An internal variable approach applied to the dynamic analysis of elastic–plastic structural systems

1993 ◽  
Vol 22 (10) ◽  
pp. 885-903 ◽  
Author(s):  
S. Rajgelj ◽  
C. Amadio ◽  
A. Nappi
Keyword(s):  
Dynamic Analysis ◽  
Internal Variable ◽  
Structural Systems ◽  
Elastic Plastic ◽  
Variable Approach

Dynamic Analysis of Elastic-Plastic Frames

1964 ◽  
Vol 90 (2) ◽  
pp. 315-346 ◽  
Author(s):  
Arthur C. Heidebrecht ◽  
Seng-Lip Lee ◽  
John F. Flemming
Keyword(s):  
Dynamic Analysis ◽  
Elastic Plastic ◽  
Elastic Plastic Frames

Internal variable formulations of elastic-plastic dynamic problems

1996 ◽  
Vol 18 (7-8) ◽  
pp. 849-858 ◽  
Author(s):  
J.B. Martin ◽  
M.A.E. Kaunda ◽  
R.D. Isted
Keyword(s):  
Internal Variable ◽  
Dynamic Problems ◽  
Elastic Plastic

Thermodynamic conditions for stability in materials with rate-independent dissipation

2005 ◽  
Vol 363 (1836) ◽  
pp. 2479-2515 ◽  
Author(s):  
Henryk Petryk
Keyword(s):  
Standard Condition ◽  
Martensitic Transformations ◽  
Internal Variable ◽  
Irreversible Processes ◽  
Deformation Bands ◽  
Stability Of Equilibrium ◽  
Variable Approach ◽  
Thermodynamic Conditions ◽  
The Stability ◽  
Time Specific

A distinctive feature of the examined class of solids is that a part of the entropy production is due to rate-independent dissipation, as in models of plasticity, damage or martensitic transformations. The standard condition for thermodynamic stability is shown to be too restrictive for such solids and, therefore, an extended condition for stability of equilibrium is developed. The classical thermodynamic theory of irreversible processes is used along with the internal variable approach, with the emphasis on the macroscopic effects of micro-scale instabilities in the presence of two different scales of time. Specific conditions for material stability against internal structural rearrangements under deformation-sensitive loading are derived within the incremental constitutive framework of multi-mode inelasticity. Application to spontaneous formation of deformation bands in a continuum is presented. Conditions for stability or instability of a quasi-static process induced by varying loading are given under additional constitutive postulates of normality and symmetry. As illustration of the theory, the stability of equilibrium or a deformation path under uniaxial tension is analysed for a class of inelastic constitutive laws for a metal crystal deformed plastically by multi-slip or undergoing stress-induced martensitic transformation.

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