scholarly journals Nonlinear morphoelastic plates I: Genesis of residual stress

2011 ◽  
Vol 16 (8) ◽  
pp. 812-832 ◽  
Author(s):  
Joseph McMahon ◽  
Alain Goriely ◽  
Michael Tabor
Keyword(s):  
Residual Stress ◽  
Elastic Body ◽  
Response Function ◽  
Deformation Gradient ◽  
Global Constraint ◽  
Balance Equations ◽  
Multiplicative Decomposition ◽  
Rigorous Analysis ◽  
Volumetric Growth ◽  
Residual Strains

Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis is given of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate. Balance equations are derived via the Global Constraint Principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed, and the existence of residually stressed states is established.

scholarly journals Mathematical Modelling of Residual-Stress Based Volumetric Growth in Soft Matter

2021 ◽  
Author(s):  
Ruoyu Huang ◽  
Raymond W. Ogden ◽  
Raimondo Penta
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Mathematical Modelling ◽  
Soft Matter ◽  
Direct Evidence ◽  
Deformation Gradient ◽  
Opening Angle ◽  
Spherically Symmetric ◽  
Volumetric Growth ◽  
Incompressibility Constraint

AbstractGrowth in nature is associated with the development of residual stresses and is in general heterogeneous and anisotropic at all scales. Residual stress in an unloaded configuration of a growing material provides direct evidence of the mechanical regulation of heterogeneity and anisotropy of growth. The present study explores a model of stress-mediated growth based on the unloaded configuration that considers either the residual stress or the deformation gradient relative to the unloaded configuration as a growth variable. This makes it possible to analyze stress-mediated growth without the need to invoke the existence of a fictitious stress-free grown configuration. Furthermore, applications based on the proposed theoretical framework relate directly to practical experimental scenarios involving the “opening-angle” in arteries as a measure of residual stress. An initial illustration of the theory is then provided by considering the growth of a spherically symmetric thick-walled shell subjected to the incompressibility constraint.

Measurement of Residual Stresses in Linear Friction Welded In-Service Inconel 718 Superalloy

2016 ◽  
Vol 879 ◽  
pp. 1800-1806 ◽  
Author(s):  
M. Smith ◽  
L. Bichler ◽  
D. Sediako
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Base Material ◽  
Peak Stress ◽  
Weld Interface ◽  
Aerospace Alloys ◽  
Aero Engine ◽  
Linear Friction ◽  
Inconel 718 Superalloy ◽  
Residual Strains

Measurement of residual strains by neutron diffraction of linear friction welded Inconel® 718 (IN 718) superalloy acquired from a mid-service aero-engine disk was undertaken in this study. Residual strain and stress throughout the various weld regions including the heat affected zone (HAZ), thermomechanical affected zone (TMAZ) and dynamically recrystallized zone (DRX) were characterized. The residual stresses were observed to increase from the base material to the weld interface, with a peak stress at the weld interface in all orthogonal directions. The trends for residual stress across the weld are in agreement with other work published in literature for solid state welding of aerospace alloys, where high residual stresses were commonly reported at the weld interface.

scholarly journals The mathematical foundations of anelasticity: existence of smooth global intermediate configurations

2021 ◽  
Vol 477 (2245) ◽  
pp. 20200462
Author(s):  
Christian Goodbrake ◽  
Alain Goriely ◽  
Arash Yavari
Keyword(s):  
Euclidean Space ◽  
Deformation Gradient ◽  
Deformation Tensor ◽  
Dimensional Euclidean Space ◽  
Multiplicative Decomposition ◽  
Mathematical Basis ◽  
Isometric Embeddings ◽  
Higher Dimensional ◽  
Mathematical Foundations ◽  
Central Tool

A central tool of nonlinear anelasticity is the multiplicative decomposition of the deformation tensor that assumes that the deformation gradient can be decomposed as a product of an elastic and an anelastic tensor. It is usually justified by the existence of an intermediate configuration. Yet, this configuration cannot exist in Euclidean space, in general, and the mathematical basis for this assumption is on unsatisfactory ground. Here, we derive a sufficient condition for the existence of global intermediate configurations, starting from a multiplicative decomposition of the deformation gradient. We show that these global configurations are unique up to isometry. We examine the result of isometrically embedding these configurations in higher-dimensional Euclidean space, and construct multiplicative decompositions of the deformation gradient reflecting these embeddings. As an example, for a family of radially symmetric deformations, we construct isometric embeddings of the resulting intermediate configurations, and compute the residual stress fields explicitly.

