Showing papers on "Displacement field published in 2008"

Three dimensional image correlation from X-Ray computed tomography of solid foam

Abstract: A new methodology is proposed to estimate 3D displacement fields from pairs of images obtained from X-ray computed microtomography (XCMT). Contrary to local approaches, a global approach is followed herein that evaluates continuous displacement fields. Although any displacement basis may be considered, the procedure is specialized to finite element shape functions. The method is illustrated with the analysis of a compression test on a polypropylene solid foam (independently studied in a companion paper). A good stability of the measured displacement field is obtained for cubic element sizes ranging from 16 to 6 voxels.

The simulation of dynamic crack propagation using the cohesive segments method

Abstract: The cohesive segments method is a finite element framework that allows for the simulation of the nucleation, growth and coalescence of multiple cracks in solids. In this framework, cracks are introduced as jumps in the displacement field by employing the partition of unity property of finite element shape functions. The magnitude of these jumps are governed by cohesive constitutive relations. In this paper, the cohesive segments method is extended for the simulation of fast crack propagation in brittle solids. The performance of the method is demonstrated in several examples involving crack growth in linear elastic solids under plane stress conditions: tensile loading of a block; shear loading of a block and crack growth along and near a bi-material interface.

On velocity gradients in PIV interrogation

Abstract: This paper presents a generalization of the description of the displacement-correlation peak in particle image velocimetry (PIV) to include the effects due to local velocity gradients at the scale of the interrogation domain. A general expression is derived that describes the amplitude, location and width of the displacement-correlation peak in the presence of local velocity gradients. Simplified expressions are obtained for the peak centroid and peak width for simple non-uniform motions. The results confirm that local gradients can be ignored provided that the variation of the displacement within the interrogation domain does not exceed the (mean) particle-image diameter. An additional bias occurs for a spatially accelerating or decelerating fluid, which implies an artificial "particle inertia" even when the particles can be considered as ideal tracers.

Simulations of textile composite reinforcement draping using a new semi-discrete three node finite element

Abstract: Continuous and discrete approaches for forming simulations of textile performs both involve difficulties and drawbacks The semi-discrete method is an alternative based on a meso-macro approach It is based on specific finite elements made of a discrete number of the components of the textile at lower scale Their strain energy in the interpolated displacement field leads to the nodal interior loads of the element In this paper a new three node element is proposed It is made up of warp and weft fibres, the tensile and in plane shear energy of which are considered The directions of the warp and weft yarns are arbitrary with regard to the element sides That is very important in case of simultaneous multiply draping simulations and when using remeshing The determination of the material data necessary to the simulation from standard tensile and bias tests is straightforward A set of elementary tests and mono and multi-ply draping shows the efficiency of the approach

Temporal Surface Tracking Using Mesh Evolution

Abstract: In this paper, we address the problem of surface tracking in multiple camera environments and over time sequences. In order to fully track a surface undergoing significant deformations, we cast the problem as a mesh evolution over time. Such an evolution is driven by 3D displacement fields estimated between meshes recovered independently at different time frames. Geometric and photometric information is used to identify a robust set of matching vertices. This provides a sparse displacement field that is densified over the mesh by Laplacian diffusion. In contrast to existing approaches that evolve meshes, we do not assume a known model or a fixed topology. The contribution is a novel mesh evolution based framework that allows to fully track, over long sequences, an unknown surface encountering deformations, including topological changes. Results on very challenging and publicly available image based 3D mesh sequences demonstrate the ability of our framework to efficiently recover surface motions .

Analysis of plates and laminates using the natural neighbour radial point interpolation method.

Abstract: In this work the natural neighbour radial point interpolation method (NNRPIM) is extended for the analysis of thick plates and laminates. In order to define the displacement field and the strain field the Reissner–Mindlin plate theory is considered. The nodal connectivity and the node dependent integration background mesh are constructed resorting to the Voronoi tessellation and to the Delaunay triangulation. Within NNRPIM the obtained shape functions pass through all nodes inside the influence-cell providing shape functions with the delta Kronecker property. Optimization tests and examples of well-known benchmark examples are solved in order to prove the high accuracy and convergence rate of the proposed method.

