Multiscale design and biomechanical evaluation of porous spinal fusion cage to realize specified mechanical properties

Backgrou nd Dense titanium(Ti)fusion cages have been commonly used in transforaminal lumbar interbody fusion.However,the stiffness mismatch between cages and adjacent bone endplates increases the risk of stress shielding and cage subsidence.Methods The current study presents a multiscale optimization approach for porous Ti fusion cage development,including microscale topology optimization based on homogenization theory that obtains a unit cell with prescribed mechanical properties,and macroscale topology optimization that determines the layout of framework structure over the porous cage while maintaining the desired stiffness.The biomechanical performance of the designed porous cage is assessed using numerical simulations of fusion surgery.Selective laser melting is employed to assists with fabricating the designed porous structure and porous cage.Results The simulations demonstrate that the designed porous cage increases the strain energy density of bone grafts and decreases the peak stress on bone endplates.The mechanical and morphological discrepancies between the as-designed and fabricated porous structures are also described.Conclusion From the perspective of biomechanics,it is demonstrated that the designed porous cage contributes to reducing the risk of stress shielding and cage subsidence.The optimization of processing parameters and post-treatments are required to fabricate the designed porous cage.The present multiscale optimization approach can be extended to the development of cages with other shapes or materials and further types of orthopedic implants.

Oblique Cutting Based Mechanical Model for Insertion Torque of Dental Implant

The insertion torque of a dental implant is an important indicator for the primary stability of dental implants.Thus,the preoperative prediction for the insertion torque is crucial to improve the success rate of implantation surgery.In this present research,an alternative method for prediction of implant torque was proposed.First,the mechanical model for the insertion torque was established based on an oblique cutting process.In the proposed mechanical model,three factors,including bone quality,implant geometry and surgical methods were considered in terms of bone-quality coefficients,chip load and insertion speeds,respectively.Then,the defined bone-quality coefficients for cancellous bone with the computed tomography(CT)value of 235–245,345–355 and 415–425 Hu were obtained by a series of insertion experiments of IS and ITI implants.Finally,the insertion experiments of DIO implants were carried out to verify the accuracy of developed model.The predicted insertion torques calculated by the mechanical model were compared with those acquired by insertion experiments,with good agreement,the relative error being less than 15%.This method allows the insertion torque for different implant types to be quickly established and enhances prediction accuracy by considering the effects of implants’geometries and surgical methods.

Introduction to the Special Issue on Novel Methods of Topology Optimization and Engineering Applications

Topology optimization,aiming to allocate the available material to maximize system performance while satisfying multiple constraints,has experienced tremendous progress.This special issue focuses on the new progress of topology optimization methods and their applications,especially theoretical development,numerical implementation and potential applications.

Topology Optimization Method for Microscale Structures Described with Integral Nonlocal Theory

The integration of additive manufacturing and topology optimization makes it possible to fabricate complex configurations,especially for microscale structures,which can guarantee the realization of high-performance structural designs.However,topology results often contain microstructures(several multicellular scales)similar to the characteristic length of local macrostructures,leading to errors in structural performance analysis based on classical theories.Therefore,it is necessary to consider the size effect in topology optimization.In this paper,we establish a novel topology optimization model utilizing the integral nonlocal theory to account for the size effect.The approach consists of an integral constitutive model that incorporates a kernel function,enabling the description of stress at a specific point in relation to strain in a distant field.Topology optimization structures based on nonlocal theory are presented for some benchmark examples,and the results are compared with those based on classical medium theory.The material layout exhibits significant differences between the two approaches,highlighting the necessity of topology optimization based on nonlocal theory and the effectiveness of the proposed method.

An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures

Additive manufacturing （AM） technologies, such as selective laser sintering （SLS） and fused deposition modeling （FDM）, have become the powerful tools for direct manufacturing of complex parts. This breakthrough in manufacturing technology makes the fabrication of new geometrical features and multiple materials possible. Past researches on designs and design methods often focused on how to obtain desired functional performance of the structures or parts, specific manufacturing capabilities as well as manufacturing constraints of AM were neglected. However, the inherent constraints in AM processes should be taken into account in design process. In this paper, the enclosed voids, one type of manufacturing constraints of AM, are investigated. In mathematics, enclosed voids restriction expressed as the solid structure is simply- connected. We propose an equivalent description of simply-connected constraint for avoiding enclosed voids in structures, named as virtual temperature method （VTM）. In this method, suppose that the voids in structure are filled with a virtual heating material with high heat conductivity and solid areas are filled with another virtual material with low heat conductivity. Once the enclosed voids exist in structure, the maximum temperature value of structure will be very high. Based upon this method, the simplyconnected constraint is equivalent to maximum temperature constraint. And this method can be easily used to formulate the simply-connected constraint in topology optimization. The effectiveness of this description method is illustrated by several examples. Based upon topology optimization, an example of 3D cantilever beam is used to illustrate the trade-off between manufacturability and functionality. Moreover, the three optimized structures are fabricated by FDM technology to indicate further the necessity of considering the simply-connected constraint in design phase for AM.

Concurrent topology optimization design of stiffener layout and cross-section for thin-walled structures

Stiffened plates or shells are widely used in engineering structures as primary or secondary load-bearing components.How to design the layout and sizes of the stiffeners is of great significance for structural lightweight.In this work,a new topology optimization method for simultaneously optimizing the layout and cross-section topology of the stiffeners is developed to solve this issue.The stilfeners and base plates are modeled by the beam and shell elements,respectively,significantly reducing the computational cost.The Giavotto beam theory,instead of the widely employed Euler or Timoshenko beam theory,is applied to model the stiffeners for considering the warping deformation in evaluating the section stiffness of the beam.A multi-scale topology optimization model is established by simultaneously optimizing the layout of the beam and the topology of the cross-section.The design space is significantly expanded by optimizing these two types of design variables.Several numerical examples are applied to illustrate the validity and effectiveness of the proposed method.The results show that the proposed two-scale optimization approach can generate better designs than the single-scale method.