The widespread proliferation of cellular lattices in engineering design has entailed a revolution in the design of lightweight and multifunctional structures. Furthermore, the development of auxetic metamaterials has led to applications in fields ranging from biomedical to civil engineering. However, cellular lattices suffer from the development of localized concentrations of strains during deformation, which lead to sub-optimal mechanical performance. Furthermore, the mechanical properties of cellular lattices are dependent on their macro-scale geometries, limiting their design space. Thus, we seek to both enhance the mechanical properties of lattices by ameliorating strain concentrations and expand the design space of cellular lattices. In attempting to do so, we can turn to nature. The bio-inspired design motif of the hierarchical arrangement of composite materials has lead to exceptional mechanical characteristics in natural materials. Moreover, morphogenetic processes such as bone remodelling play a vital role in the structural development of natural materials and their hierarchical material arrangement. Motivated by these concepts, we developed an algorithm that optimised the hierarchical material arrangement of hard and soft voxels in an auxetic and non-auxetic unit cell. Our algorithm does so based on a bone remodelling-like approach of strain energy optimisation, whereby elements are transitioned to a hard or soft material based on local strain energy. Our finite element (FE) simulation results demonstrate the considerable expansion of the range of mechanical properties we can achieve simply by modifying material placement on a micron scale. We also observe clear mitigation of peak strain energies and more homogeneous distributions of strain energy density, which affirm the amelioration of strain concentrations. Furthermore, we were able to increase the stiffnesses of our unit cells without substantially affecting its Poisson’s ratio, disentangling previously interdependent mechanical properties. We further validated our FE simulations by additively manufacturing our optimised unit cells with state-of-the-art voxel-based printing. Both the mechanical properties predicted by our FE simulations and the strain distributions correlated well with digital image correlation recordings, validating our models. Our mechanical testing also revealed the considerable in- creases in ultimate tensile strength of our optimised designs, demonstrating the benefits of hierarchical material arrangement. To conclude, we demonstrate the efficacy of strain energy-based material optimisation to improve the mechanical properties of unit cells and mitigate strain concentrations. The design paradigms of hierarchical arrangement of composite materials remarkably improved the material space of a unit cell without changing its macro-scale geometry. Findings from this study could enable the optimisation of existing cellular lattices and the development of novel unit cell designs with distinct intrinsic mechanical properties.

The mechanical failure of a temporomandibular joint (TMJ) replacement system can stem from various factors, with one notable cause being the unnatural kinematics and loading observed in prosthetic joint function. Given that,. the primary objective of the study was to investigate whether including functionally graded materials (FGMs) at the site of the prosthetic joint was feasible for achieving a greater resemblance to natural mandibular kinematics, while simultaneously reducing the reaction force exerted on the prosthetic joint. To this end, an FGM-based TMJ implant was designed with the intention of reducing joint reaction forces and enhancing joint flexibility to achieve a more natural kinematic behavior. In this study, patient-specific finite element models of the intact and implanted mandible were simulated for two different biting tasks: incisal biting (INC) and left group biting (LGF). To incorporate FGMs into the implant design, an initial implant design was voxelized (with a voxel size of 0.25mm x 0.25mm x 0.25mm), allowing each voxel to be assigned a specific material. Subsequently, 10 voxel layers of the same size were added onto the implant head/prosthetic condyle. To investigate the impact of FGMs on mandibular biomechanics, a comprehensive analysis was performed on five distinct implant designs. These designs were differentiated solely by the functional gradient in material properties across the additional 10 voxel layers on top of the implant head. Each voxel (layer) was assigned a value of ρ, which represented the volume fraction of the hard phase. The five distinct implant designs were as follows: (1) The first design was labelled as the "Polymeric Implant" consisting solely of the hard phase with a volume fraction of ρ=100%. It served as the reference for comparisons with other designs. (2) The second design featured an abrupt hard-soft connection without a gradient. This design was specifically examined to demonstrate the presence of stress concentrations at discrete interfaces between the hard and soft materials in layered composites. It was named "Implant with abrupt hard-soft connection without a gradient". (3) The third design was characterized by an FGM comprising ten discrete values of the volume fraction of the hard phase, ranging from ρ=0% at the surface layer to ρ=90% at the 10th layer with an increment of 10%. This design was designated as "FGM, ρ= [0, 10,…, 90]". (4) The fourth design encompassed an FGM featuring nine distinct values of the volume fraction of the hard phase, ranging from ρ=10% at the two surface layers to ρ=90% at the 10th layer with an increment of 10%. It was referred to as "FGM, ρ= [10, 20,…, 90]". (5) The fifth design comprised an FGM incorporating eight discrete values of the volume fraction of the hard phase, ranging from ρ=20% at the three surface layers to ρ=90% at the 10th layer with an increment of 10%. This design was named "FGM, ρ= [20, 30,…, 90]". The primary objective of investigating the fourth and fifth designs was to analyse the influence of a relatively less soft material at the surface (outer layer) of the implant head. The biomechanical performance of an implant design was determined by utilizing normalized cross-correlation (similarity) and Euclidean distance (closeness) measurements between the displacement fields of the intact and implanted mandible. The performance of an implant design for a specific biting task was assessed by calculating the average of the percentage errors in each of these quantities. Additionally, the reaction forces on the prosthetic joint were compared between the implanted models. The results showed that the second design, which featured an abrupt hard-soft connection without a gradient, was not viable. This was due to the presence of stress concentrations, stress increase up to more than ninefold was observed, at discrete interface between materials of contrasting hardness. This phenomenon could result in crack initiation and delamination, significantly compromising the overall performance and durability of the design. The study also revealed that material properties distribution on the surface of the implant head had a crucial impact on regulating mandibular displacements. Notably, greater displacements were observed when the outer layer of the implant head featured relatively softer material. In comparison to the polymeric implant, “FGM,ρ=[0,10,…90]” implant exhibited an average performance increase of 19% for INC and a 3% performance decrease for LGF regarding mandibular displacement. Additionally, it reduced the joint reaction forces on the prosthetic joint by 8% and 12% during INC and LGF, respectively. Moreover, the "FGM, ρ=[0,10,…90]" implant increased the mandibular range of motion by 20% during INC and 88% during LGF. Furthermore, it contributed to more symmetrical mandibular movement during INC, while the concept of symmetry was not applicable in the context of LGF. These results have provided valuable insights for future research and development of TMJ implants, potentially leading to the creation of implants with improved long-term behavior.

