Mechanics of Materials最新文献

An effective statistical higher-order three-scale reduced homogenization (SHTRH) method is established to analyze the nonlinear random heterogeneous materials with multiple micro-configurations. Firstly, the various unit cell functions based on the microscale and mescoscale regions are given, and two expected homogenization coefficients are computed through Kolmogorov's strong laws of large number. Further, the nonlinear homogenized equations are formulated, and the corresponding reduced-order multiscale systems for displacement and stress solutions are derived by using the high-order unit cell solutions and homogenized solutions. The key features of the new statistical multiscale methods are (i) the novel reduced models established to solve the inelastic problems of random composites at a fraction of cost, (ii) the high-order homogenized solutions which do not need high-order continuity for the macro solutions of the random problems and (iii) the statistical high-order multiscale algorithms developed for analyzing the nonlinear random composites with three-scale structures. Finally, the effectiveness and correctness of the algorithm are confirmed according to several hyperelastic, plasticity and damage periodic/random composites with multiple-scale configurations. The computation shows that the proposed SHTRH methods are useful for analyzing the macroscopic nonlinear performance, and can efficiently catch the microscopic and mesoscopic information for the random heterogeneous composites.

A short survey on the experimental testing of solid propellants has highlighted finite strain responses that are temperature-dependent, viscoelastic with damage, and exhibit tension/compression asymmetry. Consequently, a finite strain viscoelastic model that satisfies the principles of thermodynamics has been developed. This model is based on the common multiplicative decomposition of the deformation gradient into elastic and viscous components, with considerations for damage and asymmetry. The model has been tested against three sets of data from the literature, carefully selected to represent the various characteristics of solid propellants. The model accurately reproduces uniaxial tension responses at different strain rates and temperatures, with the capability to account for superimposed hydrostatic pressure. Notably, these satisfactory representations require only five fitting parameters, in addition to the typical identification of polymer linear viscoelasticity and time–temperature superposition. Finally, an attempt to reproduce both tension and compression tests conducted independently on the same material underscores the need to account for tension–compression asymmetry, as defined in the proposed constitutive equations. This finding advocates for new tests, such as compression following tension and vice versa.

Modeling the evolution of voids during plastic flow as well as their effects on plastic dissipation is critical for both component manufacturing and lifetime estimation purposes. To this end, we propose a rate-dependent constitutive model to homogenize the effects of semi-randomly distributed voids on single crystal plasticity whilst capturing void interaction and plastic anisotropy. The present work focuses on the case of face centered cubic crystals to introduce an anisotropic gauge function applicable within the crystal plasticity formalism. The approach combines analytical methods to describe the micromechanics of the system in combination with symbolic regression to capture analytically intractable mechanisms from data. The hybrid framework uses a physics-informed genetic programming-based symbolic regression algorithm to solve a multiform optimization problem simultaneously producing a new gauge function and a new strain rate equation. This is also a multi-objective optimization problem with many competing objectives. A new search and selection step is introduced to the genetic algorithm that promotes convergence toward a global solution that better satisfies all the objectives. Overall, the symbolic equations produced leverage data-driven methods to achieve greater accuracy than comparable alternatives on an analytically intractable problem while maintaining model transparency.

The flexoelectric effect implies a wide application potential in micro- and nanoscale electromechanical systems, where cylinders are widely used due to their wide range of applications. At the same time, functionally graded materials combine the advantages of different materials to achieve optimized material properties. Motivated by these considerations, we use the generalized power series method for the first time to derive exact solutions to functionally graded flexoelectric cylinder problems, including pressure and shear scenarios. This research systematically investigates the effects of material gradation, characteristic length parameters, and flexoelectric coefficients on the intricate electromechanical coupling behavior of functionally graded flexoelectric micro-cylinders. In addition, a comparative analysis between the exact and mixed finite element solutions demonstrates remarkable agreement. In particular, this investigation pioneers the extension of the Lamé problem, a cornerstone of classical elasticity, into the advanced realm of higher-order electroelasticity in inhomogeneous materials. This advance holds great promise for the design and optimization of micro- and nanoscale electromechanical systems based on the principles of flexoelectricity.

The inclusions in a high-temperature resistant matrix can significantly influence the radiative heat transfer of composite materials at elevated temperatures; therefore, the microstructure design of composites for thermal protection during atmospheric re-entry require a more accurate prediction of thermal insulation performance. In this paper, the Rosseland approximation was used to investigate the radiative heat transfer within thermal protection materials, e.g., porous carbon-based material and ultra-high-temperature ceramics (e.g., ZrB₂-SiC), and the discrete dipole scattering method was used to evaluate the extinction efficiency across the inclusions with different types of microstructures. The effect of inclusion parameters, such as inclusion size, shape coefficient, volume fraction, orientation, and size distribution, on the radiative and effective thermal conductivity (ETC) at various temperatures was analyzed in detail. Test results obtained from the existing literature were used to validate the ETC of porous ceramics predicted by the proposed model. The results indicated that the microstructures in thermal protection materials play a fundamental role in improving the heat-shielding properties. The present study deepens the understanding of the relationship between microstructures and thermal radiation properties and provides theoretical design guidelines for thermal protection materials with improved thermal insulation properties.

In this work, a hybrid physics-based data-driven surrogate model for the microscale analysis of heterogeneous material is investigated. The proposed model benefits from the physics-based knowledge contained in the constitutive models used in the full-order micromodel by embedding the material models in a neural network. Following previous developments, this paper extends the applicability of the physically recurrent neural network (PRNN) by introducing an architecture suitable for rate-dependent materials in a finite strain framework. In this model, the homogenized deformation gradient of the micromodel is encoded into a set of deformation gradients serving as input to the embedded constitutive models. These constitutive models compute stresses, which are combined in a decoder to predict the homogenized stress, such that the internal variables of the history-dependent constitutive models naturally provide physics-based memory for the network. To demonstrate the capabilities of the surrogate model, we consider a unidirectional composite micromodel with transversely isotropic elastic fibers and elasto-viscoplastic matrix material. The extrapolation properties of the surrogate model trained to replace such micromodel are tested on loading scenarios unseen during training, ranging from different strain-rates to cyclic loading and relaxation. Speed-ups of three orders of magnitude with respect to the runtime of the original micromodel are obtained.