Title: A Semiempirical Model for Post‐Yield Stress Instability in the Stress–Strain Response of 3D Lattice Structures under Compressive Loads
Mechanical behavior of lattice structures is important for a range of engineering applications. Herein, a new semiempirical model is proposed that describes the entire range of stress–strain response of lattice structures, including the stress‐instability region which is modeled as an oscillator. The model can be fit to individual stress–strain curves to extract elastic modulus, yield stress, collapse stress, post‐yield collapse ratio, densification strain, and the energy absorbed per unit volume. The model is fit to 119 unique experimental stress–strain curves from 13 research papers in literature covering four different lattice designs, namely, octet truss, body‐centered cubic with vertical members, body‐centered cubic, and hexagonal. Manufacturing methods (additive and conventional) and materials (metals and polymers) were also included in the analysis. The fitted model yields several new insights into the compression behavior of previously tested lattice structures and can be applied to additional lattice designs. Among other results, analysis of variance (ANOVA) reveals that the octet truss lattice demonstrates the highest post‐yield collapse ratio and the smallest normalized energy absorption per unit volume amongst the lattice structures investigated. The proposed model is a powerful tool for designers to quantitatively compare and select 3D lattice structures with the desired mechanical characteristics.
Engineered micro- and macro-structures via additive manufacturing (AM) or 3D-Printing can create structurally varying properties in a part, which is difficult via traditional manufacturing methods. Herein we have utilized powder bed fusion-based selective laser melting (SLM) to fabricate variable lattice structures of Ti6Al4V with uniquely designed unit cell configurations to alter the mechanical performance. Five different configurations were designed based on two natural crystal structures – hexagonal closed packed (HCP) and body centered cubic (BCC). Under compressive loading, as much as 74% difference was observed in compressive strength, and 71% variation in elastic modulus, with all samples having porosities in a similar range of 53 to 65%, indicating the influence of macro-lattice designs alone on mechanical properties. Failure analysis of the fracture surfaces helped with the overall understanding of how configurational effects and unit cell design influences mechanical properties of these samples. Our work highlights the ability to leverage advanced manufacturing techniques to tailor the structural performance of multifunctional components.
Triply periodic minimal surface lattices have mechanical properties that derive from the unit cell geometry and the base material. Through computation software like nTopology and Abaqus, these geometries are used to tune nonlinear stress–strain curves not readily achievable with solid materials alone and to change the compliance by two orders of magnitude compared to the constituent material. In this study, four elastomeric TPMS gyroids undergo large deformation compression and tension testing to investigate the impact of the structure's geometry on the mechanical properties. Among all the samples, the modulus at strainεvaries by over one order of magnitude (7.7–293.4 kPa from FEA under compression). These lattices are promising candidates for designing multifunctional systems that can perform multiple tasks simultaneously by leveraging the geometry's large surface area to volume ratio. For example, the architectural functionality of the lattice to bear loads and store mechanical energy along with the larger surface area for energy storage is combined. A compliant double‐gyroid capacitor that can simultaneously achieve three functions is demonstrated: load bearing, energy storage, and sensing.
Hadikhan Tehrani, Mohammad(
, The University of Oklahoma Libraries)
null
(Ed.)
Loss of operation or devastating damage to buildings and industrial structures, as well as equipment housed in them, has been observed due to earthquake-induced vibrations. A common source of operational downtime is due to the performance reduction of vital equipment, which are sensitive to the total transmitted acceleration. A well-known method of protecting such equipment is seismic isolation of the equipment itself (or a group of equipment), as opposed to the entire structure due to the lower cost of implementation. The first objective of this dissertation is assessing a rolling isolation system (RIS) based on existing design guidelines for telecommunications equipment. A discrepancy is observed between the required response spectrum (RRS) and the one and only accelerogram recommended in the guideline. Several filters are developed to generate synthetic accelerograms that are compatible with the RRS. The generated accelerograms are used for probabilistic assessment of a RIS that is acceptable per the guideline. This assessment reveals large failure probability due to displacement demands in excess of the displacement capacity of the RIS. When the displacement demands on an isolation system are in excess of its capacity, impacts result in spikes in transmitted acceleration. Therefore, the second objective of this dissertation is to design impact prevention/mitigation mechanisms. A dual-mode system is proposed where the behavior changes when the displacement exceeds a predefined threshold. A new piecewise optimal control approach is developed and applied to find the best possible mechanism for the region beyond the threshold. By utilizing the designed curves obtained from the proposed optimal control procedure, a Kelvin-Voigt device is tuned for illustrative purposes. On the other hand, the preference for protecting equipment decreases as the earthquake intensity increases. In extreme seismic loading, the response mitigation of the primary structure (i.e., life safety and collapse prevention) is of greater concern than protecting isolated equipment. Therefore, the third objective of this dissertation is to develop an innovative dual-mode system that can behave as equipment isolation under low to moderate seismic loading and passively transition to behave as a vibration absorber for the primary structure under extreme seismic loading. To reduce the computational cost of simulating a large linear elastic structure with nonlinear attachments (i.e., equipment isolation with cubic hardening nonlinearity), a reduced order modeling method is introduced that can capture the behavior of such nonlinear coupled systems. The method is applied to study the feasibility of dual-mode vibration isolation/absorber. To this end, nonlinear transmissibility curves for the roof displacement and isolated mass total acceleration are developed from the steady-state responses of dual-mode systems using the harmonic balanced method. The final objective of this dissertation is to extend the reduced order modeling method developed for linear elastic structure with nonlinear attachment to inelastic structures (without attachments). The new inelastic model condensation (IMC) method uses the modal properties of the full structural model (in the elastic range) to construct a linear reduced order model in conjunction with a hysteresis model to capture the hysteretic inter-story restoring forces. The parameters of these hysteretic forces are easily tuned, in order to fit the inelastic behavior of the condensed structure to that of the full model under a variety of simple loading scenarios. The fidelity of structural models condensed in this way is demonstrated via simulation for different ground motion intensities on three different building structures with various heights. The simplicity, accuracy, and efficiency of this approach could significantly alleviate the computational burden of performance-based earthquake engineering.