Effect of membrane bending stiffness on the deformation of capsules in simple shear flow

2001 ◽  
Vol 440 ◽  
pp. 269-291 ◽  
Author(s):  
C. POZRIKIDIS
Keyword(s):  
Curvature Tensor ◽  
Deformation Gradient ◽  
Bending Stiffness ◽  
Boundary Element Methods ◽  
Simple Shear Flow ◽  
Normal Vector ◽  
Membrane Thickness ◽  
Bending Moments ◽  
Balance Equations ◽  
Capsule Deformation

The effect of interfacial bending stiffness on the deformation of liquid capsules enclosed by elastic membranes is discussed and investigated by numerical simulation. Flow-induced deformation causes the development of in-plane elastic tensions and bending moments accompanied by transverse shear tensions due to the non-infinitesimal membrane thickness or to a preferred configuration of an interfacial molecular network. To facilitate the implementation of the interfacial force and torque balance equations involving the hydrodynamic traction exerted on either side of the interface and the interfacial tensions and bending moments developing in the plane of the interface, a formulation in global Cartesian coordinates is developed. The balance equations involve the Cartesian curvature tensor defined in terms of the gradient of the normal vector extended off the plane of the interface in an appropriate fashion. The elastic tensions are related to the surface deformation gradient by constitutive equations derived by previous authors, and the bending moments for membranes whose unstressed shape has uniform curvature, including the sphere and a planar sheet, arise from a constitutive equation that involves the instantaneous Cartesian curvature tensor and the curvature of the resting configuration. A numerical procedure is developed for computing the capsule deformation in Stokes flow based on standard boundary-element methods. Results for spherical and biconcave resting shapes resembling red blood cells illustrate the effect of the bending modulus on the transient and asymptotic capsule deformation and on the membrane tank-treading motion.

Residual stresses in a SiC whisker-reinforced alumina composite by high-temperature X-ray diffraction

1994 ◽  
Vol 9 (1) ◽  
pp. 50-53 ◽  
Author(s):  
Benjamin L. Ballard ◽  
Paul K. Predecki ◽  
Camden R. Hubbard
Keyword(s):  
Residual Stress ◽  
Single Crystal Silicon ◽  
Linear Extrapolation ◽  
X Ray Diffraction ◽  
Crystal Silicon ◽  
X Ray ◽  
Fine Grained ◽  
Silicon Carbide Whiskers ◽  
Alumina Composite ◽  
Residual Strains

Residual strains and microstresses are evaluated for both phase of a hot-pressed, fine-grained α-alumina reinforced with 25 wt% (29 vol%) single-crystal silicon carbide whiskers at temperatures from 25 to 1000 °C. The sample was maintained in a nonoxidizing environment while measurements of the interplaner spacing of alumina (146) and SiC (511 + 333) were made using X-ray diffraction methods. The residual strains were profiled at temperature increments of 250 °C from which the corresponding microstresses were calculated. Linear extrapolation of the SiC ε33 profile indicates that the strains are completely relaxed at a temperature of approximately 1470 °C. These residual stress relaxation results suggest that elevated temperature toughness and fracture strength of this composite may result from cooperative mechanisms.

NUMERICAL INVESTIGATION OF THERMOMECHANICAL PROCESSES UNDER SHORT-PULSED LASER IRRADIATION OF A HALF-SPACE

2021 ◽  
Vol 6 ◽  
pp. 55-65
Author(s):  
Kamila Storchak ◽  
◽  
Nina Yakovenko ◽  
Olga Polonevych ◽  
Irina Sribna ◽  
...  
Keyword(s):  
Residual Stress ◽  
Laser Irradiation ◽  
Half Space ◽  
Strain State ◽  
Thermal Stresses ◽  
Equations Of Motion ◽  
Thermomechanical Loading ◽  
Stress Strain ◽  
Stress Strain State ◽  
Residual Strains

