Form for the Relation Between Stress and Finite Elastic and Plastic Strains under Impulsive Loading

Backman, Marvin E.

doi:10.1063/1.1702893

Cited by 29 publications

(4 citation statements)

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“…Eq. (4)) with reference to linearized theory, but was subsequently utilized by Backman (1964), Lee and Liu (1967) and Lee (1969) in the context of finite deformation 9 . Issues regarding nonuniqueness and possible nonexistence of the multiplicative decomposition (4.1), as well as the matter of appropriate invariance requirements under s.r.b.m.…”

Section: Figure Imentioning

confidence: 99%

A Critical Review of the State of Finite Plasticity

Naghdi¹

1990

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Section: Figure Imentioning

confidence: 99%

A Critical Review of the State of Finite Plasticity

Naghdi¹

1990

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“…Eq. (4)) with reference to linearized theory, but was subsequently utilized by Backman (1964), Lee and Liu (1967) and Lee (1969) in the context of finite deformation'. Issues regarding nonuniqueness and possible nonexistence of the multiplicative decomposition (4.1), as well as the matter of appropriate invariance requirements under s.r.b.m.…”

Section: A Identification Of Plastic Strainmentioning

confidence: 99%

A Critical Review of the State of Finite Plasticity

Naghdi¹

1990

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“…(the first authors introducing the decomposition are those of references [4][5][6]17,19]; for historical reasons we tend to call it the Kröner-Lee decomposition). Let be a fit region in the three-dimensional point space, endowed with piecewise Lipschitz boundary, a region that we take as a reference.…”

Section: Introductionmentioning

confidence: 99%

Micro-Slip-Induced Multiplicative Plasticity: Existence of Energy Minimizers

Mariano

Mucci

2023

Arch Rational Mech Anal

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To account for material slips at microscopic scale, we take deformation mappings as SBV functions $$\varphi $$ φ , which are orientation-preserving outside a jump set taken to be two-dimensional and rectifiable. For their distributional derivative $$F=D\varphi $$ F = D φ we examine the common multiplicative decomposition $$F=F^{e}F^{p}$$ F = F e F p into so-called elastic and plastic factors, the latter a measure. Then, we consider a polyconvex energy with respect to $$F^{e}$$ F e , augmented by the measure $$|\textrm{curl}\,F^{p}|$$ | curl F p | . For this type of energy we prove the existence of minimizers in the space of SBV maps. We avoid self-penetration of matter. Our analysis rests on a representation of the slip system in terms of currents (in the sense of geometric measure theory) with both $$\mathbb {Z}^{3}$$ Z 3 and $$\mathbb {R}^{3}$$ R 3 valued multiplicity. The two choices make sense at different spatial scales; they describe separate but not alternative modeling options. The first one is particularly significant for periodic crystalline materials at a lattice level. The latter covers a more general setting and requires to account for an energy extra term involving the slip boundary size. We include a generalized (and weak) tangency condition; the resulting setting embraces gliding and cross-slip mechanisms. The possible highly articulate structure of the jump set allows one to consider also the resulting setting even as an approximation of climbing mechanisms.

show abstract

Form for the Relation Between Stress and Finite Elastic and Plastic Strains under Impulsive Loading

Cited by 29 publications

References 6 publications

A Critical Review of the State of Finite Plasticity

A Critical Review of the State of Finite Plasticity

A Critical Review of the State of Finite Plasticity

Micro-Slip-Induced Multiplicative Plasticity: Existence of Energy Minimizers

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