Functional gradients in hard-soft interfaces are abundant in nature, and we often mimic them to create strong and tough composites. A powerful tool for the designs and fabrication of biomimetic composites is voxel-based multi-material 3D printing. Earlier researches mainly focused on using this technique in the creation of gradients based on morphology. While this is a great way to create a gradient, the outcome material properties are often unknown. In this research, we attempted to create a gradient based on the desired outcome material properties rather than morphology. We created a linear gradient in density using a voxel-based 3D printing technique and tested it through nanoindentation. Furthermore, we created a Finite Element Model based on this sample. Out of the nanoindentation and Finite Element Model results, we extracted the b-value for a power-law function in the form of E(x)= E_h 〖ρ(x)〗^b+E_s. With the inverse of this power-law function, we designed three different gradients based on the desired material properties: a linear, stepwise, and sigmoid gradient. Nanoindentation experiments and Finite Element analyses showed that we achieved the desired outcome in material properties with our newly created approach of designing gradients. However, the nanoindentation experiments showed that using a machine suitable for the wide range of Young’s moduli present in these kinds of composites is crucial. To display the possible applications of our new approach, we designed a knee model with graded ligaments and tested it with a tensile test and digital image correlation. Results of these tests showed an energy before failure that was twice as high as its non-graded counterpart. Furthermore, with the introduction of the gradient, we achieved to change to loading condition on the ligaments. Overall, our results show that our new approach can create gradients based on material properties rather than morphology and opens many new doors in creating biomimetic composites.

The distribution of multiple materials within a single structure is a strategy that various biological systems rely on to achieve outstanding mechanical performances. These biological examples illustrate the effective utilization of hard rigid and soft flexible materials in particular. The proper composition of such hard-soft materials exceeds the structural limitations found in their individual material counterparts. The manufacturing of hard-soft material structures is especially relevant today due to recent developments in additive manufacturing that certify the technology with local material-specific functionalities and enlarged design spaces. However, to unravel the next generation of unprecedented structural performance, today’s state of engineering and research has yet to overcome the challenges encountered in multi-material design. The dissimilar material junctions within multi-material structures are prone to load transmissions, so they carry a crucial structural responsibility. Therefore, the interface design process must be subjected to representative interface characteristics which are often overlooked in the literature. In this work, we present a method to characterize and model multi-material structures to provide an optimal interface design in terms of the multi-material’s joining strength. We consider the joining strength of 3D printed hard Verocyan and soft Agilus30 by its fundamental joining principles of material bonding and mechanical interlocking. Material bonding is characterized by the extent of allowable traction between the two materials. We experimentally quantify the loading-dependent critical stress at which interface debonding initiates through mapping of digital image correlation deformations on a finite element model. We numerically define the extent of mechanical interlocking by the force required to achieve an unlocked multi-material state. The finite element models contain experimentally calibrated elastoplastic and hyperelastic material models to represent the hard and soft material behaviors, respectively. Subsequently, a structural optimization based on a genetic algorithm iteratively updates a constrained parametrized interface design according to material bonding and mechanical interlocking objectives. The numerical evaluations of calibrated hard and soft material characteristics show good agreement in structural response with their real-world equivalents. The digital image correlation deformation method successfully acquires the loading-dependent critical stresses at which the two materials debond from one another. The finite element analyses of individual joining principles adequately determine a design’s material bonding and mechanical interlocking performances. The optimization’s objective function value evolution suggests a trade-off in joining contributions where mechanical interlocking maximizes performance in more shallow, wider interface designs, whereas material bonding performs better in narrow, deeper ones. Validation experiments illustrate the dominating contribution of material bonding in A30-VC structures. Optimizing for two distinct hypotheses of interface failure equations shows no significant difference in physical joining strength. However, they do support the concept that the interface characteristics affect the optimal joining shape. Despite adequate estimation of the individual joining principle performances, a more accurate approximation of the multi-material physical joining strength necessitates the consideration of the effects induced by the interaction of material bonding and mechanical interlocking. Nonetheless, this work underlines the emphasis regarding interface characteristics in the promising structures of multi-material.