propSym: a tool to establish relationships between property constants for material property tensors of any order

2021 ◽  
Vol 54 (6) ◽  
Author(s):  
Anubhav Roy ◽  
Darren W. Branch ◽  
Daniel S. Jensen ◽  
Christopher M. Kube
Keyword(s):  
Material Properties ◽  
Point Group ◽  
Nonlinear Material ◽  
Material Modeling ◽  
Crystalline Materials ◽  
Independent Components ◽  
Index Form ◽  
Higher Rank ◽  
Index Notation ◽  
Higher Order Tensors

The properties of crystalline materials can be described mathematically by tensors whose components are generally known as property constants. Tabulations of these constants in terms of the independent components are well known for common material properties (e.g. elasticity, piezoelectricity etc.) aptly described by tensors of lower rank (e.g. ranks 2–4). General relationships between constants of higher rank are often unknown and sometimes reported incorrectly. A computer program is developed here to calculate the property constant relationships of a property of any order, represented by a tensor of any rank and point group. Tensors up to rank 12, e.g. the tensor of sixth-order elastic constants c 6 ijklmnpqrs , can be calculated on a standard computer, while ranks higher than 12 are best handled on a supercomputer. Output is provided in either full index form or a reduced index form, e.g. the Voigt index notation common to elasticity. As higher-order tensors are often associated with nonlinear material responses, the program provides an accessible means to investigate the important constants involved in nonlinear material modeling. The routine has been used to discover several incorrect relationships reported in the literature.

Design of an Isotropic Metamaterial With Constant Stiffness and Zero Poisson's Ratio Over Large Deformations

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
A. Delissen ◽  
G. Radaelli ◽  
L. A. Shaw ◽  
J. B. Hopkins ◽  
J. L. Herder
Keyword(s):  
Young’S Modulus ◽  
Material Properties ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Sufficient Conditions ◽  
Material Design ◽  
Poisson's Ratio ◽  
Nonlinear Material ◽  
Large Strains ◽  
Planar Lattice

A great deal of engineering effort is focused on changing mechanical material properties by creating microstructural architectures instead of modifying chemical composition. This results in meta-materials, which can exhibit properties not found in natural materials and can be tuned to the needs of the user. To change Poisson's ratio and Young's modulus, many current designs exploit mechanisms and hinges to obtain the desired behavior. However, this can lead to nonlinear material properties and anisotropy, especially for large strains. In this work, we propose a new material design that makes use of curved leaf springs in a planar lattice. First, analytical ideal springs are employed to establish sufficient conditions for linear elasticity, isotropy, and a zero Poisson's ratio. Additionally, Young's modulus is directly related to the spring stiffness. Second, a design method from the literature is employed to obtain a spring, closely matching the desired properties. Next, numerical simulations of larger lattices show that the expectations hold, and a feasible material design is presented with an in-plane Young's modulus error of only 2% and Poisson's ratio of 2.78×10−3. These properties are isotropic and linear up to compressive and tensile strains of 0.12. The manufacturability and validity of the numerical model is shown by a prototype.

Evaluation of the Temperature Effect on the Viscoelastic Responses of Flexible Risers

2019 ◽  
Author(s):  
Junpeng Liu ◽  
Jinsheng Ma ◽  
Murilo Augusto Vaz ◽  
Menglan Duan
Keyword(s):  
Material Properties ◽  
Global Analysis ◽  
Viscoelastic Behavior ◽  
Step Test ◽  
Nonlinear Material ◽  
Polymer Layer ◽  
Axial Stiffness ◽  
Loading Frequency ◽  
Flexible Risers ◽  
Improved Model

Abstract Mechanical behavior of flexible risers can be challenging due largely to its complex design generating strong nonlinear problems. Nonlinear material properties, as one of them, from polymer layers dominate the overall viscoelastic responses of flexible risers which may play an inevitable role on the global analysis in deepwater application. An alternative to predict the viscoelastic behavior comprising of the time domain and the frequency domain has been proposed recently by the authors (Liu and Vaz, 2016). Given the fact that polymeric material properties are temperature-dependent and that the temperature profiles in flexile risers vary continuously in both axial and radial direction, the temperature of the internal hydrocarbons must affect the viscoelastic responses. However, such phenomenon dose not draw much attention in previous studies. This paper presents an improved model for overcoming some drawbacks in the proposed model involving assumption of steady temperature distribution in polymer layer and no gap appearance between the adjacent layers. The computing method of model is developed by using a step by step test approach. Consequently, some important parameters like equivalent axial stiffness, contact pressure or gap between the near layers, and force-deformation relationship can be observed. Parametric studies are conducted on the axisymmetric viscoelastic behavior of flexible risers to study the role of input temperature and loading frequency. Results show that equivalent axial stiffness given by the improved model is smaller than before. It can also be found that the gap between metal layer and polymer layer appear easily and increases as time goes on.

Fracture Prediction for the Proximal Femur Using Finite Element Models: Part I—Linear Analysis

1991 ◽  
Vol 113 (4) ◽  
pp. 353-360 ◽  
Author(s):  
J. C. Lotz ◽  
E. J. Cheal ◽  
W. C. Hayes
Keyword(s):  
Finite Element ◽  
Fracture Risk ◽  
Strain Gage ◽  
Proximal Femur ◽  
Material Properties ◽  
The United States ◽  
Nonlinear Material ◽  
Finite Element Models ◽  
Model Predictions

Over 90 percent of the more than 250,000 hip fractures that occur annually in the United States are the result of falls from standing height. Despite this, the stresses associated with femoral fracture from a fall have not been investigated previously. Our objectives were to use three-dimensional finite element models of the proximal femur (with geometries and material properties based directly on quantitative computed tomography) to compare predicted stress distributions for one-legged stance and for a fall to the lateral greater trochanter. We also wished to test the correspondence between model predictions and in vitro strain gage data and failure loads for cadaveric femora subjected to these loading conditions. An additional goal was to use the model predictions to compare the sensitivity of several imaging sites in the proximal femur which are used for the in vivo prediction of hip fracture risk. In this first of two parts, linear finite element models of two unpaired human cadaveric femora were generated. In Part II, the models were extended to include nonlinear material properties for the cortical and trabecular bone. While there was poor correspondence between strain gage data and model predictions, there was excellent agreement between the in vitro failure data and the linear model, especially using a von Mises effective strain failure criterion. Both the onset of structural yielding (within 22 and 4 percent) and the load at fracture (within 8 and 5 percent) were predicted accurately for the two femora tested. For the simulation of one-legged stance, the peak stresses occurred in the primary compressive trabeculae of the subcapital region. However, for a simulated fall, the peak stresses were in the intertrochanteric region. The Ward’s triangle (basicervical) site commonly used for the clinical assessment of osteoporosis was not heavily loaded in either situation. These findings suggest that the intertrochanteric region may be the most sensitive site for the assessment of fracture risk due to a fall and the subcapital region for fracture risk due to repetitive activities such as walking.

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