Shape memory materials as an object of solid state mechanics: Experimental study, constitutive relations, solution of boundary value problems

2012 ◽  
Vol 15 (3-4) ◽  
pp. 214-223 ◽  
Author(s):  
Andrey A. Movchan ◽  
S. A. Kazarina
Keyword(s):  
Experimental Study ◽  
Solid State ◽  
Shape Memory ◽  
Boundary Value Problems ◽  
Constitutive Relations ◽  
Boundary Value ◽  
Shape Memory Materials

scholarly journals Some Applications of Eigenvalue Problems for Tensor and Tensor–Block Matrices for Mathematical Modeling of Micropolar Thin Bodies

2019 ◽  
Vol 24 (1) ◽  
pp. 33 ◽  
Author(s):  
Mikhail Nikabadze ◽  
Armine Ulukhanyan
Keyword(s):  
Boundary Value Problems ◽  
Anisotropic Medium ◽  
Eigenvalue Problems ◽  
Constitutive Relations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Theory Of Elasticity ◽  
Initial Boundary Value Problems ◽  
Special Cases ◽  
Initial Boundary Value

The statement of the eigenvalue problem for a tensor–block matrix (TBM) of any orderand of any even rank is formulated, and also some of its special cases are considered. In particular,using the canonical presentation of the TBM of the tensor of elastic modules of the micropolartheory, in the canonical form the specific deformation energy and the constitutive relations arewritten. With the help of the introduced TBM operator, the equations of motion of a micropolararbitrarily anisotropic medium are written, and also the boundary conditions are written down bymeans of the introduced TBM operator of the stress and the couple stress vectors. The formulationsof initial-boundary value problems in these terms for an arbitrary anisotropic medium are given.The questions on the decomposition of initial-boundary value problems of elasticity and thin bodytheory for some anisotropic media are considered. In particular, the initial-boundary problems of themicropolar (classical) theory of elasticity are presented with the help of the introduced TBM operators(tensors–operators). In the case of an isotropic micropolar elastic medium (isotropic and transverselyisotropic classical media), the TBM operator (tensors–operators) of cofactors to TBM operators(tensors–tensors) of the initial-boundary value problems are constructed that allow decomposinginitial-boundary value problems. We also find the determinant and the tensor of cofactors to the sumof six tensors used for decomposition of initial-boundary value problems. From three-dimensionaldecomposed initial-boundary value problems, the corresponding decomposed initial-boundary valueproblems for the theories of thin bodies are obtained.

Experimental Study on the Magnetic Characteristics of Magnetic Shape Memory Alloy Materials

2013 ◽  
Vol 446-447 ◽  
pp. 230-234
Author(s):  
Tao Li ◽  
She Liang Wang ◽  
Tao Yang ◽  
Guang Yuan Weng
Keyword(s):  
Magnetic Field ◽  
Experimental Study ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Constitutive Relations ◽  
Memory Function ◽  
Magnetic Characteristics ◽  
Magnetic Shape Memory ◽  
Magnetic Shape Memory Alloy ◽  
Magnetic Induction Intensity

With shape memory function of new smart material, the magnetic control properties of magnetic shape memory alloy could be used to fabricate intelligent actuators for vibration control of structures. In order to study its magnetic properties, this text selected Ni53Mn25Ga22 as the material for the research and development of actuator drive, And two MSMA test specimens were prepared for the experimental study under the coupled action of the temperature, preload pressure and magnetic field. The results showed that the strain of MSMA induced by magnetic field decreased with the increase of the preload pressure at constant magnetic field. The deformation performance was best when the magnetic induction intensity was about 0.5T. And the constitutive relations were fitted for the actuator production to lay the foundation for later.

