Efficient and reliable nonlocal damage models

We present an efficient and reliable approach for the numerical modelling of failure with nonlocal damage models. The two major numerical challenges––the strongly nonlinear, highly localized and parameter-dependent structural response of quasi-brittle materials, and the interaction between nonadjacent finite elements associated to nonlocality––are addressed in detail. Reliability of the numerical results is ensured by an h-adaptive strategy based on error estimation. We use a residual-type error estimator for nonlinear FE analysis based on local computations, which, at the same time, accounts for the nonlocality of the damage model. Efficiency is achieved by a proper combination of load-stepping control technique and iterative solver for the nonlinear equilibrium equations. A major issue is the computation of the consistent tangent matrix, which is nontrivial due to nonlocal interaction between Gauss points. With computational efficiency in mind, we also present a new nonlocal damage model based on the nonlocal average of displacements. For this new model, the consistent tangent matrix is considerably simpler to compute than for current models. The various ideas discussed in the paper are illustrated by means of three application examples: the uniaxial tension test, the three-point bending test and the single-edge notched beam test.Peer ReviewedPostprint (author’s final draft

Clinical science: The influence of modification of cavity design on distribution of stresses in a restored molar

In this study, two different cavity designs were compared from a mechanical point of view: (a) an axisymmetric model of a conventional class 1 cavity preparation and restoration; and (b) an axisymmetric model of a modified cavity design. The modified design was characterized by a cavo-surface angle (c.s.a.) of approximately 90 degrees and a stepped cavity wall. Using a mathematical model, stresses were calculated by finite element analysis to compare the force distribution. It is concluded that the clinical superiority of the modified cavity design, with respect to the marginal breakdown of the amalgam restoration, can be supported by stress calculations. [Journal Article; In English; United States

Distributed crack analysis of ceramic inlays

In all-ceramic restorations, crack formation and propagation phenomena are of major concern, since they may result in intra-oral fracture. The objective of this study was calculation of damage in porcelain MOD inlays by utilization of a finite-element (FE) implementation of the distributed crack theory. Damage is defined as the parameter that describes the local decrease of stiffness caused by microdefects. In the simulated MOD ceramic inlay, the crack initiation starts at the internal occlusal surface near the pulpo-axial line angle. This initiation is invisible from the external surface and cannot be detected by the clinician. The crack initiation at the internal surface started as soon as 55-60% of the loading needed for complete fracture was reached. The use of FE techniques for calculation of the fracture in loaded ceramic inlays offers prospects for further detailed study of the crack behavior, including three-dimensional modeling and cyclic loading situations

Continuum damage mechanics for softening of brittle materials

Continuum 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

Gradient enhanced damage for quasi-brittle materials

Conventional continuum damage descriptions of material degeneration suffer fromloss of well-posedness beyond a certain level of accumulated damage. As aconsequence, numerical solutions are obtained which are unacceptable from aphysical point of view. The introduction of higher-order deformationgradients in the constitutive model is demonstrated to be an adequate remedyto this deficiency of standard damage models. A consistent numericalsolution procedure of the governing partial differential equations ispresented, which is shown to be capable of properly simulating localizationphenomena

Virtual analysis of stresses in human teeth restored with esthetic posts

The use of intra-radicular posts for rebuilding of damaged teeth is a normal practice in contemporary dentistry. However, dental roots restored with posts are subjected to the risk of failure under occlusal loads, particularly in cases of small dentin thickness. This study adopted the finite element analysis to compare the elastic stress distribution in simulated endodontically treated maxillary central incisor restored with two different esthetic posts, a ceramic post and a prefabricated fiber glass post. Under masticatory load, the shear stress and von Mises equivalent stress were determined for the different regions of the two models. The results demonstrated that stress concentrations occurred mainly in the cervical dentin in the prefabricated fiber glass post model. The ceramic post model presented stress concentration in a region limited to the proper post adjacent to its apical end, thus preserving the root dentin