iMechanica - Commercial Software
https://imechanica.org/taxonomy/term/7466
enObjective Stress Rates in Finite Strain of Inelastic Solid and Their Energy Consistency
https://imechanica.org/node/12432
<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/248">finite element analysis</a></div><div class="field-item odd"><a href="/taxonomy/term/472">large deformation</a></div><div class="field-item even"><a href="/taxonomy/term/7465">Variational Methods</a></div><div class="field-item odd"><a href="/taxonomy/term/7466">Commercial Software</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>In many practical problems of solid mechanics, it is sufficient to characterize material deformation by the small (or linearized) strain tensor. But there are also many problems where the finiteness of strain must be taken into account. These are of two kinds: 1) Large nonlinear elastic deformations possessing a potential energy (exhibited, e.g., by rubber), in which the stress components are obtained as the partial derivatives of potential energy; and 2) inelastic deformations possessing no potential, in which the stress-strain relation is defined incrementally and the stress increment or rate must be formulated objectively (i.e., independently of coordinate rotations). The present paper reviews the latter kind. The presentations is focused on energy consistency (or work-conjugacy of the stress rate and the finite strain increment), which requires a variational energy approach instead of the narrow classical viewpoint of tensorial coordinate transformations The objective stress rates corresponding to various choices of the finite strain measure are presented and it is shown that the energy consistency is violated by the rate used in most commercial structural analysis software (using finite element analysis). While in many applications this causes only a negligible error, it is pointed out that the error in forces or displacements can reach 30% to 100% in some practical situations. These include highly compressible materials (e.g., rigid forms, honeycomb, compressible soils, soft wood, osteoporotic bone, various biologic tissues) and highly orthotropic materials very soft in shear (e.g., some fiber composites, sandwich plates, solids weakened by unidirectional cracking, layered elastomeric bearings).</p>
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<tr class="odd"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://imechanica.org/files/12-05-22-FinStrain-ObjStrRate.pdf" type="application/pdf; length=1347860" title="12-05-22-FinStrain-ObjStrRate.pdf">12-05-22-FinStrain-ObjStrRate.pdf</a></span></td><td>1.29 MB</td> </tr>
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</div></div></div>Sat, 12 May 2012 01:38:15 +0000bazant12432 at https://imechanica.orghttps://imechanica.org/node/12432#commentshttps://imechanica.org/crss/node/12432