A Multiscale Energy-Absorbing Lattice Framework for Impact Modeling

Thesis Abstract

The study addresses the escalating demand for predictive, lightweight, and energy-dissipative structures in automotive and protective equipment by developing a multiscale lattice framework capable of accurately modeling impact energy absorption across nominal and mesoscale regimes. The aim is to establish a rigorous theoretical and computational framework that links lattice microstructure to macroscopic impact response, enabling optimized design for injury mitigation and crash energy management. Specific objectives include (1) formulating a multiscale constitutive model that integrates unit-cell geometry, material nonlinearity, and rate-dependent effects; (2) deriving homogenization-based transfer relations to couple mesoscale lattice behavior with macroscale structural response; (3) implementing a computational workflow that couples finite element analysis with topology-optimized lattice generation and experimental validation; (4) assessing the influence of lattice parameters (cell aspect ratio, connectivity, and porosity) on energy absorption efficiency under varying impact velocities; and (5) providing design guidelines and a decision-support framework for engineer practitioners. A mixed-methods approach is employed. The research adopts a theoretical-empirical design, combining analytical homogenization theory, computational simulations, and experimental validation. The population comprises polymer- and metal-based lattice specimens manufactured via additive manufacturing for controlled geometry. A purposive sample of 60 lattice unit cells, spanning cubic, body-centered, and octet-truss topologies, will be fabricated in triplicate, totaling 180 specimens. Instrumentation includes high-speed videography (10,000 fps) and laser-assisted digital image correlation (DIC) for full-field strain measurement, complemented by Instron servo-hydraulic testing rigs for quasi-static and dynamic impact loads. Data collection integrates (i) load–displacement histories, (ii) energy absorption metrics (absorbed energy, peak stress, and crushing strength), and (iii) microstructural characterizations via scanning electron microscopy to verify unit-cell integrity. Analytical techniques include nonlinear finite element analysis (FEA) with explicit dynamics to capture inertia and strain-rate effects, supplemented by micromorphic homogenization to derive effective constitutive relations. Regression analysis and multivariate ANOVA will quantify the relationships between lattice parameters and energy absorption outcomes. A Bayesian calibration framework will be used to update material and geometric priors against experimental results, ensuring robust predictive capability. The model specification encompasses a hierarchical multiscale framework where unit-cell stiffness and damping properties inform a mesoscale lattice network, which in turn feeds a macroscale structural response through homogenization operators. The theoretical underpinning draws on energy-absorption theory, metamaterial mechanics, and two-scale homogenization, with explicit reference to theories of rate-dependent plasticity and topology optimization. Expected findings indicate that energy absorption is maximized by lattices with optimized connectivity and anisotropic cell geometries that promote progressive cell collapse, reducing peak forces while maintaining total absorbed energy. It is anticipated that the multiscale framework will predict macroscopic impact responses within 8–12% of experimental results across impact energies from 0.5 to 5 kJ and velocities up to 8 m/s. Sensitivity analyses are expected to reveal critical thresholds for porosity and cell aspect ratio beyond which energy absorption efficiency declines due to premature global buckling. The study also anticipates that topology-optimized lattices offer superior energy absorption per unit weight relative to conventional foams or solid lattices under similar mass constraints. Contribution to knowledge includes (i) a validated multiscale lattice framework that couples unit-cell design to macroscopic impact performance, (ii) a generalized homogenization procedure for diverse lattice topologies applicable to polymers and metals, (iii) an experimental-analytical workflow linking additive manufacturing to predictive impact engineering, and (iv) pragmatic design guidelines for energy-absorbing lattice structures in protective equipment and automotive crash components. The conclusion emphasizes the framework’s potential to transform energy-absorbing design by enabling predictable, tunable performance through targeted microstructural customization. Recommendations for practice include integrating the framework into computer-aided engineering pipelines, extending the model to thermo-mechanical coupling for high-temperature impacts, and pursuing multi-objective optimization that balances energy absorption with stiffness and weight constraints. Further research is suggested to explore long-term durability under repetitive impacts and environmental aging effects on lattice performance.