Mechanics of Materials最新文献

Neural network based models have emerged as a powerful tool in multiscale modeling of materials. One promising approach is to use a neural network based model, trained using data generated from repeated solution of an expensive small scale model, as a surrogate for the small scale model in application scale simulations. Such approaches have been shown to have the potential accuracy of concurrent multiscale methods like FE${}^2$, but at the cost comparable to empirical methods like classical constitutive models or parameter passing. A key question is to understand how much and what kind of data is necessary to obtain an accurate surrogate. This paper examines this question for history dependent elastic–plastic behavior of an architected metamaterial modeled as a truss. We introduce an iterative approach where we use the rich arbitrary class of trajectories to train an initial model, but then iteratively update the class of trajectories with those that arise in large scale simulation and use transfer learning to update the model. We show that such an approach converges to a highly accurate surrogate, and one that is transferable.

In recent years, magnetic-responsive soft materials with high remanent magnetization have received significant attention due to their capacity for untethered and rapid actuation under magnetic fields, with diverse applications spanning robotics, biomedicine, and vibration mitigation. Most designs of the magnetic soft materials rely on discrete remanent magnetization orientations, which could limit the actuation performance because of the restricted selection of magnetization orientations and potentially cause fabrication challenges due to the sharp changes in magnetization orientations at the interfaces that may induce strong repelling forces. To expand the programmability and improve the fabricability of the magnetic soft materials, we enable design capability with optimal continuous magnetization orientations. This paper proposes a multiphysics topology optimization framework that concurrently optimizes topologies and continuous remanent magnetization distributions in the magnetic soft materials and structures. Employing the proposed approach, we design and investigate problems of letter programming, actuators, and metamaterials with magnetic actuation under large deformations. We demonstrate that the proposed strategy enhances design flexibility, improves performance, eliminates sharp changes in magnetization orientations, and is capable of creating non-intuitive designs that can achieve multiple functionalities. Finally, we prototype our optimized design to highlight its potential to bridge design optimization and direct-ink-writing fabrication of magnetic materials with continuously varying magnetization orientations.

The dimensional reduction of a hyperelastic coated fabric from 3D to 2D is accomplished asymptotically using the Variational Asymptotic Method (VAM). This method integrates constrained calculus of variations and asymptotics. The VAM bifurcates the analysis into two: a 1D through-the-thickness analysis and a 2D reference surface analysis. The 1D analysis leads to the derivation of an asymptotically correct 3D warping functions and a 2D non-linear constitutive law. The 2D non-linear reference surface analysis utilizes the derived 2D non-linear constitutive law to obtain 2D displacements and strains through the 2D non-linear FEA. The classification of 3D strain energy density into distinct orders is enabled by introducing two intrinsic small parameters: 1) a geometric small parameter denoted by the ratio of thickness to characteristic length $\left(h/l\ll 1\right)\text{,}$ and 2) a physical small parameter that ensures the largest component of 3D strain is restricted to 20 percent, which is less than 1. The model takes into account both geometric and material nonlinearities. The strain energy function, which describes the anisotropic characteristics of the coated fabric has contributions from the strain energies of fiber, matrix, and fiber-fiber interaction. The findings of the study include analytically derived 3D warping functions, a 2D nonlinear constitutive law, and the prediction of warp and weft stresses and strain for a biaxial loaded tensile specimen. These findings align with the experimental outcomes.

A comprehensive analysis of experimental data is presented for 316LN stainless steel subjected to isothermal and thermal-mechanical fatigue loading conditions within the temperature range of 350–600 °C. The study aims to provide a thorough understanding of the cyclic behavior through meticulous data integration, supplementation, and the use of stress decomposition methods combined with a classical damage evolution definition. The modeling approach employed in this study is based on the classical AF-OW-Kang model, with the incorporation of the Arrhenius term in the plastic flow rate equation. Furthermore, to consider the effect of dynamic strain aging at varying temperatures, temperature-dependent terms are introduced into the equations that govern the evolution of isotropic stress and backstress, resulting in enhanced accuracy in describing cyclic hardening behavior. Additionally, a modified damage evolution equation is utilized, along with equations for isotropic stress and backstress evolution, to address cyclic softening. Simulation results confirm the effectiveness of the modified model in capturing the cyclic hardening/softening behavior of 316LN stainless steel throughout the whole-life time, under both isothermal and thermal-mechanical fatigue loading conditions.

