scholarly journals Micromechanical study of elastic moduli of three-dimensional granular assemblies

2014 ◽  
Vol 51 (13) ◽  
pp. 2336-2344 ◽  
Author(s):  
N.P. Kruyt
Keyword(s):  
Elastic Moduli ◽  
Three Dimensional ◽  
Granular Assemblies

Mechanics of Three-Dimensional Printed Lattices for Biomedical Devices

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Paul F. Egan ◽  
Isabella Bauer ◽  
Kristina Shea ◽  
Stephen J. Ferguson
Keyword(s):  
Elastic Moduli ◽  
Nutrient Transport ◽  
Three Dimensional ◽  
Integrated Design ◽  
Mechanical Efficiency ◽  
Lattice Structures ◽  
Effective Elastic Moduli ◽  
Biomedical Devices ◽  
Fully Integrated ◽  
Polyjet Printing

Advances in three-dimensional (3D) printing are enabling the design and fabrication of tailored lattices with high mechanical efficiency. Here, we focus on conducting experiments to mechanically characterize lattice structures to measure properties that inform an integrated design, manufacturing, and experiment framework. Structures are configured as beam-based lattices intended for use in novel spinal cage devices for bone fusion, fabricated with polyjet printing. Polymer lattices with 50% and 70% porosity were fabricated with beam diameters of 0.4–1.0mm, with measured effective elastic moduli from 28MPa to 213MPa. Effective elastic moduli decreased with higher lattice porosity, increased with larger beam diameters, and were highest for lattices compressed perpendicular to their original build direction. Cages were designed with 50% and 70% lattice porosities and included central voids for increased nutrient transport, reinforced shells for increased stiffness, or both. Cage stiffnesses ranged from 4.1kN/mm to 9.6kN/mm with yielding after 0.36–0.48mm displacement, thus suggesting their suitability for typical spinal loads of 1.65kN. The 50% porous cage with reinforced shell and central void was particularly favorable, with an 8.4kN/mm stiffness enabling it to potentially function as a stand-alone spinal cage while retaining a large open void for enhanced nutrient transport. Findings support the future development of fully integrated design approaches for 3D printed structures, demonstrated here with a focus on experimentally investigating lattice structures for developing novel biomedical devices.

A Stochastic Nonlinear Constitutive Law for Concrete

1989 ◽  
Vol 111 (4) ◽  
pp. 443-449 ◽  
Author(s):  
A. Fafitis ◽  
Y. H. Won
Keyword(s):  
Stochastic Model ◽  
Elastic Moduli ◽  
Three Dimensional ◽  
Path Dependency ◽  
Experimental Results ◽  
Constitutive Law ◽  
Induced Anisotropy ◽  
Nonproportional Loading ◽  
Strain Relationship ◽  
Good Agreement

An incremental three-dimensional stress-strain relationship for concrete with induced anisotropy has been developed. The nonlinearity and path-dependency are modeled by expressing the elastic moduli at each increment as function of the octahedral and deviatoric strains, based on a uniaxial stochastic model developed earlier. Predictions of multiaxial response under proportional and nonproportional loading are in good agreement with experimental results.

New Micromechanics Formulations for the Assessment of Elastic Moduli of Granular Assemblies

2002 ◽  
Author(s):  
Linbing Wang ◽  
Emir Macari ◽  
Eyassu Woldesenbet
Keyword(s):  
Elastic Moduli ◽  
New Method ◽  
Granular Mechanics ◽  
Volume Fractions ◽  
Granular Assemblies ◽  
The Matrix ◽  
Particle Shapes

The elastic moduli of granular assemblies are sensitive to the confining conditions as well as the volume fractions of each of its constituents (i.e. solid, fluid, gas). Theoretical estimations using granular mechanics are based on assumed distributions of contact normals and branch vectors using idealized particle shapes and therefore cannot quantitatively predict the moduli. This paper presents a new method to use the moduli of the granular skeleton and those of the matrix to estimate the moduli of the composite and makes it possible to back-calculate the moduli of the skeleton from the moduli of the composite and the matrix.

