Deformation of Inhomogeneous Elastic Solids With Two-Dimensional Damage

2001 ◽  
Vol 68 (4) ◽  
pp. 528-536
Author(s):  
J. J. Luo ◽  
I. M. Daniel
Keyword(s):  
Periodic Structures ◽  
Elastic Behavior ◽  
Two Dimensional ◽  
Elastic Solids ◽  
Inhomogeneous Materials ◽  
Linear Elastic ◽  
Reinforced Composite ◽  
Macroscopic Deformation ◽  
Microscopic Damage ◽  
Microscopic Deformation

A general correlation is derived between macroscopic stresses/strains and microscopic deformation on the damage surfaces for inhomogeneous elastic solids with two-dimensional damage. Assuming linear elastic behavior for the undamaged materials, the macroscopic deformation associated with nonlinear strains, or damage strains, is shown to be the weighted sum of the microscopic deformations on the damage surfaces. For inhomogeneous materials with periodic structures (laminated composites, for example) and various identifiable damage modes, simple relations are derived between the macroscopic deformation and microscopic damage. When the number of identifiable damage modes is less than or equal to the number of relevant measurable macroscopic strains, the correlation can be used to evaluate the damage progression from simple macroscopic stress and strain measurements. The simple case of a unidirectional fiber-reinforced composite under longitudinal load is used to show how the results can help detect and characterize the damage using macroscopic measurements, without resorting to assumptions of detailed microscopic deformation mechanisms.

A modified Fourier series-based solution with improved rate of convergence for two-dimensional rectangular isotropic linear elastic solids

2021 ◽  
pp. 108128652110255
Author(s):  
Néstor Darío Barulich ◽  
Aharon Deutsch ◽  
Moshe Eisenberger ◽  
Luis Augusto Godoy ◽  
Patricia Mónica Dardati
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Rate Of Convergence ◽  
Rectangular Domain ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Elastic Solids ◽  
Linear Elastic ◽  
Present Solution ◽  
Stress States

This paper presents a new displacement solution based on a Modified Fourier Series (MFS) for isotropic linear elastic solids under plane strain or plane stress states subject to continuous displacement and traction boundary conditions in a two-dimensional rectangular domain. In contrast with existing approaches that are restricted to Fourier series with a rate of convergence of second order O(m-2), the MFS allows increasing the rate of convergence of the solution. The governing Partial Differential Equations (PDEs) are satisfied exactly by two displacement solutions while the boundary conditions are approximated after solving a finite system of algebraic equations. Numerical results for a solution with an MFS with rate of convergence O(m-3) are compared with results from existing numerical and analytical methods, showing the enhanced behavior of the present solution.

Modes of Wave Propagation and Dispersion Relations in Inclusion Reinforced Composite Plates

2010 ◽  
Author(s):  
Yu Cheng Liu ◽  
Jin Huang Huang
Keyword(s):  
Composite Plate ◽  
Elastic Moduli ◽  
Lamb Waves ◽  
Plate Thickness ◽  
Composite Plates ◽  
Dispersion Relations ◽  
Elastic Behavior ◽  
Effective Elastic Moduli ◽  
Aspect Ratios ◽  
Reinforced Composite

This paper mainly analyzes the wave dispersion relations and associated modal pattens in the inclusion-reinforced composite plates including the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thickness. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Using the Mori-Tanaka mean-field theory, the effective elastic moduli which are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior can be predicted explicitly. Then, the dispersion relations and the modal patterns of Lamb waves determined from the effective elastic moduli can be obtained by using the dynamic stiffness matrix method. Numerical simulations have been given for the various inclusion types and the resulting dispersions in various wave types on the composite plate. The types (symmetric or antisymmetric) of Lamb waves in an isotropic plate can be classified according to the wave motions about the midplane of the plate. For an orthotropic composite plate, it can also be classified as either symmetric or antisymmetric waves by analyzing the dispersion curves and inspecting the calculated modal patterns. It is also found that the inclusion contents, aspect ratios and plate thickness affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns.

Model of vibration in drilling into fibre-reinforced composite materials

2009 ◽  
Vol 223 (9) ◽  
pp. 1107-1114
Author(s):  
B W Huang
Keyword(s):  
Composite Materials ◽  
Vibration Amplitude ◽  
Time Dependent ◽  
Process Time ◽  
Drilling Process ◽  
Improve Product Quality ◽  
Analysis Model ◽  
Inhomogeneous Materials ◽  
Reinforced Composite ◽  
Twisted Beam

A model of the dynamic drill characteristics while drilling through fibre-reinforced composite materials (FRCMs) is investigated in this study. Anisotropic and inhomogeneous materials such as FRCMs, which are used to improve product quality, make it possible to improve production rate and avoid drill breakage. Such materials were used to study the dynamic characteristics of the drilling process. A theoretical analysis model for drilling composite materials is proposed. A pre-twisted beam is used to simulate the drill. A moving Winkler-type elastic foundation is used to approximate the drilling process time-dependent boundary. Numerical analysis indicates that the vibration amplitude changes significantly as the drill moves through composite material.

Implementation of p and h-p Versions of the Finite Element Method

1992 ◽  
Author(s):  
Ye-Chen Lai ◽  
Timothy C. S. Liang ◽  
Zhenxue Jia
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Analysis ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Linear Elastic ◽  
Finite Element Software ◽  
Analysis Process ◽  
Adaptive Analysis

Abstract Based on hierarchic shape functions and an effective convergence procedure, the p-version and h-p adaptive analysis capabilities were incorporated into a finite element software system, called COSMOS/M. The range of the polynomial orders can be varied from 1 to 10 for two dimensional linear elastic analysis. In the h-p adaptive analysis process, a refined mesh are first achieved via adaptive h-refinement. The p-refinement is then added on to the h-version designed mesh by uniformly increasing the degree of the polynomials. Some numerical results computed by COSMOS/M are presented to illustrate the performance of these p and h-p analysis capabilities.

Performance Based Evaluation of Bridge Substructure in North Mississippi Using Nonlinear FEM and Field Vibration Measurement

2000 ◽  
Author(s):  
Chris L. Mullen ◽  
Prabin R. Tuladhar
Keyword(s):  
Finite Element ◽  
Transfer Functions ◽  
Response Spectrum ◽  
Three Dimensional ◽  
Vibration Measurement ◽  
Elastic Behavior ◽  
Evaluation Procedure ◽  
Vibration Measurements ◽  
Linear Elastic ◽  
Performance Based Evaluation

Abstract Discussion of a Performance - Based Engineering evaluation procedure for an existing interstate highway bridge in north Mississippi. The bridge is in a highly trafficked location near the Memphis Metropolitan area and is reflective of modern design practices in Mississippi. Results are presented of nonlinear damage response and displacement ductility performance of the reinforced concrete bents and their foundations predicted using static finite element (FE) computations. The model considers the composite action of the concrete and the reinforcing steel materials under axial force, shear, torsion and flexure. The performance-based evaluation includes three-dimensional computational simulations of the nonlinear bridge system, including substructures and superstructure. The response spectrum dynamic analysis method will also be carried out on the linear elastic three-dimensional model to predict the linear elastic behavior. Field vibration measurements, including ambient and hammer-impact, were performed to calibrate the models. The computed transfer functions are currently being evaluated to correlate vibration measurements and the Finite element models.

Sign in / Sign up

Export Citation Format

Share Document