Viscoelastic effective creep compliances were predicted for symmetric composite laminates with constant matrix crack density. Following previous analytical models, the governing equations were solved in the Laplace domain, and the resulting displacement field was inverse Laplace transformed to obtain the displacement field, damage variables, and strain response to a given stress in the time domain. For the displacement field, both a series solution and a non-series solution were obtained. The non-series solution was then used to calculate the strain response of a cross-ply laminate subjected to constant stress under constant matrix crack density via the numerical inverse Laplace transform. To validate the model, the creep strains predicted using the model were compared with a finite element analysis solution, experimental results, and a synergistic damage mechanics solution.

A novel analytical probabilistic progressive damage model (PPDM) is introduced for multiphase composites to predict the damage behavior of hybrid composites. The PPDM is based on effective field methods and the stochastic nature of fiber damage is captured by including weakest link theory and Weibull statistics. Three additional models are developed to compare with the PPDM. A stochastic model analogous to the PPDM (called SPDM), and two finite element models, one stochastic (SFEM) and one probabilistic (PFEM). All models are developed in a thermodynamically consistent framework and are extended to include residual thermal stresses. Finally, the four models are compared with models from the open literature for an AS4-M50S hybrid carbon–carbon composite with different hybridization ratios of high to low elongation fibers. The comparison reveals a great agreement between all models and indicates that the stochastic nature of fiber damage is the most influential parameter leading to damage.

Networks of beams are a subject of increasing interest to create architected materials with exceptional mechanical properties and low density. This paper investigates the mechanical properties of one dimensional (1D) hierarchical beams for the development of three dimensional (3D) truss lattice materials. These 1D hierarchical beams are constructed in two configurations by placing axial and inclined struts in single and double laced Warren truss patterns in each side of a beam with polygon cross section. Analytical and numerical analyses have been used to characterize their mechanical properties, including the elastic modulus, second moment of area, and shear stiffness of hierarchical beams drawn from a broad design space. Also, the failure limits of the beams with respect to parent material failure and various buckling modes are probed. Finally, the hierarchical beams have been implemented as the constituent members of Kelvin and octet lattices, and the elastic modulus and failure boundaries of the second-order hierarchical lattices are evaluated. The investigation reveals the competition between the elastic properties in the individual hierarchical beams based on different combinations of the design variables. The stiffness of the designs under compression and bending is found to be a function of the axial member size and cross sectional shape of the hierarchical beam. On the other hand, the shear stiffness of hierarchical beam designs is a function of the inclined member size and their inclination angle. It is demonstrated that incorporating hierarchy in the Kelvin and octet truss lattices can enhance the load bearing capacity of designs at low relative densities when compared to their hollow counterparts. Also, it is shown that second-order hierarchical stretching and bending-dominated lattices incorporating first-order hierarchical beams, can not only achieve but also surpass the strength and stiffness scaling relations established for first-order lattices. This becomes particularly noteworthy when considering bending-dominated lattices, as the hierarchy can drive their stiffness toward the boundaries, enabling them to outperform their equivalent stretching-dominated rivals.

