A stabilised displacement–volumetric strain formulation for nearly incompressible and anisotropic materials

2021 ◽  
Vol 377 ◽  
pp. 113701
Author(s):  
R. Rossi ◽  
R. Zorrilla ◽  
R. Codina
Keyword(s):  
Volumetric Strain ◽  
Anisotropic Materials ◽  
Strain Formulation

Three-Dimensional Ultrasonic Crack Detection in Anisotropic Materials

1997 ◽  
Vol 9 (2) ◽  
pp. 59-79 ◽  
Author(s):  
J. Mattsson ◽  
A. J. Niklasson ◽  
A. Eriksson
Keyword(s):  
Crack Detection ◽  
Three Dimensional ◽  
Anisotropic Materials

Ductile Fracture of a Marine Structural Steel based on HC-DSSE Combined Fracture Strain Formulation

2019 ◽  
Vol 56 (1) ◽  
pp. 82-93
Author(s):  
Sung-Ju Park ◽  
Kangsu Lee ◽  
Burak Can Cerik ◽  
Younghyn Kim ◽  
Joonmo Choung
Keyword(s):  
Ductile Fracture ◽  
Structural Steel ◽  
Fracture Strain ◽  
Strain Formulation

Anisotropic Elasticity

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Composite Materials ◽  
Elastic Constants ◽  
Piezoelectric Materials ◽  
Anisotropic Materials ◽  
Anisotropic Elasticity ◽  
Stress Singularities ◽  
Comprehensive Survey ◽  
The Subject ◽  
Key Topics ◽  
First Time

Anisotropic Elasticity offers for the first time a comprehensive survey of the analysis of anisotropic materials that can have up to twenty-one elastic constants. Focusing on the mathematically elegant and technically powerful Stroh formalism as a means to understanding the subject, the author tackles a broad range of key topics, including antiplane deformations, Green's functions, stress singularities in composite materials, elliptic inclusions, cracks, thermo-elasticity, and piezoelectric materials, among many others. Well written, theoretically rigorous, and practically oriented, the book will be welcomed by students and researchers alike.

Physical Ultrasonics of Composites

2011 ◽  
Author(s):  
Dale Chimenti ◽  
Stanislav Rokhlin ◽  
Peter Nagy
Keyword(s):  
Composite Laminates ◽  
Stiffness Matrix ◽  
Composite Plates ◽  
Anisotropic Media ◽  
Anisotropic Materials ◽  
Ultrasonic Waves ◽  
Laminated Plates ◽  
Structure Characteristic ◽  
Major Advance

Physical Ultrasonics of Composites is a rigorous introduction to the characterization of composite materials by means of ultrasonic waves. Composites are treated here not simply as uniform media, but as inhomogeneous layered anisotropic media with internal structure characteristic of composite laminates. The objective here is to concentrate on exposing the singular behavior of ultrasonic waves as they interact with layered, anisotropic materials, materials which incorporate those structural elements typical of composite laminates. This book provides a synergistic description of both modeling and experimental methods in addressing wave propagation phenomena and composite property measurements. After a brief review of basic composite mechanics, a thorough treatment of ultrasonics in anisotropic media is presented, along with composite characterization methods. The interaction of ultrasonic waves at interfaces of anisotropic materials is discussed, as are guided waves in composite plates and rods. Waves in layered media are developed from the standpoint of the "Stiffness Matrix", a major advance over the conventional, potentially unstable Transfer Matrix approach. Laminated plates are treated both with the stiffness matrix and using Floquet analysis. The important influence on the received electronic signals in ultrasonic materials characterization from transducer geometry and placement are carefully exposed in a dedicated chapter. Ultrasonic wave interactions are especially susceptible to such influences because ultrasonic transducers are seldom more than a dozen or so wavelengths in diameter. The book ends with a chapter devoted to the emerging field of air-coupled ultrasonics. This new technology has come of age with the development of purpose-built transducers and electronics and is finding ever wider applications, particularly in the characterization of composite laminates.

scholarly journals Study of Influence of Width to Thickness Ratio in Sheet Metals on Bendability under Ambient and Superimposed Hydrostatic Pressure

2021 ◽  
Vol 2 (3) ◽  
pp. 542-558
Author(s):  
Mohammadmehdi Shahzamanian ◽  
David Lloyd ◽  
Amir Partovi ◽  
Peidong Wu
Keyword(s):  
Hydrostatic Pressure ◽  
Stress Ratio ◽  
Fracture Strain ◽  
Stress Triaxiality ◽  
Volumetric Strain ◽  
Thickness Ratio ◽  
Sheet Metals ◽  
The Finite Element Method ◽  
Bending Strain ◽  
Good Agreement

The effect of the width to thickness ratio on the bendability of sheet metal is investigated using the finite element method (FEM) employing the Gurson–Tvergaard–Needleman (GTN) model. Strain path changes in the sheet with change in the width/thickness ratio. It is shown that bendability and fracture strain increase significantly by decrease in the width/thickness ratio. The stress state is almost uniaxial when the stress ratio (α) is close to zero for narrow sheets. Stress ratio is nothing but the major stress to minor stress ratio. This delays the growth and coalescence of micro-voids as the volumetric strain and stress triaxiality (pressure/effective stress) decrease. On the other hand, ductility decreases with increase in α for wider sheets. Fracture bending strain is calculated and, as expected, it increases with decrease in the width/thickness ratio. Furthermore, a brief study is performed to understand the effect of superimposed hydrostatic pressure on fracture strain for various sheet metals with different width/thickness ratios. It is found that the superimposed hydrostatic pressure increases the ductility, and that the effect of the width/thickness ratio in metals on ductility is as significant as the effect of superimposed hydrostatic pressure. Numerical results are found to be in good agreement with experimental observations.

scholarly journals A higher-order parametric nonlinear reduced-order model for imperfect structures using Neumann expansion

2021 ◽  
Author(s):  
J. Marconi ◽  
P. Tiso ◽  
D. E. Quadrelli ◽  
F. Braghin
Keyword(s):  
Reduced Order Model ◽  
Galerkin Projection ◽  
Order Model ◽  
Displacement Fields ◽  
Reduced Order ◽  
Total Displacement ◽  
Elastic Forces ◽  
Strain Formulation ◽  
The One ◽  
Definition Of

AbstractWe present an enhanced version of the parametric nonlinear reduced-order model for shape imperfections in structural dynamics we studied in a previous work. In this model, the total displacement is split between the one due to the presence of a shape defect and the one due to the motion of the structure. This allows to expand the two fields independently using different bases. The defected geometry is described by some user-defined displacement fields which can be embedded in the strain formulation. This way, a polynomial function of both the defect field and actual displacement field provides the nonlinear internal elastic forces. The latter can be thus expressed using tensors, and owning the reduction in size of the model given by a Galerkin projection, high simulation speedups can be achieved. We show that the adopted deformation framework, exploiting Neumann expansion in the definition of the strains, leads to better accuracy as compared to the previous work. Two numerical examples of a clamped beam and a MEMS gyroscope finally demonstrate the benefits of the method in terms of speed and increased accuracy.

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