Elastic properties of reinforced solids: Some theoretical principles

1963/09/01 by R. Hill · 4,828 citations
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #Materials science #Mechanical Behavior of Composites

paper · doi:10.1016/0022-5096(63)90036-x

published in Journal of the Mechanics and Physics of Solids 11(5), 357-372 (Elsevier BV)

openalex publication_date 1963/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Cited by

• Elastic constants of textured short-fiber composites
• The effect of fibre length on the overall moduli of composite materials
• Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme
• Higher-order pathwise theory of fluctuations in stochastic homogenization
• Deep material networks for fiber suspensions with infinite material contrast
• On the choice of homogenization method to achieve effective mechanical properties of composites reinforced by ellipsoidal and spherical particles
• Variationally Consistent Framework for Finite-Strain Microelasticity
• The elastic, mechanical, and thermodynamic properties of NaXH (X = B, Al) intended for the storage of hydrogen: An ab-initio study
• A data-driven multiscale scheme for anisotropic finite strain magneto-elasticity
• Computational Crystal Plasticity Homogenization using Empirically Corrected Cluster Cubature (E3C) Hyper-Reduction
• A topological counting rule for shells
• Homogenization-based optimization of wall thickness distribution for TPMS two-fluid heat exchangers
• Capillarity in Stationary Random Granular Media: Distribution-Aware Screening and Quantitative Supercell Sizing
• The structure of fluctuations in stochastic homogenization
• Symmetries in stochastic homogenization and adjustments for the RVE method
• A machine learning accelerated FE² homogenization algorithm for elastic solids
• Metal additive manufacturing of lattice-based orthopedic implants: A comprehensive review of requirements and design strategies
• High P-T single-crystal elasticity of zircon by Brillouin spectroscopy
• E²-TFA based multiscale analysis of failure in elasto-plastic composites
• Representative volume elements for matrix-inclusion composites -- a computational study on periodizing the ensemble
• Multiscale modeling of cancellous bone considering full coupling of mechanical, electrical and magnetic effects
• A Nonlinear Finite Element Heterogeneous Multiscale Method for the Homogenization of Hyperelastic Solids and a Novel Staggered Two-Scale Solution Algorithm
• Single- to multi-fidelity history-dependent learning with uncertainty quantification and disentanglement: application to data-driven constitutive modeling
• Universal Fourier Neural Operators for periodic homogenization problems in linear elasticity
• The effect of fiber plasticity on domain formation in soft biological composites -- Part I: a bifurcation analysis
• On the spectral asymptotics of waves in periodic media with Dirichlet or Neumann exclusions
• Predicting the mechanical response of oligocrystals with deep learning
• Exploring metamaterials' structures through the relaxed micromorphic model: switching an acoustic screen into an acoustic absorber
• Plasticity models of material variability based on uncertainty quantification techniques
• Estimating the Effective Elasticity Properties of a Diamond/β-SiC Composite Thin Film by 3D Reconstruction and Numerical Homogenization
• Computational homogenization of heterogeneous media under dynamic loading
• Diffraction Stress Factors Calculated Using a Maximum Entropy Method
• Maximum-Entropy Based Estimates of Stress and Strain in Thermoelastic Random Heterogeneous Materials
• Determination of Diffraction Elastic Constants Using the Maximum Entropy Method
• Time domain analysis of microstructured materials through the reduced relaxed micromorphic model
• Seismic Properties of Coastal and Inland Sabkhas: Implications for Static Corrections
• The correspondence between Voigt and Reuss bounds and the decoupling constraint in a two-grid staggered solution algorithm to coupled flow and deformation in heterogeneous poroelastic media
• Multiple Scattering of Elastic Waves in Polycrystals
• Association of macroscopic laboratory testing and micromechanics modelling for the evaluation of the poroelastic parameters of a hardened cement paste
• A bimodal plasticity theory of fibrous composite materials
• Simulations on the electromechanical poling of ferroelectric ceramics