Designing metamaterials with unprecedented coefficients of thermal expansion (CTEs) is an urgent demand for the majority engineering structures suffering from ambient temperature variation. Current studies on such artificial materials are mainly focused on achieving CTE tunnability through the purposeful design of material microstructure using an intuition based mechanism. In this study, the mechanical properties including maximum bulk modulus, specific stiffness and high thermal conductivity are combined with desired CTEs for designing multifunctional lattice metamaterials through the application of a non-intuitive topology optimization method. Toward this end, the continuous variable of member cross-sectional area is adopted to optimize lattice topology, section sizes of lattice members and material distributions, simultaneously. To meet the manufacturing requirements, an improved member intersection constraint that can cooperate with the present continuous design variable is introduced. A self-programmed routine that can be coupled with any commercial FEA software is developed to implement the present optimization method for the design of lattice metamaterials. Four typical optimization cases corresponding to different practical engineering issues are completed. Compared with the previously reported representative lattice metamaterials that are devised from the intuition or experience of designers, the optimization results obtained in this work demonstrate an obvious superiority in bulk modulus and specific stiffness. Additionally, a bimetallic specimen, fabricated using mechanical processing technology and composed of the metallic constituents Invar and Aluminum alloy, is presented to demonstrate the manufacturability of the optimized lattice microstructures.

Nematic liquid crystal elastomers (LCEs) are a unique class of network polymers with the potential for enhanced mechanical energy absorption and dissipation capacity over conventional network polymers because they exhibit both conventional viscoelastic behavior and soft-elastic behavior (nematic director changes under shear loading). This additional inelastic mechanism makes them appealing as candidate damping materials in a variety of applications from vibration to impact. The lattice structures made from the LCEs provide further mechanical energy absorption and dissipation capacity associated with packing out the porosity under compressive loading.

Understanding the extent of mechanical energy absorption, which is the work per unit mass (or volume) absorbed during loading, versus dissipation, which is the work per unit mass (or volume) dissipated during a loading cycle, requires measurement of both loading and unloading response. In this study, a bench-top linear actuator was employed to characterize the loading-unloading compressive response of polydomain and monodomain LCE polymers and polydomain LCE lattice structures with two different porosities (nominally, 62% and 85%) at both low and intermediate strain rates at room temperature. As a reference material, a bisphenol-A (BPA) polymer with a similar glass transition temperature (9 °C) as the nematic LCE (4 °C) was also characterized at the same conditions for comparing to the LCE polymers. Based on the loading-unloading stress-strain curves, the energy absorption and dissipation for each material at different strain rates (0.001, 0.1, 1, 10 and 90 s^-1) were calculated with considerations of maximum stress and material mass/density. The strain-rate effect on the mechanical response and energy absorption and dissipation behaviors was determined. The energy dissipation ratio was also calculated from the resultant loading and unloading stress-strain curves. All five materials showed significant but different strain rate effects on energy dissipation ratio. The solid LCE and BPA materials showed greater energy dissipation capabilities at both low (0.001 s⁻¹) and high (above 1 s⁻¹) strain rates, but not at the strain rates in between. The polydomain LCE lattice structure showed superior energy dissipation performance compared with the solid polymers especially at high strain rates.

Probing the mechanical behavior of the region formed between a nanoparticle reinforcement and a polymer matrix in a polymer nanocomposite structure, denoted as the “interphase”, is a main challenge as such regions are difficult to investigate by experimental methods. Here, we accurately characterize the heterogeneous mechanical behavior of polymer nanocomposites, focusing on polymer/nanofiller interphases via a combination of nanomechanical simulations and numerical homogenization techniques. Initially, the global mechanical performance of a glassy poly(ethylene oxide) polymer nanocomposite reinforced with silica nanoparticles is studied using detailed atomistic molecular dynamics simulations for 1.9% and 12.7% silica volume fractions. Next, the polymer/silica interphase thickness is identified by probing the polymer atom-based density distribution profile in the vicinity of the nanofiller at equilibrium. On the basis of this thickness, the interphase is subdivided to check the position-dependent change in mechanical properties. Then, using continuum mechanics and atomistic simulations, we proceed to compute the effective Young’s modulus and Poisson’s ratio of the polymer/nanoparticle interphase as function of the distance from the nanoparticle. In the last step, an inverse numerical homogenization model is proposed to predict the mechanical properties of the interphase on the basis of a comparison criteria with the data from MD. The results were found to be acceptable, raising the possibility of accurately and efficiently predicting interfacial properties in nanostructured materials.