A Method for Gradient Enhancement of Continuum Damage Models

Abstract: A method for the regularization of continuum damage material models based on gradient-type enhancement of the free-energy functional is presented. Direct introduction of the gradient of the damage variable would require C 1 interpolation of the displacements, which is a complicated task to achieve with quadrilateral elements. Therefore a new variable field is introduced, which makes the model non-local in nature, while preserving C 0 interpolation order of the variables at the same time. The strategy is formulated as a pure minimization problem, therefore the LBB-condition does not apply in this case. However, we still take the interpolation of the displacement field one order higher than the interpolation of the field of additional (non-local) variables. That leads to increased accuracy and removes the post-processing step necessary to obtain consistent results in the case of equal interpolation order. Several numerical examples which show the performance of the proposed gradient enhancement are presented. The pathological mesh dependence of the damage model is efficiently removed, together with the difficulties of numerical calculations in the softening range. Calculations predict a development of the damage variable which is mesh-objective for fixed internal material length. When utilizing conventional inelastic material models with softening effects, the presence of softening leads to ill-posed boundary value problems due to the loss of ellipticity of the governing field equations. Ill-posedness manifests itself by the fact that the resulting algebraic system has no unique solution or by a strong mesh dependence of the obtained results. For softening material behavior the deformation tends to localize in a narrow band, the band width only restricted by the mesh resolution. To overcome this problem there are several strategies proposed that take into consideration an internal material length scale. The most effective ones introduce non-local terms in the model. That task can be accomplished following two approaches: integral-type and gradient-type. The integral strategy introduces non-local variables as weighted averages of the local internal variables of the

Digital Image Mechanical Identification (DIMI)

Abstract: A continuous pathway from digital images acquired during a mechanical test to quantitative identification of a constitutive law is presented herein based on displacement field analysis. From images, displacement fields are directly estimated within a finite element framework. From the latter, the application of the equilibrium gap method provides the means for rigidity field evaluation. In the present case, a reconditioned formulation is proposed for a better stability. Last, postulating a specific form of a damage law, a linear system is formed that gives a direct access to the (non-linear) damage growth law in one step. The two last procedures are presented, validated on an artificial case, and applied to the case of a biaxial tension of a composite sample driven up to failure. A quantitative estimate of the quality of the determination is proposed, and in the last application, it is shown that no more than 7% of the displacement field fluctuations are not accounted for by the determined damage law.

A New Method for Registration-Based Medical Image Interpolation

Abstract: A new technique is presented for interpolating between grey-scale images in a medical data set. Registration between neighboring slices is achieved with a modified control grid interpolation algorithm that selectively accepts displacement field updates in a manner optimized for performance. A cubic interpolator is then applied to pixel intensities correlated by the displacement fields. Special considerations are made for efficiency, interpolation quality, and compression in the implementation of the algorithm. Experimental results show that the new method achieves good quality, while offering dramatic improvement in efficiency relative to the best competing method.

A phase field model for fracture

Abstract: The variational formulation of brittle fracture as formulated for example by Francfort and Marigo in [1], where the total energy is minimized with respect to any admissible crack set and displacement field, allows the identification of crack paths, branching of preexisting cracks and even crack initiation without additional criteria. For its numerical treatment a continuous approximation of the model in the sense of Γ-convergence has been presented by Bourdin in [2]. In the regularized Francfort–Marigo model cracks are represented by an additional field variable (secondary variable) s∈[0,1] which is 0 if the material is cracked and 1 if it is undamaged. In this work, we reinterpret the crack variable as a phase field order parameter and address cracking as a phase transition problem. The crack growth is governed by the evolution equation of the order parameter which resembles the Ginzburg–Landau equation. The numerical treatment is done by finite elements combined with an implicit Euler scheme for the time integration. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Local friction at a sliding interface between an elastomer and a rigid spherical probe.

Abstract: This paper reports on spatially resolved measurements of the shear stress distribution at a frictional interface between a flat rubber substrate and a glass lens. Silicone rubber specimens marked close to their surface by a colored pattern have been prepared in order to measure the surface displacement field induced by the steady-state friction of the spherical probe. The deconvolution of this displacement field then provides the actual shear stress distribution at the contact interface. When a smooth glass lens is used, a nearly constant shear stress is achieved within the contact. On the other hand, a bell-shaped shear stress distribution is obtained with rough lenses. These first results suggest that simple notions of real contact area and constant interface shear stress cannot account for the observed changes in local friction when roughness is varied.

