Issues on the constitutive formulation at large elastoplastic deformations, part 1: Kinematics

1987 ◽  
Vol 69 (1-4) ◽  
pp. 119-138 ◽  
Author(s):  
Y. F. Dafalias
Keyword(s):  
Elastoplastic Deformations ◽  
Constitutive Formulation

Dynamic Rate Effects on Timoshenko Beam Response

1985 ◽  
Vol 52 (2) ◽  
pp. 439-445 ◽  
Author(s):  
T. J. Ross
Keyword(s):  
Timoshenko Beam ◽  
Bending Moment ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Rate Effects ◽  
The Laplace Transform ◽  
Step Loading ◽  
Fixed End ◽  
Constitutive Formulation ◽  
Viscoelastic Timoshenko Beam

The problem of a viscoelastic Timoshenko beam subjected to a transversely applied step-loading is solved using the Laplace transform method. It is established that the support shear force is amplified more than the support bending moment for a fixed-end beam when strain rate influences are accounted for implicitly in the viscoelastic constitutive formulation.

scholarly journals A Computational Model of Viscoelastic Composite Materials for Ligament or Tendon Prostheses

2000 ◽  
Vol 9 (3) ◽  
pp. 096369350000900
Author(s):  
P. Vena
Keyword(s):  
Composite Materials ◽  
Constitutive Relations ◽  
Strain Energy Function ◽  
Time Dependent ◽  
Element Formulation ◽  
Viscoelastic Composite ◽  
Uniaxial Test ◽  
The Matrix ◽  
Tissue Reconstruction ◽  
Constitutive Formulation

A constitutive model and a finite element formulation for viscoelastic anisotropic materials subject to finite strains is expounded in this paper. The composite material is conceived as a matrix reinforced with stiff fibres. The constitutive relations are obtained by defining a strain energy function and a relaxation function for each constituent. By means of this approach, the viscoelastic properties of the material constituents can be taken into account and therefore different time dependent behaviour can be assigned to the matrix and to the reinforcing fibres. The response provided by this kind of constitutive formulation allows for the description of mechanical behaviour for either natural anisotropic tissues (such as tendons and ligaments) and for the composite materials which are currently adopted for tissue reconstruction. The main features of those mechanical properties observed in an ideal uniaxial test are: a non linear stress-strain response and a time dependent response which is observed in relaxation of stresses for a prescribed constant stretch and in a moderate strain rate dependence of the measured response.

A New Micromechanical Model to Study Transformation Plasticity in High-Carbon Steels

2019 ◽  
Author(s):  
Rohit Voothaluru ◽  
Vikram Bedekar ◽  
Praveen Pauskar
Keyword(s):  
Finite Element ◽  
Micromechanical Model ◽  
Inelastic Strain ◽  
Material Model ◽  
Carbon Steels ◽  
Transformation Plasticity ◽  
Element Approach ◽  
In Situ Neutron Diffraction ◽  
Constitutive Formulation

Abstract Hardened steels in engineering applications tend to have gradient microstructures with varying amounts of retained austenite alongside harder phases such as martensite or bainite. However, the metastable austenite can transform into martensite under mechanical loads, resulting in an inelastic strain within the material from the volumetric mismatch between FCC austenite and BCT martensite. In this work, a new constitutive formulation based upon the critical driving force for austenite transformation is presented. The model was implemented into a crystal plasticity formulation, and empirical data from in-situ neutron diffraction was used to determine the local micro-plasticity and transformation plasticity parameters. The results from finite element modeling also show that using a homogenized finite element approach could help to establish a material model that can capture the transformation plasticity within these materials with good accuracy.

On instability of constitutive models for isotropic elastic-perfectly plastic material behaviour at finite deformations

2020 ◽  
pp. 095440622092068
Author(s):  
Marina Trajković-Milenković ◽  
Otto T Bruhns ◽  
Andrija Zorić
Keyword(s):  
Plastic Material ◽  
Constitutive Relations ◽  
Relevant Literature ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Elastoplastic Deformations ◽  
Perfectly Plastic ◽  
User Subroutine ◽  
Shear Problem ◽  
Elastic Perfectly Plastic

The main goal of this work is to test the possibility of a newly introduced constitutive law to model the behaviour of the isotropic elastic-perfectly plastic material which is exposed to large elastoplastic deformations. The proposed constitutive relation is based on the hypo-elastic relation and the inelastic INTERATOM model. The verification of the model is done by its implementation into the commercial software ABAQUS/Standard via the user subroutine UMAT. For that purpose, the large simple shear problem is studied where selected objective corotational rates, i.e. the logarithmic rate, the Jaumann rate and the Green-Naghdi rate, are individually implemented in the aforementioned constitutive relations. The obtained results are compared mutually and with the relevant literature. The proposed constitutive model is also used to test the behaviour of the part of a real engineering structure, i.e. a seismic isolator, in order to obtain the correct input data for further analysis of superstructure behaviour due to seismic excitation.

scholarly journals Influence of the Elastoplastic Strain on Fatigue Durability Determined with the Use of the Spectral Method

Materials ◽  
2020 ◽  
Vol 13 (2) ◽  
pp. 423 ◽  
Author(s):  
Michał Böhm ◽  
Mateusz Kowalski ◽  
Adam Niesłony
Keyword(s):  
Fatigue Life ◽  
Probability Density ◽  
Spectral Method ◽  
Fatigue Tests ◽  
Life Assessment ◽  
Loading Conditions ◽  
Random Loading ◽  
Elastoplastic Deformations ◽  
Fatigue Life Assessment ◽  
Safe Side

The paper presents experimental static and fatigue tests results under random loading conditions for the bending of 0H18N9 steel. The experimental results were used in performing calculations, according to the theoretical assumptions of the spectral method of fatigue life assessment, including elastoplastic deformations. The presented solution extends the use of the spectral method for material fatigue life assessment, in terms of loading conditions, above Hooke’s law theorem. The work includes computational verification of the proposal to extend the applicability of the spectral method of determining fatigue life for the range of elastoplastic deformations. One of the aims of the proposed modification was to supplement the stress amplitudes used to calculate the probability density function of the power spectral density of the signal with correction, due to the plastic deformation and its use for notched elements. The authors have tested the method using four of the most popular probability density functions used in commercial software. The obtained results of comparisons between the experimental and calculation results show that the proposed algorithm, tested using the Dirlik, Benasciutti–Tovo, Lalanne, and Zhao–Baker models, does not overestimate fatigue life, which means that the calculations are on the safe side. The obtained results prove that the elastoplastic deformations can be applied within the frequency domain for fatigue life calculations.

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