Dynamical systems, rate and gradient effects in material instability

Béda, Péter B.

doi:10.1016/s0020-7403(00)00007-2

Cited by 17 publications

(31 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, let be the material isotropic and all the material coefficients are constant (strictly linear approximation). Finally, let us write the entropy in the canonical form (14), but with constant inductivities m. Now there are two coupled terms in the linear laws, because the current of the extensives j a and the current multiplier A have same tensorial order…”

Section: Now the Dissipation Inequality Transforms Tomentioning

confidence: 99%

“…For the case of simplicity, we consider isotropic material and constant thermal inductivity m. In this case m = mI, therefore the entropy function (14) can be written as…”

Section: Weakly Nonlocal Heat Conduction -Guyer-krumhansl Equationmentioning

confidence: 99%

“…Here we exploited the Gyarmati form entropy (14) and wrote ∂ j s = − m · j a . Because the entropy function is the primary constitutive quantity we can conclude that (55) resulted in a solvable inequality for the two (!)…”

Section: Are the Dynamic Equations Of Internal Variables Balances Or mentioning

confidence: 99%

See 2 more Smart Citations

Weakly nonlocal irreversible thermodynamics

Ván

2003

Ann. Phys.

View full text Add to dashboard Cite

Weakly nonlocal thermodynamic theories are critically revisited. A relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so called current multipliers. The treatment is restricted to deal with nonlocality connected to dynamic thermodynamic variables. Several classical equations are derived, including Guyer-Krumhansl, Ginzburg-Landau and Cahn-Hilliard type equations.Comment: 30 pages, no figure

show abstract

Section: Now the Dissipation Inequality Transforms Tomentioning

confidence: 99%

“…For the case of simplicity, we consider isotropic material and constant thermal inductivity m. In this case m = mI, therefore the entropy function (14) can be written as…”

Section: Weakly Nonlocal Heat Conduction -Guyer-krumhansl Equationmentioning

confidence: 99%

See 1 more Smart Citation

Weakly nonlocal irreversible thermodynamics

Ván

2003

Ann. Phys.

View full text Add to dashboard Cite

show abstract

“…It can be a static or a dynamic bifurcation. For a classification we should study the real parts of the eigenvalues of differential operators defined by the fundamental equations of the continuum [2]. Let state S 0 of a solid continuum be studied, which can be identified by fixed values of the stress, strain or velocity fields σ 0 , ε 0 , v 0 The solid body is described by a set of equations.…”

Section: Continuum As Dynamical Systemmentioning

confidence: 99%

Dynamical effects at material instability phenomena

Béda¹

2009

Proc Appl Math and Mech

View full text Add to dashboard Cite

In a phenomenon called the Portevin-Le Chatelier (PLC) effect negative rate dependence is coupled with the appearance of a self-sustained oscillatory behavior in solid bodies. When PLC is treated as a type of dynamic material instability, the tools of the theory of dynamical system can be applied. The results of such investigation lead to an interpretation of PLC as a flutter type of loss of stability.

show abstract

“…That is, coexistent static and dynamic bifurcations may occur at the loss of stability. By introducing strain rate dependent terms into the constitutive equation the stability investigation can be performed as a generic stability investigation [6,7]. Now we can study the real parts of the eigenvalues of differential operators defined by the fundamental equations of the continuum.…”

Section: Introductionmentioning

confidence: 99%

The Portevin-Le Chatelier effect and dynamical systems

Béda¹

2007

Per. Pol. Mech. Eng.

View full text Add to dashboard Cite

Let us consider Portevin-Le Chatelier (PLC) effect as a form of dynamic material instability. The tools of the investigation are the same as of the theory of dynamical systems. While at the PLC phenomenon negative rate dependence is coupled with the appearance of a self-sustained oscillatory behaviour in solid bodies, the results present us an interpretation of PLC as a flutter type of loss of material stability.

show abstract

Dynamical systems, rate and gradient effects in material instability

Cited by 17 publications

References 5 publications

Weakly nonlocal irreversible thermodynamics

Weakly nonlocal irreversible thermodynamics

Dynamical effects at material instability phenomena

The Portevin-Le Chatelier effect and dynamical systems

Contact Info

Product

Resources

About