de Jhp Henk Vree

Gradient enhanced damage for quasi-brittle materials

SUMMARY Conventional continuum damage descriptions of material degeneration suffer from loss of well-posedness beyond a certain level of accumulated damage. As a consequence, numerical solutions are obtained which are unacceptable from a physical point of view. The introduction of higher-order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models. A consistent numerical solution procedure of the governing partial differential equations is presented, which is shown to be capable of properly simulating localization phenomena.

Comparison of nonlocal approaches in continuum damage mechanics

Abstract A local continuum damage theory and two distinct nonlocal variants are applied to model the failure behaviour of a construction made of macroscopically brittle material. In the nonlocal formulations a material characteristic length parameter is introduced associated with the width of the microstructural damage zone. The numerical implementation of the approaches has been performed in a finite element code. Simulation results calculated for a plane stress configuration are compared. The local approach solutions show severe lack of mesh objectivity, whereas both the nonlocal solutions converged after mesh refinement. By adequate tuning of the nonlocal descriptions mutually similar responses can be obtained, although intrinsic differences are present in the resulting damage distributions.

Reduction of mesh sensitivity in continuum damage mechanics

SummaryContinuum damage theories can be applied to simulate the failure behaviour of engineering constructions. In the constitutive equations of the material a damage parameter is incorporated. A damage criterion and a damage evolution law are postulated and quantified based on experimental data. The elaboration of the mathematical formulation is performed by common finite element techniques. Without special precautions the numerical results appear to be unacceptably dependent on the measure of the spatial discretization. It is shown that a simple but effective procedure leads to the conservation of objectivity.

Mechanical Performance of a Dental Composite: Probabilistic Failure Prediction

In clinical situations, the mechanical performances of dental structures-for example, composite restorations-depend on many factors. Most of them have a probabilistic character. Because composites are brittle materials, their strength should also be considered as a probabilistic quantity. For successful prediction of mechanical failure of structures consisting of these materials, a probabilistic approach is indispensable, and a suitable definition of equivalent stress must be introduced. An equivalent stress facilitates the transfer of strength data of laboratory specimens to situations where the stress state is much more complicated. The tensile and compressive strengths of composites differ considerably. Of two equivalent stress definitions that potentially describe this experimental fact (the Driicker-Prager and the Modified von Mises equivalent stress), the predictive capacity was investigated for a microfine composite. In a probabilistic approach to failure, use of the Driicker-Prager equivalent stress appeared to be superior, because the average failure load of notched beams was predicted with an error smaller than 8%.

Continuum damage mechanics for softening of brittle materials

SummaryContinuum damage theory is used to model the failure behaviour of brittle materials. In the constitutive equations a damage parameter is incorporated. A damage criterion is postulated such that large differences between tension and compression strength can be described. A damage growth law is quantified based on experimental data for concrete. For the elaboration of the mathematical formulation the finite element method is applied. Numerical results obtained for a plane strain example show the merits of the procedure.

Size Effect Predictions by Fracture Models for a Refractory Ceramic

Refractory ceramics used as kiln furniture are designed to operate at elevated temperatures with a high thermal shock resistance. In practice, however, the material fails due to thermal fatigue after a limited number of cycles. To predict this failure behaviour, it is generally not possible to use linear elastic fracture mechanics due to the fact that the coarse grained, porous material shows a dissipative mechanical behaviour. Differently sized specimens are tested to determine the size effect associated with this material. Four different finite element models widely used for concrete modelling are investigated on their ability to describe this nonlinear failure behaviour, in particular the associated size effect phenomenon. The results of the initially promising Nonlocal Continuum Damage Mechanics (CDM) model indicate that this approach cannot properly describe the observed size effect. The other three models (Adapted Local CDM, Fictitious Crack and Smeared Crack), however, give comparable results with a good description of the observed size effect phenomenon.

Phenomenological modelling of damage in polymer blends

To describe the constitutive behaviour of a certain class of polymer blends an elasto-perfectly-viscoplastic and creep damageable material characterization is proposed. For a composite of 80% Polystyrene and 20% Ethylene Propylene Diene Monomer rubber (PS/EPDM) the specific parameters are determined from tensile tests in a particular range of strain velocities. To investigate the applicability of the model, the results of a finite element analysis for a laterally loaded thin plate (plane stress) with a circular hole are compared to measurements. Numerically calculated values are in reasonable agreement with reality; discrepancies can be ascribed to noise in experimental data. The finite element approach is evaluated with respect to the occurrence of mesh-dependence. Mesh-refinement shows convergence of solutions, attributable to the stabilizing influence of the viscous contribution in the constitutive equations.