Inhomogeneous Deformation Examples and Applications of Light Activated Shape Memory Polymers

2012 ◽  
Author(s):  
Jaskirat S. Sodhi ◽  
Swapnil Moon ◽  
I. Joga Rao
Keyword(s):  
Constitutive Model ◽  
Shape Memory ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Aerospace Industry ◽  
Shape Memory Polymers ◽  
Inhomogeneous Deformation ◽  
The Past ◽  
Innovative Materials ◽  
Biomedical Industry

Light Activated Shape Memory Polymers (LASMP) are recently developed innovative materials defined by their capacity to store a deformed (temporary) shape and recover an original (parent) shape. This change in shape and the return to original shape is achieved by exposing the polymer to light at different wavelengths. These unique properties have led to the use of LASMP’s in a wide variety of applications. These SMP’s have a great potential in the biomedical industry as well as the aerospace industry. In the past, the authors have introduced a constitutive model to model the mechanics of these LASMP [1] and used it to solve a few cases of boundary value problems of interest. In this paper, the developed model is used to solve some other inhomogeneous deformation boundary value problems.

Verification of Plasticity Theory with Isotropic Hardening and Additive Decomposition of Left Deformation Tensor Using Digital Image Correlation System

2015 ◽  
Vol 240 ◽  
pp. 61-66 ◽  
Author(s):  
Marcin Gajewski ◽  
Cezary Ajdukiewicz ◽  
Andrzej Piotrowski
Keyword(s):  
Digital Image Correlation ◽  
Boundary Value Problems ◽  
Digital Image ◽  
Constitutive Relations ◽  
Boundary Value ◽  
Experimental Tests ◽  
Image Correlation ◽  
Deformation Tensor ◽  
Isotropic Hardening ◽  
Complex Boundary

The development of measurement methods, and in particular digital image correlation (DIC) systems, which are designed to measure of entire displacements and deformations fields, opens up new areas of research. In general, the materials constitutive relations are formulated in such a way that material parameters could be determined with relatively simple experimental tests carried out on samples with uniform (approximately) stress and strain fields. Then it is possible to apply them to complex boundary value problems formulated e.g. in the small or large deformation theories. The application of DIC allows to verify the accuracy of their predictions by comparing the results of the experiment with solutions to boundary value problems obtained using the finite element method (FEM).

scholarly journals Implicit constitutive relations for nonlinear magnetoelastic bodies

2015 ◽  
Vol 471 (2175) ◽  
pp. 20140959 ◽  
Author(s):  
R. Bustamante ◽  
K. R. Rajagopal
Keyword(s):  
Boundary Value Problems ◽  
Large Deformations ◽  
Constitutive Relations ◽  
Boundary Value ◽  
Small Displacement ◽  
Elastic Bodies ◽  
Classical Models ◽  
Linearized Model ◽  
Implicit Constitutive Relations

Implicit constitutive relations that characterize the response of elastic bodies have greatly enhanced the arsenal available at the disposal of the analyst working in the field of elasticity. This class of models were recently extended to describe electroelastic bodies by the present authors. In this paper, we extend the development of implicit constitutive relations to describe the behaviour of elastic bodies that respond to magnetic stimuli. The models that are developed provide a rational way to describe phenomena that have hitherto not been adequately described by the classical models that are in place. After developing implicit constitutive relations for magnetoelastic bodies undergoing large deformations, we consider the linearization of the models within the context of small displacement gradients. We then use the linearized model to describe experimentally observed phenomena which the classical linearized magnetoelastic models are incapable of doing. We also solve several boundary value problems within the context of the models that are developed: extension and shear of a slab, and radial inflation and extension of a cylinder.

On Obtaining Solutions in Nonlinear Viscoelasticity

1968 ◽  
Vol 35 (1) ◽  
pp. 129-133 ◽  
Author(s):  
R. M. Christensen
Keyword(s):  
Boundary Value Problems ◽  
Constitutive Relation ◽  
Nonlinear Viscoelasticity ◽  
Constitutive Relations ◽  
Boundary Value ◽  
Static Solution ◽  
Fading Memory ◽  
Viscoelastic Cylinder ◽  
Nonlinear Stress

A derivation is given of a particular form of the isothermal nonlinear stress constitutive relation for materials with fading memory. This particular derivation results in a form for the constitutive relations that is well suited for application in solving boundary-value problems. The resulting forms are applied to obtain the exact quasi-static solution for the torsion of a right circular isotropic viscoelastic cylinder. Several effects due to the nonlinearity of the problem are discussed.

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