A regularized XFEM model for the transition from continuous to discontinuous displacements

Abstract: This work focuses on the modelling through the extended finite element method of structural problems characterized by discontinuous displacement. As a model problem, an elastic isotropic domain characterized by a displacement discontinuity across a surface is studied. A regularization of the displacement field is introduced depending on a scalar parameter. The regularized solution is defined in a layer. The emerging strain and stress fields are independently modelled using specific constitutive assumptions. In particular, it is shown that the mechanical work spent within the regularization layer can be interpreted as an interface work provided that a spring-like constitutive law is adopted. The accuracy of the integration procedures adopted for the stiffness matrix is assessed, as highly non-linear terms appear. Standard Gauss quadrature is compared with adaptive quadrature and with a new technique, based on an equivalent polynomial approach. One- and two-dimensional results are reported for varying discretization size, regularization parameter, and constitutive parameters. Copyright © 2007 John Wiley & Sons, Ltd.

A thermo-mechanical cohesive zone formulation for ductile fracture

Abstract: The paper addresses the possibility to project both mechanical and thermal phenomena pertinent to the fracture process zone into a cohesive zone. A wider interpretation of the notion cohesive zone is thereby suggested to comprise not only stress degradation due to micro-cracking but also heat generation and energy transport. According to our experience, this widening of the cohesive zone concept allows for a more efficient finite element simulation of ductile fracture. The key feature of the formulation concerns the thermo-mechanical cohesive zone model, evolving within the thermo-hyperelastoplastic continuum, allowing for the concurrent modelling of both heat generation, due to the fracture process, and heat transfer across the fracture process zone. This is accomplished via thermodynamic arguments to obtain the coupled governing equation of motion, energy equation, and constitutive equations. The deformation map is thereby defined in terms of independent continuous and discontinuous portions of the displacement field. In addition, as an extension of the displacement kinematics, to represent the temperature field associated with the discontinuous heat flux across the fracture interface, a matching discontinuous temperature field involving the interface (or band) temperature is proposed. In the first numerical example, concerning dynamic quasi-brittle crack propagation in a thermo-hyperelastoplastic material, we capture the initial increase in temperature close to the crack surface due to the energy dissipating fracture process. In the second example, a novel application of ductile fracture simulation to the process of high velocity (adiabatic) cutting is considered, where some general trends are observed when varying the cutting velocity.

Solutions to intra-ply shear locking in finite element analyses of fibre reinforced materials

Abstract: Intra-ply shear locking results in unrealistic fibre stresses and spurious wrinkling in composite forming simulations. Three remedies were investigated: aligning the mesh, applying reduced integration and using multi-field elements. Several triangular and quadrilateral elements were tested on their capability to avoid locking in a two-dimensional bias extension simulation. The resulting locking-free elements were tested in a realistic three-dimensional drape simulation of a biaxial fabric as well. The new triangular multi-field element seems to be the best locking-free element for unaligned meshes. It has a semi-quadratic in-plane and a linear out-of-plane displacement field. This combination improves the accuracy of the element and avoids contact problems in 3D simulations.

Effect of a compliant fault zone on the inferred earthquake slip distribution

Abstract: [1] We present a new semi-analytic method to evaluate the deformation due to a screw dislocation in arbitrarily heterogeneous and/or anisotropic elastic half plane. The method employs integral transformations to reduce the governing partial differential equations to the integral Fredholm equation of the second kind. Dislocation sources, as well as spatial perturbations in the elastic properties are modeled using equivalent body forces. The solution to the Fredholm equation is obtained in the Fourier domain using a method of successive over-relaxation, and is mapped into the spatial domain using the inverse Fast Fourier Transform. We apply this method to investigate the effect of a soft damage zone around an earthquake fault on the co-seismic displacement field, and on the earthquake slip distribution inferred from inversions of geodetic data. In the presence of a kilometer-wide damage zone with a reduction of the effective shear modulus of a factor of 2, inversions that assume a laterally homogeneous model tend to underestimate the amount of slip in the middle of the seismogenic layer by as much as 20%. This bias may accentuate the inferred maxima in the seismic moment release at depth between 3–6 km suggested by previous studies of large strike-slip earthquakes.