The laser irradiation of metallic surfaces by intense heat sources is used for the generation of short probing pulses, which propagate into thin specimens and enable one to estimate their structure and mechanical properties within the framework of the classical acoustic approach. High thermal stresses and residual strains occur during the short-term irradiation of the surface of a construction by an energy source of high density. In the present work, we solve the axially symmetric problem of a half-space under thermomechanical loading. We take into account the influence of volume and inelastic characteristics of separate phases on the residual stress-strain state of the half-space. The statement of the problem includes: Cauchy relations, equations of motion, heat conduction equation, initial conditions, thermal and mechanical boundary conditions. The thermomechanical behavior of an isotropic material is described by the Bodner-Partom unified model of flow. The problem is solved with using the finite element technique. The numerical realization of our problem is performed with the help of step-by-step time integration. The equations of motion are integrated by the Newmark method. The residual stress-strain state is described using the method of numerical solution of the axisymmetric dynamic problem for a half-space under thermomechanical loading and the flow model. We established that microstructural transformations, which are taken into account due to the thermophase volume strain and dependence of inelastic characteristics of the material on the phase composition, significantly reduce residual inelastic strain and promote the appearance of compressive stresses. The three-zone region of residual stresses field formation is obtained.

scholarly journals Three-dimensional residual strain in midanterior canine left ventricle

1997 ◽  
Vol 273 (4) ◽  
pp. H1968-H1976 ◽  
Author(s):  
Kevin D. Costa ◽  
Karen May-Newman ◽  
Dyan Farr ◽  
Walter G. O’Dell ◽  
Andrew D. McCulloch ◽  
...  
Keyword(s):  
Residual Stress ◽  
Left Ventricle ◽  
Residual Strain ◽  
Three Dimensional ◽  
Element Analysis ◽  
Primary Mechanism ◽  
Dimensional Measurements ◽  
Residual Strains ◽  
Shear Strains ◽  
Pressure State

All previous studies of residual strain in the ventricular wall have been based on one- or two-dimensional measurements. Transmural distributions of three-dimensional (3-D) residual strains were measured by biplane radiography of columns of lead beads implanted in the midanterior free wall of the canine left ventricle (LV). 3-D bead coordinates were reconstructed with the isolated arrested LV in the zero-pressure state and again after local residual stress had been relieved by excising a transmural block of tissue. Nonhomogeneous 3-D residual strains were computed by finite element analysis. Mean ± SD ( n = 8) circumferential residual strain indicated that the intact unloaded myocardium was prestretched at the epicardium (0.07 ± 0.06) and compressed in the subendocardium (−0.04 ± 0.05). Small but significant longitudinal shortening and torsional shear residual strains were also measured. Residual fiber strain was tensile at the epicardium (0.05 ± 0.06) and compressive in the subendocardium (−0.01 ± 0.04), with residual extension and shortening, respectively, along structural axes parallel and perpendicular to the laminar myocardial sheets. Relatively small residual shear strains with respect to the myofiber sheets suggest that prestretching in the plane of the myocardial laminae may be a primary mechanism of residual stress in the LV.

scholarly journals Nonlinear morphoelastic plates II: Exodus to buckled states

2011 ◽  
Vol 16 (8) ◽  
pp. 833-871 ◽  
Author(s):  
Joseph McMahon ◽  
Alain Goriely ◽  
Michael Tabor
Keyword(s):  
General Theory ◽  
Deformation Gradient ◽  
Companion Paper ◽  
Kirchhoff Plate ◽  
Geometric Description ◽  
Elastic Materials ◽  
Multiplicative Decomposition ◽  
Linear Elastic ◽  
Kirchhoff Plates ◽  
The Stability

Morphoelasticity is the theory of growing elastic materials. The theory is based on the multiplicative decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing non-linear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed.

Temperature Dependence of Residual Stresses and Stress Relaxation in Blanket Films of Various Thicknesses

1994 ◽  
Vol 356 ◽  
Author(s):  
A. P. Clarke ◽  
G. Langelaan ◽  
S. Saimoto
Keyword(s):  
Residual Stress ◽  
Stress Relaxation ◽  
Residual Stresses ◽  
Back Stress ◽  
Temperature Cycling ◽  
Misfit Dislocations ◽  
X Rays ◽  
Heating Rates ◽  
Residual Strains ◽  
Continuous Temperature

AbstractA rapid method to measure residual strains using x-rays during continuous temperature ramping has been developed whereby resolution of ±5xl0-5 can be attained with 2θ scans of about one minute using low index reflections. The method was used to make residual stress measurements during temperature cycling at heating rates of 2 to 15°C/min with interrupted stress relaxations at 235°C and 130°C on pure Al blanket films of 0.24μm, 0.58μm and 1.01 μm thicknesses. The results are consistent with the notion that surface sources are activated by the back stress of misfit dislocations.

Sign in / Sign up

Export Citation Format

Share Document