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residual stress

arash_yavari's picture

Accretion-Ablation Mechanics

In this paper we formulate a geometric nonlinear theory of the mechanics of accreting-ablating bodies. This is a generalization of the theory of accretion mechanics of Sozio and Yavari (2019). More specifically, we are interested in large deformation analysis of bodies that undergo a continuous and simultaneous accretion and ablation on their boundaries while under external loads.

arash_yavari's picture

Finite Extension of Accreting Nonlinear Elastic Solid Circular Cylinders

In this paper we formulate and solve the initial-boundary value problem of accreting circular cylindrical bars under finite extension. We assume that the bar grows by printing stress-free cylindrical layers on its boundary cylinder while it is undergoing a time-dependent finite extension. Accretion induces eigenstrains, and consequently residual stresses. We formulate the anelasticity problem by first constructing the natural Riemannian metric of the growing bar. This metric explicitly depends on the history of deformation during the accretion process.

arash_yavari's picture

Accretion Mechanics of Nonlinear Elastic Circular Cylindrical Bars Under Finite Torsion

In this paper we formulate the initial-boundary value problem of accreting circular cylindrical bars under finite torsion. It is assumed that the bar grows as a result of printing stress-free cylindrical layers on its boundary while it is under a time-dependent torque (or a time-dependent twist) and is free to deform axially. In a deforming body, accretion induces eigenetrains, and consequently residual stresses. We formulate the anelasticity problem by first constructing the natural Riemannian metric of the growing bar.

Mike Prime's picture

Residual short course at SEM conference

We will be teaching a short course on residual stress on June 12, 2022 at the SEM Experimental Mechanics conference in Pittsburgh. 

See below and (under PROGRAMS/COURSES) for details.

Residual stress short courses don't happen too often. The course should be appropriate for students, industrialists, and researchers. Hope you can make it. The proceeds all benefit SEM.


Residual Stress 101

arash_yavari's picture

Nonlinear Mechanics of Thermoelastic Accretion

In this paper, we formulate a theory for the coupling of accretion mechanics and thermoelasticity. We present an analytical formulation of the thermoelastic accretion of an infinite cylinder and of a two-dimensional block.

Mike Prime's picture

Residual Stress 101: One day course at SEM conference

The day before the SEM Conference this June in Reno, Nevada, USA, we will be teaching a short course entitled Residual Stress 101: See below for a description of the course. We will cover lots of practical material on residual stresses, much of which is not covered in standard engineering curricula. This is great material for any interested researcher who never got a comprehensive background in residual stress. It will also be great for graduate students or advanced undergrads, and students pay half price.

peppezurlo's picture

Nonlinear elasticity of incompatible surface growth

In this manuscript with Lev Truskinovsky, we developed a new nonlinear theory of large-strain incompatible surface growth. Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems, surface growth is usually accompanied by the development of geometrical incompatibility leading to residual stresses and triggering various instabilities. Here we developed a nonlinear theory of incompatible surface growth which quantitatively linkes deposition protocols with post-growth states of stress.

arash_yavari's picture

The Anelastic Ericksen's Problem: Universal Eigenstrains and Deformations in Compressible Isotropic Elastic Solids

The elastic Ericksen's problem consists of finding deformations in isotropic hyperelastic solids that can be maintained for arbitrary strain-energy density functions.  In the compressible case, Ericksen showed that only homogeneous deformations are possible. Here, we solve the anelastic version of the same problem, that is we determine both the deformations and the eigenstrains such that a solution to the anelastic problem exists for arbitrary strain-energy density functions. Anelasticity is described by finite eigenstrains.

arash_yavari's picture

Small-on-Large Geometric Anelasticity

In this paper we are concerned with finding exact solutions for the stress fields of nonlinear solids with non-symmetric distributions of defects (or more generally finite eigenstrains) that are small perturbations of symmetric distributions of defects with known exact solutions. In the language of geometric mechanics this corresponds to finding a deformation that is a result of a perturbation of the metric of the Riemannian material manifold. We present a general framework that can be used for a systematic analysis of this class of anelasticity problems.

Is it possible to solve buckling in Abaqus with only residual stress defined as predefined load?

Hi Sirs,

As title, I wondering if the problem can be solved with only material residual stress but no other external load applied?

