE) and equal channel angular pressing (ECAP), often referred to as equal-channel angular extrusion. Each of these processes has certain advantages and drawbacks with respect to compaction. A comparative study of these two extrusion processes influencing the relative density of compacts has been conducted by numerical simulation using commercial finite element software DEFORM2D. The results have been validated by experiments with titanium and magnesium powders and chips

Deformation mechanics of non-planar topologically interlocked assemblies with structural hierarchy and varying geometry

Abstract Structural hierarchy is known to enhance the performance of many of Nature’s materials. In this work, we apply the idea of hierarchical structure to topologically interlocked assemblies, obtained from measurements under point loading, undertaken on identical discrete block ensembles with matching non-planar surfaces. It was demonstrated that imposing a hierarchical structure adds to the load bearing capacity of topological interlocking assemblies. The deformation mechanics of these structures was also examined numerically by finite element analysis. Multiple mechanisms of surface contact, such as slip and tilt of the building blocks, were hypothesised to control the mechanical response of topological interlocking assemblies studied. This was confirmed using as a model a newly designed interlocking block, where slip was suppressed, which produced a gain in peak loading. Our study highlights the possibility of tailoring the mechanical response of topological interlocking assemblies using geometrical features of both the element geometry and the contact surface profile

Mechanical properties and in vitro behavior of additively manufactured and functionally graded Ti6Al4V porous scaffolds

Functionally graded lattice structures produced by additive manufacturing are promising for bone tissue engineering. Spatial variations in their porosity are reported to vary the stiffness and make it comparable to cortical or trabecular bone. However, the interplay between the mechanical properties and biological response of functionally graded lattices is less clear. Here we show that by designing continuous gradient structures and studying their mechanical and biological properties simultaneously, orthopedic implant design can be improved and guidelines can be established. Our continuous gradient structures were generated by gradually changing the strut diameter of a body centered cubic (BCC) unit cell. This approach enables a smooth transition between unit cell layers and minimizes the effect of stress discontinuity within the scaffold. Scaffolds were fabricated using selective laser melting (SLM) and underwent mechanical and in vitro biological testing. Our results indicate that optimal gradient structures should possess small pores in their core (~900 µm) to increase their mechanical strength whilst large pores (~1100 µm) should be utilized in their outer surface to enhance cell penetration and proliferation. We suggest this approach could be widely used in the design of orthopedic implants to maximize both the mechanical and biological properties of the implant