• Micromechanics analysis of thermal expansion and thermal pressurization of a hardened cement paste
• Capillary forces in the acoustics of patchy-saturated porous media
• Effective interface forces to model boundary effects in a finite-size metamaterial through the reduced relaxed micromorphic model
• Numerical Models in Discontinuous Media: Review of Advances for Rock Mechanics Applications
• Evaluation of hyperelastic models for unidirectional short fibre reinforced materials using a representative volume element with refined boundary conditions
• A three-dimensional mechanistic study of the drivers of classical twin nucleation and variant selection in Mg alloys: A mesoscale modelling and experimental study
• Materials knowledge system for nonlinear composites
• Topology optimization of nonlinear elastic micro-structures by a domain reduction technique
• Development of an ABAQUS plugin tool for periodic RVE homogenisation
• Pressure dependent ab initio study of the physical properties of hexagonal BeB2C: a possible high-Tc superconductor
• Correlation structure in the elasticity tensor for short fiber-reinforced composites
• A coarse-grained model for the elastic properties of cross linked short carbon nanotube/polymer composites
• Microstructure and tensile properties of high strength duplex ferrite–martensite (DFM) steels
• Heterogeneous multiscale methods for fourth-order singular perturbations
• A jigsaw puzzle framework for homogenization of high porosity foams
• Multi-scale modelling of elastic moduli of trabecular bone. [europepmc]
• Hierarchical analysis and multi-scale modelling of rat cortical and trabecular bone. [europepmc]
• Poromicromechanics reveals that physiological bone strains induce osteocyte-stimulating lacunar pressure. [europepmc]
• Hybrid vertex-midline modelling of elongated plant organs. [europepmc]
• Materials Knowledge Systems in Python - A Data Science Framework for Accelerated Development of Hierarchical Materials. [europepmc]
• Water Uptake Behavior and Young Modulus Prediction of Composites Based on Treated Sisal Fibers and Poly(Lactic Acid). [europepmc]
• Plant Fibre: Molecular Structure and Biomechanical Properties, of a Complex Living Material, Influencing Its Deconstruction towards a Biobased Composite. [europepmc]
• Finite Element Modeling of Tensile Deformation Behaviors of Iron Syntactic Foam with Hollow Glass Microspheres. [europepmc]
• A Tensile Constitutive Relationship and a Finite Element Model of Electrospun Nanofibrous Mats. [europepmc]
• Relationship between the Size of the Samples and the Interpretation of the Mercury Intrusion Results of an Artificial Sandstone. [europepmc]
• Improving the Mechanical Stability of Metal-Organic Frameworks Using Chemical Caryatids. [europepmc]
• Analytical Micromechanics Models for Elastoplastic Behavior of Long Fibrous Composites: A Critical Review and Comparative Study. [europepmc]
• Atomic Simulations of Grain Structures and Deformation Behaviors in Nanocrystalline CoCrFeNiMn High-Entropy Alloy. [europepmc]
• Design of Reinforcement in Nano- and Microcomposites. [europepmc]
• Multiscale Thermoelastic Analysis of the Thermal Expansion Coefficient and of Microscopic Thermal Stresses of Mature Concrete. [europepmc]
• Strength increase during ceramic biomaterial-induced bone regeneration: a micromechanical study. [europepmc]
• Elastic modulus evolution of rocks under heating-cooling cycles. [europepmc]
• Magneto-Mechanical Coupling in Magneto-Active Elastomers. [europepmc]
• A Facile and Scalable Approach in the Fabrication of Tailored 3D Graphene Foam via Freeze Drying. [europepmc]
• Machine learning assisted design of new lattice core for sandwich structures with superior load carrying capacity. [europepmc]
• Analysis of the Parameters Affecting the Stiffness of Short Sisal Fiber Biocomposites Manufactured by Compression-Molding. [europepmc]
• Mono- and Multi-Objective CFD Optimization of Graded Foam-Filled Channels. [europepmc]
• Effect of collagen fibre orientation on the Poisson's ratio and stress relaxation of skin: an ex vivo and in vivo study. [europepmc]
• Multiscale micromechanics modeling of plant fibers: upscaling of stiffness and elastic limits from cellulose nanofibrils to technical fibers. [europepmc]
• Calculation of Mechanical Properties, Electronic Structure and Optical Properties of CsPbX 3 (X = F, Cl, Br, I). [europepmc]