Body-centered Cubic (BCC) lattice structures demonstrate promising performance for applications that require simultaneous mechanical energy absorption and thermal management. However, current optimization approaches are typically confined to single-domain objectives, such as mechanical parameters like impact energy and peak stress, neglecting the role of multiple physics in real-world performance. To address this, we propose a multi-objective optimization framework for density-graded BCC lattices that effectively dissipates heat while maximizing absorbed impact energy. A parametric three-zone lattice configuration is investigated to explore various trade-offs between mechanical and thermal properties. Each design is evaluated through independent impact and forced-convection simulations using commercial solvers. Specific Energy Absorption (SEA) and peak stresses at the distal end quantify impact absorption performance, while the Nusselt number and pressure drop characterize thermal dissipation performance. Surrogate models constructed from this data enable multi-objective optimization via Goal Programming to identify an optimal design. Two Pareto-optimal lattice designs are identified with reduced pressure drop and peak stress, underlining the superiority of strategic density gradation. Analysis of the optimal designs reveals how material distribution and geometric design variables influence mechanical-thermal trade-offs, establishing quantitative design guidelines for lattice structures in this multi-physics application.
The physical properties of metamaterials (specifically mechanical metamaterials) are often dictated by their intricate internal geometries and high specific surface areas. The ability to control the geometry enables the design of structures with tailored mechanical, thermal, and even multi-functional attributes that are unattainable with conventional monolithic counterparts [1]. Such materials exhibit properties Fig. 1 A BCC lattice-based heat sink consisting of (a) uniform struts is replaced with (b) a lattice consisting of diameter-graded struts. A cross-section of the hypothesized FG-BCC lattice with a density gradient is also . that are not typically found in nature and are often the result of purpose-driven designs, having found applications in aerospace [2][3][4][5], automotive [6][7][8][9], biomedical, and thermal management systems [10][11][12][13].
Lattice structures, a class of metamaterials, are gaining prominence for their tunability, especially since the advent of additive manufacturing [14]. While known for crashworthiness, they are increasingly explored for thermal dissipation as traditional heat sinks face limitations from rising power densities [15]. Compared to other cellular structures like metal foams or Triply-Periodic Minimal Surfaces (TPMS), lattices offer a compelling alternative due to their high surface area-to-volume ratio and interconnected pores, which balance efficient thermal conduction with low fluid flow resistance [16,17]. Studies show lattices can be more efficient heat sinks than conventional finned designs [17][18][19]. There exist several attempts in the literature to optimize specific topologies, such as BCC lattices, which show superior heat transfer [20], and functionally graded structures, which vary geometry to further enhance thermal performance [14,15,21,22].
Beyond thermal management, lattice structures possess remarkable mechanical properties for energy absorption and crashworthiness. Their performance is characterized by their deformation mechanism: bending-dominated or stretching-dominated [23]. Stretching-dominated structures (such as Octet lattices) exhibit high nodal connectivity, making them weight-efficient and offering superior stiffness and strength for load-bearing applications. Conversely, bending-dominated structures (like BCC lattices) have lower connectivity, offering less resistance to bending, which is ideal for energy absorption [24,25]. The capacity of lattices to endure large compressive strains at a near-constant stress makes them suitable for protective applications [26,27]. Researchers are maximizing specific energy absorption by exploring configurations such as BCC and Octet lattices, applying functional grading, developing novel hybrid structures (e.g., FCC-BCC), and using topology optimization to achieve uniform performance regardless of impact direction [26][27][28][29][30][31][32].
Due to the numerous possibilities in lattice cell topologies, dimensions, and spatial arrangements, it is often not feasible to conduct experiments or even numerical simulations, given the associated costs and time. To address this issue, significant efforts have been made to utilize surrogate modeling as a powerful technique to interpolate between discrete simulation/experimental data points, especially for improving the crashworthiness of cellular structures [33][34][35][36][37][38]. However, the potential to tune lattice structures to meet multiple functional requirements simultaneously is often overlooked and remains underexplored. While a particular lattice may not perform the best across all considered functional needs, an optimal design that performs reasonably well with minimal trade-offs can still be achieved. Combining surrogate modeling with multi-objective optimization has been shown to yield such optimal structures [39,40].
The aim of this paper is to explore the BCC lattice structures for their simultaneous energy absorption and heat dissipation capabilities. To meet the multi-functional requirements mentioned above, we leverage the inherent advantages of the BCC topology, combined with functional grading, to create a lattice that excels at both thermal dissipation and impact absorption. Such structures can be particularly useful in the front-end automotive electronic enclosures (such as Electronic Storage Units (ESUs)) due to strong air convection. Heat sinks made using these lattices for automotive electronic enclosures would prevent severe component damage upon impact, whilst providing superior passive heat extraction.
When referring to the thermal (mechanical) aspect of the lattice, we denote the end of the lattice in contact with the chip as the heat side (support end) and the other end facing the cold incoming air as the air side (impact end). The key idea behind this study is to create an optimized Functionally-Graded BCC (FG-BCC) lattice with thicker struts on the hot side and thinner struts on the cold side. This is beneficial wh
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