The Effect of Microstructural Morphologies on the Effective Electromechanical Properties of Piezoelectric Particle Composites

2012 ◽  
Author(s):  
Vahid Tajeddini ◽  
Chien-hong Lin ◽  
Anastasia Muliana ◽  
Martin Lévesque
Keyword(s):  
Mechanical Properties ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Micromechanical Model ◽  
Three Dimensional ◽  
Particle Sizes ◽  
Reinforced Composites ◽  
Electromechanical Properties ◽  
Particle Volume ◽  
Self Consistent

This study introduces a micromechanical model that incorporates detailed microstructures for analyzing the effective electro-mechanical properties, such as piezoelectric and permittivity constants as well as elastic moduli, of piezoelectric particle reinforced composites. The studied composites consist of polarized spherical piezoelectric particles dispersed into a continuous and elastic polymeric matrix. A micromechanical model generated using three-dimensional (3D) continuum elements within a finite element (FE) framework. For each volume fraction (VF) of particles, realization with different particle sizes and arrangements were generated in order to represent microstructures of a particle composite. We examined the effects of microstructural morphologies, such as particle sizes and distributions, and particle volume fractions on the overall effective electro-mechanical properties of the active composites. The overall electro-mechanical properties determined from the present micromechanical model were compared to those generated using the Mori-Tanaka, self-consistent, and simplified unit-cell micromechanical models.

Sufficient Symmetry Conditions for Isotropy of the Elastic Moduli Tensor

1987 ◽  
Vol 54 (4) ◽  
pp. 772-777 ◽  
Author(s):  
R. M. Christensen
Keyword(s):  
Elastic Moduli ◽  
Fiber Composite ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Axial Deformation ◽  
Space Network ◽  
Plane Normal ◽  
Rank Tensor ◽  
Three Space

Symmetry conditions are found that assure isotropy of the fourth rank tensor of elastic moduli. Crystallography provides the answer to this problem in the two-dimensional context, namely one axis of three-fold symmetry assures the isotropy of properties in the plane normal to the axis. The present work provides the answer in the three-dimensional problem: 6 axes of five-fold symmetry are sufficient to give isotropy of the elastic moduli. An important restriction must accompany the present result. The derivation is given in the special form appropriate to low density materials which have a microstructure that transmits load according to the axial deformation of a space network of material distributed into micro-struts. The corresponding fiber composite idealization is that of a fiber dominated system, it therefore follows that if the fibers take the 6 specific orientations in three-space then isotropy is obtained.

scholarly journals How does static granular matter re-arrange for different isotropic strain rate?

2021 ◽  
Vol 249 ◽  
pp. 10001
Author(s):  
Stefan Luding
Keyword(s):  
Elastic Moduli ◽  
Large Strain ◽  
Granular Matter ◽  
Three Dimensional ◽  
Model Systems ◽  
Strain Rates ◽  
State Variables ◽  
New States ◽  
Hyper Elastic ◽  
Particle Simulations

The question of how soft granular matter, or dense amorphous systems, re-arrange their microstructure under isotropic compression and de-compression, at different strain rates, will be answered by particle simulations of frictionless model systems in a periodic three-dimensional cuboid. Starting compression below jamming, the systems experience the well known jamming transition, with characteristic evolutions of the state variables elastic energy, elastic stress, coordination number, and elastic moduli. For large strain rates, kinetic energy comes into play and the evolution is more dynamic. In contrast, at extremely slow deformation, the system relaxes to hyper-elastic states, with well-defined elastic moduli, in static equilibrium between irreversible (plastic) re-arrangement events, discrete in time. Small, finite strains explore those reversible (elastic) states, before larger strains push the system into new states, by irreversible, sudden re-arrangements of the micro-structure.

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