iMechanica - small strain
https://imechanica.org/taxonomy/term/2538
enA numerical study of elastic bodies that are described by constitutive equations that exhibit limited strains
https://imechanica.org/node/15699
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/2538">small strain</a></div><div class="field-item odd"><a href="/taxonomy/term/9330">Implicit elasticity</a></div><div class="field-item even"><a href="/taxonomy/term/9331">Nonlinear finite elements</a></div><div class="field-item odd"><a href="/taxonomy/term/9332">Unbounded stress</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Recently, a very general and novel class of implicit bodies has been developed to describe the elastic response of solids. It contains as a special subclass the classical Cauchy and Green elastic bodies. Within the class of such bodies, one can obtain through a rigorous approximation, constitutive relations for the linearized strain as a nonlinear function of the stress. Such an approximation is not possible within classical theories of Cauchy and Green elasticity, where the process of linearization will only lead to the classical linearized elastic body.
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In this paper, we study numerically the states of stress and strain in a finite rectangular plate with an elliptic hole and a stepped flat tension bar with shoulder fillets, within the context of the new class of models for elastic bodies that guarantees that the linearized strain would stay bounded and limited below a value that can be fixed a priori, thereby guaranteeing the validity of the use of the model. This is in contrast to the classical linearized elastic model, wherein the strains can become large enough in the body leading to an obvious inconsistency.
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<a href="http://camlab.cl/alejandro/publications/a-numerical-study-of-elastic-bodies-that-are-described-by-constitutive-equations-that-exhibit-limited-strains/">Link to the paper</a>
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</div></div></div>Mon, 25 Nov 2013 19:36:39 +0000Alejandro Ortiz-Bernardin15699 at https://imechanica.orghttps://imechanica.org/node/15699#commentshttps://imechanica.org/crss/node/15699fracture mechanics
https://imechanica.org/node/12812
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/77">opinion</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/2538">small strain</a></div><div class="field-item odd"><a href="/taxonomy/term/4258">large strain</a></div><div class="field-item even"><a href="/taxonomy/term/7731">small scale yielding</a></div><div class="field-item odd"><a href="/taxonomy/term/7732">large scale yielding</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
i want some one to clarify fundamental definition ,inter relationship or difference between the following terminologies .
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small strain
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large strain
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small scale yielding
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large scale yielding
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</div></div></div>Fri, 20 Jul 2012 13:06:59 +0000s.r.ranganatha12812 at https://imechanica.orghttps://imechanica.org/node/12812#commentshttps://imechanica.org/crss/node/12812Inverse eigenstrain analysis based on residual strains in the case of small strain geometric nonlinearity
https://imechanica.org/node/9509
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/2538">small strain</a></div><div class="field-item odd"><a href="/taxonomy/term/2640">eigenstrain</a></div><div class="field-item even"><a href="/taxonomy/term/4435">inverse problem</a></div><div class="field-item odd"><a href="/taxonomy/term/5335">Geometric nonlinearity</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Hi,
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I was wondering if someone knows literature related to "<strong>Inverse eigenstrain analysis</strong> based on residual strains in the case of <strong>small strain geometric nonlinearity</strong>"? (elongated bodies)
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In the case of lineralized elasticity I guess one could postulate an eigenstrain distribution as the sum of a finite set of basic eigenstrain distribution and minimize the difference between the predicted and the actual residual strain distribution (retrieved from a synchroton mapping for example).
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As done in the paper:
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<p><em>Alexander M. Korsunsky, Gabriel M. Regino, David Nowell, Variational eigenstrain analysis of residual stresses in a welded plate, International Journal of Solids and Structures, Volume 44, Issue 13, 15 June 2007, Pages 4574-4591, ISSN 0020-7683, DOI: 10.1016/j.ijsolstr.2006.11.037.</em></p>
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But, I'm afraid this procedure (as well as FFT) is not suited in case of nonlinear geometric effects as one can not add solutions. I'm not even sure if the problem is not ill-posed, as the solution might not be unique. In the context of an isotropic elastic media, can we define an energetically optimized eigenstrain distribution that would result in a residual strain distribution mapping a given objective?
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I'd be pleased to read your comments
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</div></div></div>Mon, 20 Dec 2010 16:49:33 +0000Sébastien Turcaud9509 at https://imechanica.orghttps://imechanica.org/node/9509#commentshttps://imechanica.org/crss/node/9509Elastic deformation of substrate due to rotation of rigid pillar
https://imechanica.org/node/3416
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/347">elasticity</a></div><div class="field-item odd"><a href="/taxonomy/term/2538">small strain</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Consider a ridig pillar ontop of a elastic substrate. Applying a moment to the pillar will lead to elastic deformation of the substrate. If the pillar is infinitly large in diameter, then this problem is the same as an infinitely sharp crack, considering the symmetry of the crack problem, i.e. there are square root singularities. However, the infinitly large diameter assumtion does not hold if the global rotation of the substrate under the pillar is of interest, because the both sides of the pillar interact.
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To identify a coordinate system: If the moment is applied along the y-axis and the z-axis is the axial direction of the pillar, then the maxium stresses in the pillar will be along the x-axis.
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In the x-direction: the stresses still form a singularity as found numerically: not square root but lower order (and arguments can be made justifying that).
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However, in the y-direction: the problem is less trivial: Two contradicting arguments can be made 1) Since the surface has to be flat also in the y-direction with a wedge like end: a singularity should be present. 2) Since it is not in the direction of the maximal deformation, the stresses have to be bound, i.e. they are not singular.
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Any thoughts?
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</div></div></div>Thu, 26 Jun 2008 18:37:27 +0000Steffen Brinckmann3416 at https://imechanica.orghttps://imechanica.org/node/3416#commentshttps://imechanica.org/crss/node/3416