Zhichao Wang
Ali Y.Tamijani(
, Aerospace science and technology)
J.A. Ekaterinaris
(Ed.)
This paper describes a methodology for designing the material distribution and orientation of three-dimensional non-uniform (heterogeneous) lattice structures. Recent advances in additive manufacturing enable fabrication across multiple length scales. Homogenization-based design optimization and the subsequent projection of the optimized design facilitate the synthesis of large-scale microstructures that form lightweight bionic designs. The main aspects of this research are (a) the construction, homogenization-based optimization, and projection of two types of lattices with different degrees of anisotropy and (b) the parallelization of the analysis, optimization, and projection framework in order to handle large-scale meshes and obtain high-resolution, heterogeneous lattice structures. Cubic and octet-truss lattices were selected to demonstrate the ability of the framework to design different types of lattices. A quadcopter arm and an internal wing structure were designed using the optimization and projection framework, verifying its capability to synthesize heterogeneous lattice structures for complex design domains. The ability to change the complexity of optimized microlattices using the characteristic parameters of the lattice is discussed. The relationship between the lattice anisotropy and the optimized, smoothed orientation is investigated, and the optimized design for each lattice is compared with those obtained using conventional design optimization procedures.
Architected metamaterials have emerged as a central topic in materials science and mechanics, thanks to the rapid development of additive manufacturing techniques, which have enabled artificial materials with outstanding mechanical properties. This Letter seeks to investigate the elastodynamic behavior of octet truss lattices as an important type of architected metamaterials for high effective strength and vibration shielding. We design, fabricate, and experimentally characterize three types of octet truss structures, including two homogenous structures with either thin or thick struts and one hybrid structure with alternating strut thickness. High elastic wave transmission rate is observed for the lattice with thick struts, while strong vibration mitigation is captured from the homogenous octet truss structure with thin struts as well as the hybrid octet truss lattice, though the underlying mechanisms for attenuation are fundamentally different (viscoelasticity induced dampening vs bandgaps). Compressional tests are also conducted to evaluate the effective stiffness of the three lattices. This study could open an avenue toward multifunctional architected metamaterials for vibration shielding with high mechanical strength.
Brenneman, Jacob, Lovalekar, Mihir, and Panat, Rahul. A Semiempirical Model for Post‐Yield Stress Instability in the Stress–Strain Response of 3D Lattice Structures under Compressive Loads. Advanced Engineering Materials 25.12 Web. doi:10.1002/adem.202201428.
Brenneman, Jacob, Lovalekar, Mihir, & Panat, Rahul. A Semiempirical Model for Post‐Yield Stress Instability in the Stress–Strain Response of 3D Lattice Structures under Compressive Loads. Advanced Engineering Materials, 25 (12). https://doi.org/10.1002/adem.202201428
Brenneman, Jacob, Lovalekar, Mihir, and Panat, Rahul.
"A Semiempirical Model for Post‐Yield Stress Instability in the Stress–Strain Response of 3D Lattice Structures under Compressive Loads". Advanced Engineering Materials 25 (12). Country unknown/Code not available: Wiley Blackwell (John Wiley & Sons). https://doi.org/10.1002/adem.202201428.https://par.nsf.gov/biblio/10419132.
@article{osti_10419132,
place = {Country unknown/Code not available},
title = {A Semiempirical Model for Post‐Yield Stress Instability in the Stress–Strain Response of 3D Lattice Structures under Compressive Loads},
url = {https://par.nsf.gov/biblio/10419132},
DOI = {10.1002/adem.202201428},
abstractNote = {Mechanical behavior of lattice structures is important for a range of engineering applications. Herein, a new semiempirical model is proposed that describes the entire range of stress–strain response of lattice structures, including the stress‐instability region which is modeled as an oscillator. The model can be fit to individual stress–strain curves to extract elastic modulus, yield stress, collapse stress, post‐yield collapse ratio, densification strain, and the energy absorbed per unit volume. The model is fit to 119 unique experimental stress–strain curves from 13 research papers in literature covering four different lattice designs, namely, octet truss, body‐centered cubic with vertical members, body‐centered cubic, and hexagonal. Manufacturing methods (additive and conventional) and materials (metals and polymers) were also included in the analysis. The fitted model yields several new insights into the compression behavior of previously tested lattice structures and can be applied to additional lattice designs. Among other results, analysis of variance (ANOVA) reveals that the octet truss lattice demonstrates the highest post‐yield collapse ratio and the smallest normalized energy absorption per unit volume amongst the lattice structures investigated. The proposed model is a powerful tool for designers to quantitatively compare and select 3D lattice structures with the desired mechanical characteristics.},
journal = {Advanced Engineering Materials},
volume = {25},
number = {12},
publisher = {Wiley Blackwell (John Wiley & Sons)},
author = {Brenneman, Jacob and Lovalekar, Mihir and Panat, Rahul},
}
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