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A Bermúdez–Moreno algorithm adapted to solve a viscoplastic problem in alloy solidification processes

P. Barral, P. Quintela, M. T. Sánchez (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The aim of this work is to present a computationally efficient algorithm to simulate the deformations suffered by a viscoplastic body in a solidification process. This type of problems involves a nonlinearity due to the considered thermo-elastic-viscoplastic law. In our previous papers, this difficulty has been solved by means of a duality method, known as Bermúdez–Moreno algorithm, involving a multiplier which was computed with a fixed point algorithm or a Newton method. In this paper, we will...

A fixed point method in dynamic processes for a class of elastic-viscoplastic materials

A. Amassad (1998)

Annales Polonici Mathematici

Two problems are considered describing dynamic processes for a class of rate-type elastic-viscoplastic materials with or without internal state variable. The existence and uniqueness of the solution is proved using classical results of linear elasticity theory together with a fixed point method.

A frictionless contact problem for elastic-viscoplastic materials with internal state variable

Lynda Selmani (2013)

Applicationes Mathematicae

We study a mathematical model for frictionless contact between an elastic-viscoplastic body and a foundation. We model the material with a general elastic-viscoplastic constitutive law with internal state variable and the contact with a normal compliance condition. We derive a variational formulation of the model. We establish existence and uniqueness of a weak solution, using general results on first order nonlinear evolution equations with monotone operators and fixed point arguments. Finally,...

A mixed variational formulation for the Signorini frictionless problem in viscoplasticity.

Sofonea, M., Matei, A. (2004)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

A new model to describe the response of a class of seemingly viscoplastic materials

Sai Manikiran Garimella, Mohan Anand, Kumbakonam R. Rajagopal (2022)

Applications of Mathematics

A new model is proposed to mimic the response of a class of seemingly viscoplastic materials. Using the proposed model, the steady, fully developed flow of the fluid is studied in a cylindrical pipe. The semi-inverse approach is applied to obtain an analytical solution for the velocity profile. The model is used to fit the shear-stress data of several supposedly viscoplastic materials reported in the literature. A numerical procedure is developed to solve the governing ODE and the procedure is validated...