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Simulation of Mechanical Behaviour in a Single-Crystal Nickel-Basis Superalloy at High Temperature
(2010)
Constitutive modeling of creep-fatigue interaction for normal strength concrete under compression
(2015)
Conventional approaches to model fatigue failure are based on a characterization of the lifetime as a function of the loading amplitude. The Wöhler diagram in combination with a linear damage accumulation assumption predicts the lifetime for different loading regimes. Using this phenomenological approach, the evolution of damage and inelastic strains and a redistribution of stresses cannot be modeled. The gradual degration of the material is assumed to not alter the stress state. Using the Palmgren–Miner rule for damage accumulation, order effects resulting from the non-linear response are generally neglected.
In this work, a constitutive model for concrete using continuum damage mechanics is developed. The model includes rate-dependent effects and realistically reproduces gradual performance degradation of normal strength concrete under compressive static, creep and cyclic loading in a unified framework. The damage evolution is driven by inelastic deformations and captures strain rate effects observed experimentally. Implementation details are discussed. Finally, the model is validated by comparing simulation and experimental data for creep, fatigue and triaxial compression.
Concrete is a complex material. Its properties evolve over time, especially at early age, and are dependent on environmental conditions, i.e. temperature and moisture conditions, as well as the composition of the material.
This leads to a variety of macroscopic phenomena such as hydration/solidification/hardening, creep and shrinkage, thermal strains, damage and inelastic deformations. Most of these phenomena are characterized by specific set of model assumptions and often an additive decomposition of strains into elastic, plastic, shrinkage and creep components is performed. Each of these phenomena are investigated separately and a number of respective independent models have been designed. The interactions are then accounted for by adding appropriate correction factors or additional models for the particular interaction. This paper discusses the importance of reconsider even in the experimental phase the model assumptions required to generalize the experimental data into models used in design codes. It is especially underlined that the complex macroscopic behaviour of concrete is strongly influenced by its multiscale and multiphyscis nature and two examples (shrinkage and fatigue) of interacting phenomena are discussed.
A Multi-scale temporal integration scheme for viscoplatic solids subjected to fatigue deterioration
(2016)
Using a continuum mechanics framework for lifetime prediction requires numerical integration of evolving damage until the onset of failure. The primary challenge for the simulation of structural fatigue failure is caused by the enormous computational costs due to cycle by cycle temporal integration throughout the whole loading history, which is in the order of 10^3 - 10^7 cycles. As a consequence, most approaches circumvent this problem and use an empirical method such as Wöhler curves. They are well suited for approximation of the lifetime, but they are not capable to capture a realistic degradation of the material with a redistribution of the stresses. The main objective of the paper is to provide a technique for the long time response of a finite element (FE) model while reducing computational costs.
A multi-scale temporal integration scheme is proposed, which adapts the conventional FE method for realistic modeling of deterioration in a structure subjected to cyclic loading. For a particular case of two-scale temporal homogenization, the displacement field is assumed to satisfy scale separation: a short time scale arises from the oscillatory loading and a long time scale is due to the slow response relating to yielding and damage evolution. The original boundary value Problem (BVP) is approximated by the time-Independent BVPs on the short time scale. Alternation of the displacement field on the long time scale is correlated with the damage evolution by means of the adaptive cycle jump method. The significant acceleration of FE simulations is demonstrated for a constitutive damage model where the progressive damage accumulation under fatigue loading is driven by viscoplastic deformation.
Die Analyse der Lebensdauer von Bauteilen unter thermomechanischer Ermüdung (TMF) erfordert ein geeignetes Stoffgesetz, welches in der Lage ist, zyklische Plastizität die Abhängigkeit der Spannungsantwort nach der Dehnrate, Kriechen und Spannungsrelaxation temperaturabhängig zu beschreiben und ein Lebensdauermodell, welches in Abhängigkeit von der örtlich aufgelösten Spannungs- und Verformungsgeschichten eine Schätzung der Anzahl der Zyklen bis zum Anriss liefern kann.
A key limitation of the most constitutive models that reproduce a Degradation of quasi-brittle materials is that they generally do not address issues related to fatigue. One reason is the huge computational costs to resolve each load cycle on the structural level. The goal of this paper is the development of a temporal Integration scheme, which significantly increases the computational efficiency of the finite element method in comparison to conventional temporal integrations.
The essential constituent of the fatigue model is an implicit gradient-enhanced formulation of the damage rate. The evolution of the field variables is computed as amultiscale Fourier series in time.On a microchronological scale attributed to single cycles, the initial boundary value problem is approximated by linear BVPs with respect to the Fourier coefficients. Using the adaptive cycle jump concept, the obtained damage rates are transferred to a coarsermacrochronological scale associated with the duration of material deterioration. The performance of the developedmethod is hence improved due to an efficient numerical treatment of the microchronological problem in combination with the cycle jump technique on the macrochronological scale. Validation examples demonstrate the convergence of the obtained solutions to the reference simulations while significantly reducing the computational costs.
A computationally efficient solution scheme is presented for the mechanical problems whose formulations include the Kuhn–Tucker or Signorini–Fichera conditions. It is proposed to reformulate these problems replacing inequalities in these conditions by equations with respect to new unknowns. The solutions of the modified problems have simple physical meanings and determine uniquely the unknowns of the original problems. The approach avoids application of multi-valued operators (inclusions or inequalities) in formulation of the problems. Hence, the modified formulations are suitable for numerical analysis using established powerful mathematical methods and corresponding solvers developed for solving systems of non-linear equations.
To demonstrate the advantages of the proposed approach, it is applied for solving problems in two different areas: constitutive modeling of single-crystal plasticity and mixed boundary value problems of elastic contact mechanics with free boundaries. The original formulations of these problems contain respectively the Kuhn–Tucker and Signorini–Fichera conditions. A problem of the former area is integrated using an implicit integration scheme based on the return-mapping algorithm. The derived integration scheme is free of any update procedure for identification of active slip systems. A problem of the latter area is reduced to solution of non-linear integral boundary equations (NBIEs). Numerical examples demonstrate stability and efficiency of the solution procedures and reflect the mathematical similarities between the both non-linear problems.