The equilibrium of material forces in a 1D phase transition problem

Balassas, K.G.; Kalpakides, V.K.

doi:10.1016/j.cma.2006.11.010

Cited by 5 publications

(1 citation statement)

References 40 publications

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“…Hence, we stick to the simplest hypothesis here. It is also worth mentioning that other theoretical approaches study the movement of an interfacial zone using either a variational principle [37] or a levelset concept [38]. In the current treatment, we prefer the simpler sharp-interface model.…”

Section: Transformation Condition and Kineticsmentioning

confidence: 99%

Thermodynamic modeling of a phase transformation in protein filaments with mechanical function

Fischer¹,

Harrington²,

Fratzl³

2013

New J. Phys.

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Protective egg capsules from whelks (intertidal marine gastropods) were recently demonstrated to derive their impressive mechanical behavior-reminiscent of the pseudoelastic behavior in some alloy systems from a reversible phase transition of component protein building blocks from a compact α-helical conformation to a more extended softer conformation, called β * . This behavior was previously modeled under equilibrium conditions, demonstrating that the transition from the αto β * -phase could account for the pronounced yield plateau and reversibility; however, a theoretical understanding of the non-equilibrium behaviors of the egg capsule (e.g. strain rate dependence and hysteresis) requires a new approach. Here, we modify the previously proposed model in order to address the time-dependent behaviors of the whelk egg capsule biopolymer. Our results indicate that hysteresis during cyclic loading originates from a mismatch between the speed of the mechanical driving force and the rate at which the phase transition occurs. Furthermore, the characteristic curved shape of the stress-strain plot arises from a nonlinear relationship between the transformation rate and the amount of applied load. These results have important implications for our understanding of the mechanics of biological polymers and may have implications for the design of biomimetic pseudoelastic polymers.

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Section: Transformation Condition and Kineticsmentioning

confidence: 99%

Thermodynamic modeling of a phase transformation in protein filaments with mechanical function

Fischer¹,

Harrington²,

Fratzl³

2013

New J. Phys.

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Configurational Forces in Continuous Theories of Elastic Ferroelectrics

Kalpakides

Arvanitakis

2009

IUTAM Symposium on Progress in the Theory and Numerics of Configurational Mechanics

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The concept of material forces in phase transition problems within the level-set framework

Arvanitakis

Kalpakides

2011

Arch Appl Mech

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The dynamics of a phase transition front in solids using the level set method is examined in this paper. Introducing an implicit representation of singular surfaces, a regularized version of the sharp interface model arises. The interface transforms into a thin transition layer of nonzero thickness where all quantities take inhomogeneous expressions within the body. It is proved that the existence of an inhomogeneous energy of the material predicts inhomogeneity forces that drive the singularity. The driving force is a material force entering the canonical momentum equation (pseudo-momentum) in a natural way. The evolution problem requires a kinetic relation that determines the velocity of the phase transition as a function of the driving force. Here, the kinetic relation is produced by invoking relations that can be considered as the regularized versions of the Rankine-Hugoniot jump conditions. The effectiveness of the method is illustrated in a shape memory alloy bar.

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The equilibrium of material forces in a 1D phase transition problem

Cited by 5 publications

References 40 publications

Thermodynamic modeling of a phase transformation in protein filaments with mechanical function

Thermodynamic modeling of a phase transformation in protein filaments with mechanical function

Configurational Forces in Continuous Theories of Elastic Ferroelectrics

The concept of material forces in phase transition problems within the level-set framework

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