Integration Of Rate Constitutive Equations Research Articles

Numerical integration of rate constitutive equations in presence of large strains and rotations

The aim of the present work is to present two operational numerical methods allowing for integrating rate constitutive equations accounting for large strains and rotations. Both methods can be applied in the development of home-made computation codes or/and in the development of user material subroutines in commercial computation codes.

Numerical integration of rate constitutive equations under finite deformation

An objective stress rate must be used in the constitutive law to accurately describe material response when large rigid body translations and rotations are present. The choice of a suitable objective stress rate has been the subject of considerable debate. For example, a basic flaw in the well known Jaumann stress rate (J-rate) has been demonstrated using the simple shear problem. A number of alternative objective stress rates have been suggested and developed. Among these is the Eulerian or E-rate in which rate constitutive calculations are performed on material axes coincident with the principal axes. The use of the principal axes technique greatly simplifies the constitutive calculations and resolves the difficulties surrounding the question of objectivity and frame invariance which arise in finite deformation problems. A numerical algorithm is presented which incorporates the principal axes technique for the Eulerian stress rate. The algorithm is intended for use in general purpose two or three dimensional solid mechanics software using the incremental or rate form of constitutive modelling. The algorithm focuses on an efficient method of integrating the material rotation tensor relating the principal axes to the fixed or global axes. The implementation of this algorithm into a general purpose non-linear transient dynamic finite element computer code is included. A number of numerical examples ranging from the simple shear problem to a large scale impact simulation demonstrates the accuracy and salient features of the algorithm.

Numerical integration of rate constitutive equations in finite deformation analysis

In analysis of finite deformation problems the use of constitutive equations in rate form is often required. In a spatial setting, these equations may express a relationship between some objective rate of spatial stress tensor and the rate of deformation. Constitutive equations of this type characterize a variety of material models including hyperelasticity, hypoelasticity and elastoplasticity. Employing geometrical concepts, a family of unconditionally stable and incrementally objective algorithms is proposed for the integration of such rate constitutive equations. These algorithms, which are appropriate for finite deformation analysis, are applicable to any choice of stress rate and, in most cases, employ quantities that arise naturally in the context of finite element analysis. Examples illustrate the objectivity and accuracy of the algorithms.

International conference on numerical methods for transient and coupled problems

In this paper the computer implementation aspects for fluid-structure interaction problems are presented. Special attention is placed on finite element fluid modelling, implicit-explicit transient algorithms and finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis. All these methodologies have been integrated into a working finite element computer code.

Computer implementation aspects for fluid-structure interaction problems

Abstract In this paper the computer implementation aspects for fluid-structure interaction problems are presented. Special attention is placed on finite element fluid modelling, implicit-explicit transient algorithms and finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis. All these methodologies have been integrated into a working finite element computer code.

Finite element procedures for fluid-structure interactions and application to liquid storage tanks

Most of the failures of large tanks after severe earthquakes are suspected to have resulted from the dynamic buckling caused by overturning moments of seismically induced liquid inertia and surface slosh waves. In this paper, a nonlinear finite element method is presented which can treated the structural behavior of the tanks in conjunction with fluid, including the dynamics and buckling. Both the formulation and computer implementation aspects are presented. The areas upon which attention is focused are: the mixed Lagrangian-Eulerian kinematical description for modeling fluid subdomains in fluid-structure interaction problems, the finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis and the implicit-explicit finite element techniques for transient analysis. All these nonlinear methodologies have been integrated into a finite element computer code [47]. A number of physically important buckling and dynamic analyses of tanks are being investigated. Various other fluid structure phenomena such as the stability of off-shore structures can be analyzed with this computer program. The proposed nonlinear finite-element procedures can serve as a basis for future developments of various other fluid-structure phenomena such as the transient motion of submerged or partially submerged structures.

Finite rotation effects in numerical integration of rate constitutive equations arising in large‐deformation analysis

AbstractAn improved algorithm is presented for integrating rate constitutive equations in large‐deformation analysis. The algorithm is shown to be ‘objective’ with respect to large rotation increments.