Multiscale, thermomechanical topology optimization of self-supporting cellular structures for porous injection molds

Purpose This paper aims to establish a multiscale topology optimization method for the optimal design of non-periodic, self-supporting cellular structures subjected to thermo-mechanical loads. The result is a hierarchically complex design that is thermally efficient, mechanically stable and suitable for additive manufacturing (AM). Design/methodology/approach The proposed method seeks to maximize thermo-mechanical performance at the macroscale in a conceptual design while obtaining maximum shear modulus for each unit cell at the mesoscale. Then, the macroscale performance is re-estimated, and the mesoscale design is updated until the macroscale performance is satisfied. Findings A two-dimensional Messerschmitt Bolkow Bolhm (MBB) beam withstanding thermo-mechanical load is presented to illustrate the proposed design method. Furthermore, the method is implemented to optimize a three-dimensional injection mold, which is successfully prototyped using 420 stainless steel infiltrated with bronze. Originality/value By developing a computationally efficient and manufacturing friendly inverse homogenization approach, the novel multiscale design could generate porous molds which can save up to 30 per cent material compared to their solid counterpart without decreasing thermo-mechanical performance. Practical implications This study is a useful tool for the designer in molding industries to reduce the cost of the injection mold and take full advantage of AM

Design for Additive Manufacturing of Conformal Cooling Channels Using Thermal-Fluid Topology Optimization and Application in Injection Molds

Additive manufacturing allows the fabrication parts and tools of high complexity. This capability challenges traditional guidelines in the design of conformal cooling systems in heat exchangers, injection molds, and other parts and tools. Innovative design methods, such as network-based approaches, lattice structures, and structural topology optimization have been used to generate complex and highly efficient cooling systems; however, methods that incorporate coupled thermal and fluid analysis remain scarce. This paper introduces a coupled thermal-fluid topology optimization algorithm for the design of conformal cooling channels. With this method, the channel position problem is replaced to a material distribution problem. The material distribution directly depends on the effect of flow resistance, heat conduction, as well as forced and natural convection. The problem is formulated based on a coupling of Navier-Stokes equations and convection-diffusion equation. The problem is solved by gradient-based optimization after analytical sensitivity derived using the adjoint method. The algorithm leads a two -dimensional conceptual design having optimal heat transfer and balanced flow. The conceptual design is converted to three-dimensional channels and mapped to a morphological surface conformal to the injected part. The method is applied to design an optimal conformal cooling for a real three dimensional injection mold. The feasibility of the final designs is verified through simulations. The final designs can be exported as both three-dimensional graphic and surface mesh CAD format, bringing the manufacture department the convenience to run the tool path for final fitting

Cluster-Based Optimization of Cellular Materials and Structures for Crashworthiness

The objective of this work is to establish a cluster-based optimization method for the optimal design of cellular materials and structures for crashworthiness, which involves the use of nonlinear, dynamic finite element models. The proposed method uses a cluster-based structural optimization approach consisting of four steps: conceptual design generation, clustering, metamodel-based global optimization, and cellular material design. The conceptual design is generated using structural optimization methods. K-means clustering is applied to the conceptual design to reduce the dimensional of the design space as well as define the internal architectures of the multimaterial structure. With reduced dimension space, global optimization aims to improve the crashworthiness of the structure can be performed efficiently. The cellular material design incorporates two homogenization methods, namely, energy-based homogenization for linear and nonlinear elastic material models and mean-field homogenization for (fully) nonlinear material models. The proposed methodology is demonstrated using three designs for crashworthiness that include linear, geometrically nonlinear, and nonlinear models

Mechanical properties and energy absorbing capabilities of Z-pinned aluminum foam sandwich

Aluminum foam sandwich (AFS) structures are suitable for impact protection in lightweight structural components due to their specific energy absorption capability under compression. However, tailoring the deformation patterns of the foam cells is a difficult task due to the randomness of their internal architecture. The objective of this study is to analyze the effect of embedding aluminum pins into an AFS panel (Z-pinning) to better control its deformation pattern and improve its energy absorption capability. This study considers a closed-cell AFS panel and analyzes the effect of multi-pin layout parallel to the direction of the uniaxial compressive loading. The results of the experimental tests on the reference (without Z-pinning) AFS are utilized to develop numerical models for the reference and Z-pinned AFS structures. Physical experiments and numerical simulations are carried out to demonstrate the advantages of Z-pinning with aluminum pins. The results exhibit a significant increase in elastic modulus, plateau stress and energy absorption capability of the Z-pinned samples. Also, the effect of the pin size and Z-pinning layout on the mechanical performance of the Z-pinned AFS is also investigated using numerical simulations

Cellular Helmet Liner Design through Bio-inspired Structures and Topology Optimization of Compliant Mechanism Lattices

The continuous development of sport technologies constantly demands advancements in protective headgear to reduce the risk of head injuries. This article introduces new cellular helmet liner designs through two approaches. The first approach is the study of energy-absorbing biological materials. The second approach is the study of lattices comprised of force-diverting compliant mechanisms. On the one hand, bio-inspired liners are generated through the study of biological, hierarchical materials. An emphasis is given on structures in nature that serve similar concussion-reducing functions as a helmet liner. Inspiration is drawn from organic and skeletal structures. On the other hand, compliant mechanism lattice (CML)-based liners use topology optimization to synthesize rubber cellular unit cells with effective positive and negative Poisson's ratios. Three lattices are designed using different cellular unit cell arrangements, namely, all positive, all negative, and alternating effective Poisson's ratios. The proposed cellular (bio-inspired and CML-based) liners are embedded between two polycarbonate shells, thereby, replacing the traditional expanded polypropylene foam liner used in standard sport helmets. The cellular liners are analyzed through a series of 2D extruded ballistic impact simulations to determine the best performing liner topology and its corresponding rubber hardness. The cellular design with the best performance is compared against an expanded polypropylene foam liner in a 3D simulation to appraise its protection capabilities and verify that the 2D extruded design simulations scale to an effective 3D design

