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Non-local damage modelling of quasi-brittle composites

Jiří Vala, Vladislav Kozák (2021)

Applications of Mathematics

Most building materials can be characterized as quasi-brittle composites with a cementitious matrix, reinforced by some stiffening particles or elements. Their massive exploitation motivates the development of numerical modelling and simulation of behaviour of such material class under mechanical, thermal, etc. loads, including the evaluation of the risk of initiation and development of micro- and macro-fracture. This paper demonstrates the possibility of certain deterministic prediction, applying...

Numerical analysis of a frictionless viscoelastic piezoelectric contact problem

Mikael Barboteu, Jose Ramon Fernández, Youssef Ouafik (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, we consider the quasistatic frictionless contact problem between a viscoelastic piezoelectric body and a deformable obstacle. The linear electro-viscoelastic constitutive law is employed to model the piezoelectric material and the normal compliance condition is used to model the contact. The variational formulation is derived in a form of a coupled system for the displacement and electric potential fields. An existence and uniqueness result is recalled. Then, a fully discrete scheme...

Numerical analysis of history-dependent quasivariational inequalities with applications in contact mechanics

Kamran Kazmi, Mikael Barboteu, Weimin Han, Mircea Sofonea (2014)

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

A new class of history-dependent quasivariational inequalities was recently studied in [M. Sofonea and A. Matei, History-dependent quasivariational inequalities arising in contact mechanics. Eur. J. Appl. Math. 22 (2011) 471–491]. Existence, uniqueness and regularity results were proved and used in the study of several mathematical models which describe the contact between a deformable body and an obstacle. The aim of this paper is to provide numerical analysis of the quasivariational inequalities...

Numerical analysis of the quasistatic thermoviscoelastic thermistor problem

José R. Fernández (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, the quasistatic thermoviscoelastic thermistor problem is considered. The thermistor model describes the combination of the effects due to the heat, electrical current conduction and Joule's heat generation. The variational formulation leads to a coupled system of nonlinear variational equations for which the existence of a weak solution is recalled. Then, a fully discrete algorithm is introduced based on the finite element method to approximate the spatial variable and an Euler scheme...

On a computational approach to multiple contacts / impacts of elastic bodies

Vala, Jiří, Rek, Václav (2023)

Programs and Algorithms of Numerical Mathematics

The analysis of dynamic contacts/impacts of several deformable bodies belongs to both theoretically and computationally complicated problems, because of the presence of unpleasant nonlinearities and of the need of effective contact detection. This paper sketches how such difficulties can be overcome, at least for a model problem with several elastic bodies, using i) the explicit time-discretization scheme and ii) the finite element technique adopted to contact evaluations together with iii) the...

On a new computational algorithm for impacts of elastic bodies

Hynek Štekbauer, Ivan Němec, Rostislav Lang, Daniel Burkart, Jiří Vala (2022)

Applications of Mathematics

Computational modelling of contact problems is still one of the most difficult aspects of non-linear analysis in engineering mechanics. The article introduces an original efficient explicit algorithm for evaluation of impacts of bodies, satisfying the conservation of both momentum and energy exactly. The algorithm is described in its linearized 2-dimensional formulation in details, as open to numerous generalizations including 3-dimensional ones, and supplied by numerical examples obtained from...

On the importance of solid deformations in convection-dominated liquid/solid phase change of pure materials

Daniela Mansutti, Edoardo Bucchignani (2011)

Applications of Mathematics

We analyse the effect of the mechanical response of the solid phase during liquid/solid phase change by numerical simulation of a benchmark test based on the well-known and debated experiment of melting of a pure gallium slab counducted by Gau & Viskanta in 1986. The adopted mathematical model includes the description of the melt flow and of the solid phase deformations. Surprisingly the conclusion reached is that, even in this case of pure material, the contribution of the solid phase to the...

Quasi-static evolution for fatigue debonding

Alessandro Ferriero (2008)

ESAIM: Control, Optimisation and Calculus of Variations

The propagation of fractures in a solid undergoing cyclic loadings is known as the fatigue phenomenon. In this paper, we present a time continuous model for fatigue, in the special situation of the debonding of thin layers, coming from a time discretized version recently proposed by Jaubert and Marigo [C. R. Mecanique333 (2005) 550–556]. Under very general assumptions on the surface energy density and on the applied displacement, we discuss the well-posedness of our problem and we give the main...

Thick obstacle problems with dynamic adhesive contact

Jeongho Ahn (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, we consider dynamic frictionless contact with adhesion between a viscoelastic body of the Kelvin-Voigt type and a stationary rigid obstacle, based on the Signorini's contact conditions. Including the adhesion processes modeled by the bonding field, a new version of energy function is defined. We use the energy function to derive a new form of energy balance which is supported by numerical results. Employing the time-discretization, we establish a numerical formulation and investigate...

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