Consistent numerical implementation of hypoelastic constitutive models

Verification of Frame Indifference for Complicated Numerical Constitutive Models

The principle of material frame indifference requires spatial stresses to rotate with the material, whereas reference stresses must be insensitive to rotation. Testing of a classical uniaxial strain problem with superimposed rotation reveals that a very common approach to strong incremental objectivity taken in finite element codes to satisfy frame indifference (namely working in an approximate...

Numerical self-consistent stellar models of thin disks

We find a numerical self-consistent stellar model by finding the distribution function of a thin disk that satisfies simultaneously the Fokker-Planck and Poisson equations. The solution of the Fokker-Planck equation is found by a direct numerical solver using finite differences and a variation of Stone’s method. The collision term in the Fokker-Planck equation is found using the local approxima...

‎A Consistent and Accurate Numerical Method for Approximate Numerical Solution of Two Point Boundary Value Problems

In this article we have proposed an accurate finite difference method for approximate numerical solution of second order boundary value problem with Dirichlet boundary conditions. There are numerous numerical methods for solving these boundary value problems. Some these methods are more efficient and accurate than others with some advantages and disadvantages. The results in experiment on model...

Constitutive Modeling and Numerical Implications

Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms

Previous studies by the authors and their co-workers show that the structure of equations representing shape Memory Alloy (SMA) constitutive behaviour can be very similar to those of rate-independent plasticity models. For example, the Boyd–Lagoudas polynomial hardening model has a stress-elastic strain constitutive relation that includes the transformation strain as an internal state variable,...