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De Souza Neto, E. A.; Perić, D.; Owen, D. R. J. (1994). "A phenomenological three-dimensional rate-independent continuum damage model for highly filled polymers : Formulation and computational aspects".
374:
545:{\displaystyle {\boldsymbol {S}}=\eta (W,W_{max}){\boldsymbol {S}}_{0},\quad {\text{where }}\eta {\begin{cases}=1,\quad &W=W_{max},\\<1,&W<W_{max}\end{cases}}\quad .}
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The key idea of pseudo-elastic material models is that the stress during the first loading process is equal to the basic stress
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It was shown that this idea can also be used to extend arbitrary inelastic material models for softening effects.
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and D. G. Roxburgh. The fundamental idea of the approach can already be found in a paper by De Souza Neto
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Ogden, R. W; Roxburgh, D. G. (1999). "A pseudo–elastic model for the
Mullins effect in filled rubber".
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675:"On the thermodynamics of pseudo-elastic material models which reproduce the Mullins effect"
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159:{\displaystyle {\boldsymbol {S}}=2{\frac {\partial W}{\partial {\boldsymbol {C}}}}\quad .}
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The basis of pseudo-elastic material models is a hyperelastic
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369:{\displaystyle W_{max}(t):=\max\{W(\tau ),\tau \leq t\}}
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227:is multiplied by a positive softening function
20:is an approach published in 1999 which extends
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648:Journal of the Mechanics and Physics of Solids
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574:Proceedings of the Royal Society of London A
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267:thereby depends on the strain energy
220:{\displaystyle {\boldsymbol {S}}_{0}}
191:{\displaystyle {\boldsymbol {S}}_{0}}
68:{\displaystyle {\boldsymbol {S}}_{0}}
7:
609:"Softening of Rubber by Deformation"
298:of the current load and its maximum
291:{\displaystyle W({\boldsymbol {C}})}
102:{\displaystyle W({\boldsymbol {C}})}
75:, which is derived from a suitable
28:. It is used in several commercial
673:Naumann, C.; Ihlemann, J. (2015).
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376:in the history of the material:
613:Rubber Chemistry and Technology
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198:. Upon unloading and reloading
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77:strain energy density function
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45:second Piola–Kirchhoff stress
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22:hyperelastic material models
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32:codes, and is named after
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260:{\displaystyle \eta }
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714:Elasticity (physics)
607:Mullins, L. (1969).
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18:Ogden–Roxburgh model
709:Continuum mechanics
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719:Rubber properties
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619:(1): 339–362.
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30:finite element
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630:16 September
628:. Retrieved
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443:where
40:from 1994.
703:Categories
559:References
34:R.W. Ogden
447:η
395:η
358:≤
355:τ
346:τ
255:η
235:η
142:∂
134:∂
582:Bibcode
38:et al.
632:2023
513:<
499:<
16:The
683:doi
656:doi
621:doi
590:doi
578:455
334:max
705::
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652:42
650:.
617:42
615:.
611:.
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331::=
109::
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685::
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540:.
527:x
524:a
521:m
517:W
510:W
505:,
502:1
492:,
487:x
484:a
481:m
477:W
473:=
470:W
464:,
461:1
458:=
452:{
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418:x
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401:W
398:(
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361:t
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343:(
340:W
337:{
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325:t
322:(
317:x
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311:m
307:W
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282:C
278:(
275:W
213:0
208:S
184:0
179:S
154:.
146:C
137:W
128:2
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121:S
97:)
93:C
89:(
86:W
61:0
56:S
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