After several trials, Abaqus returns message

Through thickness residual stress

I am modeling through thickness residual stresses as follows:
*Initial Conditions, Type=Stress, Section Points
all_elements, 1, 50,25, 0
all_elements, 2, 50,25, 0
all_elements, 3, 50,25, 0
all_elements, 4, 50,25, 0
ABAQUS documentation 6.14:


First line:

Element number or element set label.
Section point number.
Value of first stress component.
Value of second stress component.
Etc., up to three stress components.
I got this warning:

arash_yavari's picture

A Geometric Theory of Nonlinear Morphoelastic Shells

We formulate a geometric theory of nonlinear morphoelastic shells that can model the time evolution of residual stresses induced by bulk growth. We consider a thin body and idealize it by a representative orientable surface. In this geometric theory, bulk growth is modeled using an evolving referential configuration for the shell (material manifold). We consider the evolution of both the first and second fundamental forms in the material manifold by considering them as dynamical variables in the variational problem.

zichen's picture

Residual Stresses and Poisson’s Effect Drive Shape Formation and Transition of Helical Structures

Strained multilayer structures are extensively investigated because of their applications in microelectromechanical/nano-elecromechanical systems. Here we employ a finite element method (FEM) to study the bending and twisting of multilayer structures subjected to misfit strains or residual stresses. This method is first validated by comparing the simulation results with analytic predictions for the bending radius of a bilayer strip with given misfit strains.

arash_yavari's picture

The Geometry of Discombinations and its Applications to Semi-Inverse Problems in Anelasticity

The geometric formulation of continuum mechanics provides a powerful approach to understand and solve problems in anelasticity where an elastic deformation is combined with a non-elastic component arising from defects, thermal stresses, growth effects, or other effects leading to residual stresses. The central idea is to assume that the material manifold, prescribing the reference configuration for a body, has an intrinsic, non-Euclidean, geometric structure. Residual stresses then naturally arise when this configuration is mapped into Euclidean space.

Mike Prime's picture

Forensics: residual stress of fractured part

I’ll present this below without the answer, in case you want to enjoy a little brain teaser. It is a solid and experimental mechanics problem that, while not terribly practical, I found very interesting:

A part fractures cleanly in two by brittle fracture (no plasticity) under the action of residual and applied stresses. You only have the broken part in front of you, no prior information.

 What were the original residual stresses on the fracture plane?

Residual stresses in elastic medium upon uniform cooling

Hi All,

I am a student working on a project involving the effect of residual stresses in elastic and viscoealstic materials. I have a related question: When an easltic body is heated to a certain temperature (say 400 deg C) and then cooled uniformly to room temperature (20 deg C) with a constant cooling rate "q", does this generate any "un-desirable" (residual) stresses within the elastic body? i.e at a steady state - room temperature, does the final stress state within the body would be non-zero? Else, it would eventually reach a state of zero stresses? How?  

[Abaqus]Residual Stress, Equlibrium step, Boundary conditions


Problem description: There is a simply supported(roller supports) shell element I-beam. There are lateral bracings too. All of this boundary conditions belongs to the Riks step(always last step in analysis).

Question: I have implemented triangular residual stresses by SIGINI subroutine, but I'm not sure what boundary conditions set up in preliminary equlibrium step. Should I include all of the lateral bracings in this step or maybe only roller support? 


Thank You 


residual stress and strain definitions (through-thickness) in ABAQUS/Explicit

Choose a channel featured in the header of iMechanica: 

Hello everyone,


I need some help regarding the definition of initial residual stresses and plastic strains in a shell finite element (S4R) model in ABAQUS/Explicit.

I have determined the residual stress distributions and initial plastic strains and I need to assign these distributions to a given element set.

I understand I should be looking at:


 ELSET_A, S11, S22, S33

Fatigue Crack Growth Under Spectrum(Random) loading

Dear all Researchers, 

 I am writing regarding for the first time about the UAA(Unified analytical aspect) on Fatigue crack growth. The idea of this technique is this question : too many fatigue life prediction relations but still those are not perfect. on the other hand, new math ways still have not been the classical fracture mechanics. I am looking for some comments as response to this concern. Clearly, how we upgrade fracture mechanics theory using atomistic development in modeling fatigue propagation?

 Let us talk about this.




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