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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 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 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...

Dynamic analysis of viscous material models

Trcala, Miroslav, Němec, Ivan, Vaněčková, Adéla, Hokeš, Filip (2021)

Programs and Algorithms of Numerical Mathematics

The article deals with the analysis of the dynamic behavior of a~concrete structural element during fast dynamic processes. The constitutive material model must be chosen appropriately so that it takes material viscosity into account when describing the behavior of material. In this analysis, it is necessary to use fairly complex viscous material models which can affect, for example, vibration damping and the dependence of strength or even of the entire stress-strain curve on the strain rate. These...

Dynamic Damping - Comparison of different concepts from the point of view of their physical nature and effects on civil engineering structures

Němec, Ivan, Trcala, Miroslav, Vaněčková, Adéla, Rek, Václav (2019)

Programs and Algorithms of Numerical Mathematics

Sources of dynamic damping may be various. Mostly, the damping is implemented into calculations in a form of introduction of damping forces, as a product of the velocity vector and the damping matrix in an equation of motion. In practice, the damping matrix is usually assumed to be a linear combination of the mass matrix and the stiffness matrix (so called Rayleigh’s damping). This kind of damping primarily assumes the external environment viscosity as the source of damping, even though the part...

Dynamical model of viscoplasticity

Kisiel, Konrad (2017)

Proceedings of Equadiff 14

This paper discusses the existence theory to dynamical model of viscoplasticity and show possibility to obtain existence of solution without assuming weak safe-load condition.

Error estimates of an iterative method for a quasistatic elastic-visco-plastic problem

Ioan Rosca, Mircea Sofonea (1994)

Applications of Mathematics

This paper deals with an initial and boundary value problem describing the quasistatic evolution of rate-type viscoplastic materials. Using a fixed point property, an iterative method in the study of this problem is proposed. A concrete algorithm as well as some numerical results in the one-dimensional case are also presented.

Numerical analysis and simulations of quasistatic frictionless contact problems

José Fernández García, Weimin Han, Meir Shillor, Mircea Sofonea (2001)

International Journal of Applied Mathematics and Computer Science

A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.

Shakedown theorems in poroplastic dynamics

Giuseppe Cocchetti, Giulio Maier (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The constitutive model assumed in this Note is poroplastic two-phase (solid-fluid) with full saturation and stable in Drucker’s sense. A solid or structure of this material is considered, subjected to dynamic external actions, in particular periodic or intermittent, in a small deformation regime. A sufficient condition and a necessary one are established, by a «static» approach, for shakedown (or adaptation), namely for boundedness in time of the cumulative dissipated energy.

Temperature-dependent hysteresis in one-dimensional thermovisco-elastoplasticity

Pavel Krejčí, Jürgen Sprekels (1998)

Applications of Mathematics

In this paper, we develop a thermodynamically consistent description of the uniaxial behavior of thermovisco-elastoplastic materials for which the total stress σ contains, in addition to elastic, viscous and thermic contributions, a plastic component σ p of the form σ p ( x , t ) = 𝒫 [ ε , θ ( x , t ) ] ( x , t ) . Here ε and θ are the fields of strain and absolute temperature, respectively, and { 𝒫 [ · , θ ] } θ > 0 denotes a family of (rate-independent) hysteresis operators of Prandtl-Ishlinskii type, parametrized by the absolute temperature. The system of momentum...

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