An efficient 3D topology optimization code written in Matlab

This paper presents an efficient and compact Matlab code to solve three-dimensional topology optimization problems. The 169 lines comprising this code include finite element analysis, sensitivity analysis, density filter, optimality criterion optimizer, and display of results. The basic code solves minimum compliance problems. A systematic approach is presented to easily modify the definition of supports and external loads. The paper also includes instructions to define multiple load cases, active and passive elements, continuation strategy, synthesis of compliant mechanisms, and heat conduction problems, as well as the theoretical and numerical elements to implement general non-linear programming strategies such as SQP and MMA. The code is intended for students and newcomers in the topology optimization. The complete code is provided in Appendix C and it can be downloaded from http://​top3dapp.​com

The Effect of the Cell Shape on Compressive Mechanical Behavior of 3D Printed Extruded Cross-sections

Additive manufacturing has been a promising technique for producing sophisticated porous structures. The pore's architecture and infill density percentage can be easily controlled through additive manufacturing methods. This paper reports on development of sandwich-shape extruded cross sections with various architecture. These lightweight structures were prepared by employing additive manufacturing technology. In this study, three types of cross-sections with the same 2-D porosity were generated using particular techniques. a) The regular cross section of hexagonal honeycomb, b) The heterogeneous pore distribution of closed cell aluminum foam cross section obtained from image processing and c) linearly patterned topology optimized 2-D unit cell under compressive loading condition. The optimized unit cell morphology is obtained by using popular two-dimensional topology optimization code know as 99-line code, and by having the same volume fraction as the heterogeneous foam. The upper edge of the unit cell was under distributed uniform loading and the lower edge was fixed. All the cross sections have the same cavity to wall area ratio on their 2-D configuration. The samples are extruded to produce 3-D CAD model of sandwich shape porous structures. The different samples are tested with universal compression machine and mechanical characteristics of the models are investigated. Furthermore, the energy absorption efficiency and load bearing capability of samples are studied. The results of the experimental procedure are compared to numerical simulations under quasi-static condition

Force Diverting Helmet Liner Achieved Through a Lattice of Multi-Material Compliant Mechanisms

This work introduces the design of a lattice array of multi-material compliant mechanisms (LCM) that diverts the impact radial force into tangential forces through the action of elastic hinges and connecting springs. When used as the helmet liner, the LCM liner design has the potential to reduce the risk of head injury through improved impact energy attenuation. The compliant mechanism array in the liner is optimized using a multi-material topology optimization algorithm. The performance of the LCM liner design is compared with the one obtained by expanded polypropylene (EPP) foam, which is traditionally used in sport helmets. An impact test is carried out using explicit, dynamic, nonlinear finite element analysis. The parameters under consideration include the internal energy, the peak linear force, as well as von Mises stress and effective plastic strain distributions. Although there is a small increase in stress and strain values, the simulations show that the maximum internal of the LCM liner design is four times the one of the foam design while the peak linear force is reduced to about half. While the use of the LCM liner design is intended for sports helmets, this design may find application in other energy absorbing structures such as crashworthy vehicle components, blast mitigating structures, and protective gear

Targeting the Force-Displacement Response of Thin-walled Structures Subjected to Crushing Load using Curve Decomposition and Topometry Optimization

This work introduces a new approach to targeting the dynamic response of thin-walled energy-absorbing structures through the decomposition of the force-displacement (FD) response and the use of topometry (thickness) optimization. The proposed method divides the nonlinear optimization problem into a series of analytical subproblems. In each iteration, an explicit dynamic analysis is carried out and the dynamic response of the structure is then used to define the subproblem. Numerical examples show that the algorithm can tailor the FD response of the structure to a target FD curve. Progressive collapse, which is a high-energy collapse mode and desired in design for crashworthy, is observed in the optimized thin-walled structures. The proposed algorithm is computationally efficient as it uses a fewer explicit simulations to reach the target response

Structural Optimization of Thin-Walled Tubular Structures for Progressive Collapse Using Hybrid Cellular Automaton with a Prescribed Response Field

The design optimization of thin-walled tubular structures is of relevance in the automotive industry due to their low cost, ease of manufacturing and installation, and high-energy absorption efficiency. This study presents a methodology to design thin-walled tubular structures for crashworthiness applications. During an impact, thin-walled tubular structures may exhibit progressive collapse/buckling, global collapse/buckling, or mixed collapse/buckling. From a crashworthiness standpoint, the most desirable collapse mode is progressive collapse due to its high-energy absorption efficiency, stable deformation, and low peak crush force (PCF). In the automotive industry, thin-walled components have complex structural geometries. These complexities and the several loading conditions present in a crash reduce the possibility of progressive collapse. The Hybrid Cellular Automata (HCA) method has shown to be an efficient continuum-based approach in crashworthiness design. All the current implementations of the HCA method use a scalar set point to design structures with a uniform distribution of a field variable, e.g., stress, strain, internal energy density (IED), mutual potential energy. For example, using IED and mutual potential energy as the field variable result in high stiffness and progressive collapsing structures, respectively. This paper presents a modified version of the HCA method to design thin-walled structures that collapse progressively. In this methodology, the set point has two components, a prescribed response field, which promotes progressive collapse, and a variable offset value, which satisfies the mass constraint. The numerical examples show that this modified HCA method is capable of finding material distributions that exhibit progressive collapse, resulting in significant improvement in specific energy absorption (SEA) with relatively little change in the PCF