A numerical solution of cavity expansion problem in sand based directly on experimental stress-strain curves: Reply

2000 ◽  
Vol 37 (2) ◽  
pp. 494-496
Author(s):  
Branko Ladanyi ◽  
Adolfo Foriero
Keyword(s):  
Numerical Solution ◽  
Cavity Expansion ◽  
Experimental Stress ◽  
Stress Strain

A numerical solution of cavity expansion problem in sand based directly on experimental stress-strain curves

1998 ◽  
Vol 35 (4) ◽  
pp. 541-559 ◽  
Author(s):  
Branko Ladanyi ◽  
Adolfo Foriero
Keyword(s):  
Numerical Solution ◽  
Strain Path ◽  
Shear Resistance ◽  
Cavity Expansion ◽  
Large Strains ◽  
Volume Changes ◽  
Stress Strain ◽  
Stress Variation ◽  
Cylindrical Cavity Expansion ◽  
State Of Stress

A numerical solution of a spherical and cylindrical cavity expansion problem in sand is presented herein. The underlying theory is unbiased in that it is based directly on experimentally determined stress-strain curves. The solution makes it possible to follow the continuous variation of strains, stresses, and volume changes produced by cavity expansion. It essentially uses the "strain path" approach to determine the state of stress around the cavity, taking into account large strains and the effect of spherical stress variation on the mobilized shear resistance and the associated volume strains. A limited comparison with experimental data shows a reasonable agreement between theory and measurements.Key words: cavities, expansion, sand, stress-strain curves, numerical solution.

An optimized constitutive model for reproducing flow stress–strain relationships of anisotropic materials

2018 ◽  
Vol 233 (4) ◽  
pp. 1357-1368 ◽  
Author(s):  
Yanli Lin ◽  
Guannan Chu ◽  
Caiyuan Lin ◽  
Yongda Yan
Keyword(s):  
Flow Stress ◽  
Fourth Order ◽  
Anisotropic Materials ◽  
Second Order ◽  
Least Square ◽  
Experimental Stress ◽  
Function Model ◽  
Stress Strain ◽  
Order Function ◽  
Ordinary Least Square

Due to the strong anisotropic property of the advanced metal materials used in automobile, aviation, and aerospace, experimental flow stress–strain relations including different stress states are necessary to provide the information of anisotropic hardening and plastic flow for constructing a constitutive model. Therefore, reasonably reproducing the experimental stress–strain relations is the most fundamental work to substitute adequate flow stress–strain curves into the constitutive equation at the same time. However, accurate and stable regression results are difficult to obtain through the current regression models such as power exponent, second-order function model, fourth-order function model, and so forth. In this paper, an optimized model named as a least square quadratic regression model (ordinary least square model) was proposed based on the most useful second-order function model. The significant difference is that all experimental points are used to reproduce the experimental stress–strain relations in ordinary least square model in place of only three experimental points adopted in second-order function model, which results in good regression accuracy. Through comparison, it is found that the regression results by power function are poor with regard to some experimental results, and the results reproduced by second-order function model or fourth-order function model are very sensitive to the experimental points selected to do the regression. The sum of squares for error (SSE) increases sharply when the selected points are unreasonable. In addition, for second-order function and fourth-order function models, only limited experimental points are adopted to do the regression, the best regression accuracy cannot be obtained even if the selected points are reasonable. In contrast, SSE of the regression curve by ordinary least square model reduces to less than 50% of the best regressed result by second-order function model, the yielding behavior and variable strain increment ratio of the anisotropic materials can be reflected more accurately. This is very important for accurately describing the plastic flow behaviors of anisotropic materials.

The interaction of a fibre tangle with an airflow

1967 ◽  
Vol 27 (3) ◽  
pp. 561-580 ◽  
Author(s):  
Paul A. Taub
Keyword(s):  
Unsteady Flow ◽  
Numerical Solution ◽  
Analytical Model ◽  
Method Of Characteristics ◽  
Solution Procedure ◽  
Governing Equations ◽  
Stress Strain ◽  
One Dimensional ◽  
The Method Of Characteristics ◽  
Flow Configurations

An analytical model of the interaction of a fibre tangle with an airflow is proposed. This model replaces the discrete fibres by a continuum medium with a non-linear stress-strain law. The governing equations have been examined for one-dimensional unsteady flow configurations and have been found to possess five characteristic directions.A numerical-solution procedure, based upon the method of characteristics, has been outlined and applied to the flow within a dilation chamber. A fibre sample is located at the centre of the chamber, which is alternately pressurized and depressurized.

Influence of Strain Rate and Yarn Number on Tensile Test Results

1992 ◽  
Vol 62 (10) ◽  
pp. 586-589 ◽  
Author(s):  
L. Vangheluwe
Keyword(s):  
Tensile Test ◽  
Strain Rate ◽  
Tensile Modulus ◽  
Experimental Stress ◽  
Test Results ◽  
Stress Strain ◽  
Tensile Curve

The influence of strain rate and yarn number on tensile test results is investigated using a model to describe the tensile curve. A good correlation is obtained with the experimental stress-strain curves. The influence of the yarn number on the tensile modulus and the tensile curve is not quite the same for ring and rotor yarns.

HYBRID EXPERIMENTAL AND NUMERICAL CHARACTERIZATION OF THE 3D RESPONSE OF WOVEN POLYMER MATRIX COMPOSITES

2021 ◽  
Author(s):  
JAVIER BUENROSTRO ◽  
HYONNY KIM ◽  
ROBERT K. GOLDBERG ◽  
TRENTON M. RICKS
Keyword(s):  
Experimental Data ◽  
Polymer Matrix ◽  
Polymer Matrix Composites ◽  
Verification And Validation ◽  
Matrix Composites ◽  
Experimental Stress ◽  
Stress Strain ◽  
Material Models ◽  
Plain Weave ◽  
Model Input

The need for advanced material models to simulate the deformation, damage, and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. The purpose of this work is to characterize carbon epoxy fabrics for composite material models that rely on a large number of input parameters to define their nonlinear and 3D response; e.g. elastic continuum damage mechanics models or plasticity damage models [1, 2]. It is challenging to obtain large sets of experimental stress-strain curves, therefore, careful selection of physical experiments that exhibit nonlinear behavior is done to significantly reduce the cost of generating threedimensional material databases. For this work, plain weave carbon fabrics with 3k and 12k tows are manufactured by VARTM. Testing is done using MTS hydraulic test frames and 2D digital image correlation (DIC) to obtain experimental stress-strain curves for in-plane tension and shear as well as transverse shear. For cases where actual experimental data is either not available or difficult to obtain, the required model input is virtually generated using the NASA Glenn developed Micromechanics Analysis Method/Generalized Method of Cells (MAC/GMC) code. A viscoplastic polymer model is calibrated and utilized to model the matrix constituent within a repeating unit cell (RUC) of a plain weave carbon fiber fabric. Verification and validation of this approach is done using MAT213, a tabulated orthotropic material model in the finite element code LS-DYNA, which relies on 12 input stress-strain curves in various coordinate directions [2]. Based on the model input generated by the micromechanics analyses in combination with available experimental data, a series of coupon level verification and validation analyses are carried out using the MAT 213 composite model.

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