Non-Linear Constitutive Equations of Viscoelastic Bodies

1975 ◽  
pp. 163-169
Author(s):  
Z. Sobotka
Keyword(s):  
Constitutive Equations ◽  
Non Linear ◽  
Viscoelastic Bodies

Localization criteria for non-linear constitutive equations of geomaterials

2000 ◽  
Vol 5 (1) ◽  
pp. 61-82 ◽  
Author(s):  
Ren� Chambon ◽  
St�phane Crochepeyre ◽  
Jacques Desrues
Keyword(s):  
Constitutive Equations ◽  
Non Linear

Effective Stress Ratio of Triangular Pattern Perforated Plates

2008 ◽  
Author(s):  
Naoto Kasahara ◽  
Hideki Takasho ◽  
Nobuchika Kawasaki ◽  
Masanori Ando
Keyword(s):  
Effective Stress ◽  
Material Properties ◽  
Constitutive Equations ◽  
Stress Ratio ◽  
Equivalent Material ◽  
Solid Materials ◽  
Perforated Plates ◽  
Non Linear ◽  
Effective Stress Ratio ◽  
Equivalent Material Properties

Tubesheet structures utilized in heat exchangers have complex perforated portions. For realistic design analysis, axisymmetric models with equivalent solid materials of perforated plate are conventionally adopted to simplify perforated area (figure1). Sec.III Appendix A-8000 (ASME 2004) provides elastic equivalent solid materials for flat tubesheets. Plastic properties were studied by Porowski et al. (1974), Gorden et al. (2002) and so on. Elevated temperature design of tubesheets requires plastic and creep properties in addition. The purpose of this study is to develop a general determination method of non-linear equivalent material properties for perforated plates and to confirm their applicability to both flat and spherical tubesheets. Main loadings of tubesheets in fast reactor heat exchanges are inner pressure and thermal stress at transient operations. Under above conditions, average stress of perforated area becomes approximately equi-biaxial. Therefore, average inelastic behaviors of various perforated plates subjected to equi-biaxial field were investigated by inelastic finite element method. Though above investigations, Authors clarified that perforated plates have their own effective stress ratio (ESR). ESR is a function of geometry and is independent from their materials. ESR can determine non-linear equivalent material properties of perforated plates for any kind of constitutive equations of base metals. For simplified inelastic analysis of perforated plates, the brief equations were proposed to determine equivalent plastic and creep material properties for perforated plates. It is considered that physical meaning of ESR is an effective stress ratio between perforated plates and equivalent solid plates. ESR is a function of geometry and is independent from constitutive equations. ESR can determine non-linear equivalent material properties for perforated plates from any kind of constitutive equations of base materials. Assumptions in ESR are von Mises’s equivalent stress-strain relationship and equi-biaxial loadings. Applicability of ESR was investigated through finite element analyses of various flat and spherical tubesheets.

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