Equivalence between incremental and hypoplastic constitutive laws

2002 ◽  
pp. 55-60
Author(s):  
P Royis
Keyword(s):  
Constitutive Laws

Analytical Solutions for Circular Bars Subjected to Large Strain Plastic Torsion

1990 ◽  
Vol 57 (2) ◽  
pp. 298-306 ◽  
Author(s):  
K. W. Neale ◽  
S. C. Shrivastava
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Flow Theory ◽  
Constitutive Laws ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Inelastic Behavior ◽  
Rate Dependent

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

scholarly journals A Uniqueness Result for a Simple Superlinear Eigenvalue Problem

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Michael Herrmann ◽  
Karsten Matthies
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Simulations ◽  
Convolution Operator ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Constitutive Laws ◽  
Parameter Family ◽  
Shape Constraint ◽  
Special Case ◽  
Nonlinear Eigenfunctions

AbstractWe study the eigenvalue problem for a superlinear convolution operator in the special case of bilinear constitutive laws and establish the existence and uniqueness of a one-parameter family of nonlinear eigenfunctions under a topological shape constraint. Our proof uses a nonlinear change of scalar parameters and applies Krein–Rutman arguments to a linear substitute problem. We also present numerical simulations and discuss the asymptotics of two limiting cases.

Constitutive Laws for Biomechanical Modeling of Refractive Surgery

1996 ◽  
Vol 118 (4) ◽  
pp. 473-481 ◽  
Author(s):  
Michael R. Bryant ◽  
Peter J. McDonnell
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Refractive Surgery ◽  
Fiber Optic ◽  
Transverse Isotropy ◽  
Constitutive Laws ◽  
Finite Element Models ◽  
Corneal Refractive Surgery ◽  
Best Fit ◽  
Membrane Inflation

Membrane inflation tests were performed on fresh, intact human corneas using a fiber optic displacement probe to measure the apical displacements. Finite element models of each test were used to identify the material properties for four different constitutive laws commonly used to model corneal refractive surgery. Finite element models of radial keratotomy using the different best-fit constitutive laws were then compared. The results suggest that the nonlinearity in the response of the cornea is material rather than geometric, and that material nonlinearity is important for modeling refractive surgery. It was also found that linear transverse isotropy is incapable of representing the anisotropy that has been experimentally measured by others, and that a hyperelastic law is not suitable for modeling the stiffening response of the cornea.

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