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| 2. |
- Alastrue, V., et al.
(författare)
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On the use of non-linear transformations for the evaluation of anisotropic rotationally symmetric directional integrals. Application to the stress analysis in fibred soft tissues
- 2009
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 1097-0207 .- 0029-5981. ; 79:4, s. 474-504
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Tidskriftsartikel (refereegranskat)abstract
- Microsphere-based constitutive models are a helpful tool in the modelling of materials with a microstructure composed of contributing elements directionally arranged. This is the case, for instance, for fibred soft tissues. In these models, the macroscopic mechanical behaviour is obtained from the integration of the micro-structural contribution of each component (e.g. each fibre) over the surface of an underlying microsphere, which allows incorporating the mechanical features of the micro-constituents to the macroscopic response. The combination of this sort of models and the associated numerical techniques constitutes a powerful modelling tool for which an efficient integration scheme is required. In this regard, the unit sphere discretizations proposed by Bazant and Oh (ZAMM-J Appl Math Mech Z Angew Math Mech 1986; 66(1):37-49) have been used for the integration of the microscopic contributions in isotropic materials. Nevertheless, the inclusion of anisotropy has important implications with regard to the integration scheme, since very fine discretizations are needed to perform the integration accurately, causing the integration process to be very costly. In addition, the storage of internal variables at each integration direction of every integration point is required for constitutive models based on the use of internal variables at the micro-structural level, which renders this approach rather complex and memory demanding. In order to reduce the number of necessary integration directions, several non-linear transformations for the integration of rotationally symmetric functions over the Surface of the unit sphere are here presented. Their accuracy in the integration of the von Mises orientation distribution function is evaluated. Furthermore, a hyperelastic microsphere-based constitutive law for the modelling of soft biological tissues is used in order to check the accuracy and computational efficiency of the proposed transformations within a Finite Element context in inhomogeneous deformation problems. Simulation results show the suitability of the proposed methodology in order to accurately approximate the Value of the integrals within reasonable computational costs. Copyright (C) 2009 John Wiley & Sons, Ltd.
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| 3. |
- Battini, Jean-Marc
(författare)
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A rotation-free corotational plane beam element for non-linear analyses
- 2008
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 75:6, s. 672-689
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a plane beam element without rotational degrees of freedom that can be used for the analysis of non-linear problems. The element is based on two main ideas. First, a corotational approach is adopted, which means that the kinematics of the element is decomposed into a rigid body motion part and a deformational part. Next, in the deformational part. the local nodal rotations are extrapolated as a function of the local displacements of the two nodes of the element and the first nodes to the left and right of the element. Six numerical applications are presented in order to assess the performance of the formulation.
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| 6. |
- Englund, Jonas
(författare)
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Efficient algorithm for edge cracked geometries
- 2006
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 1097-0207 .- 0029-5981. ; 66:11, s. 1791-1816
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Tidskriftsartikel (refereegranskat)abstract
- The stress field in a finite, edge cracked specimen under load is computed using algorithms based on two slightly different integral equations of the second kind. These integral equations are obtained through left regularizations of a first kind integral equation. In numerical experiments it is demonstrated that the stress field can be accurately computed. Highly accurate stress intensity factors and T-stresses are presented for several setups and extensive comparisons with results from the literature are made. For simple geometries the algorithms presented here achieve relative errors of less than 10(-10). It is also shown that the present algorithms can accurately handle both geometries with arbitrarily shaped edge cracks and geometries containing several hundred edge cracks. All computations were performed on an ordinary workstation. Copyright (c) 2005 John Wiley & Sons, Ltd.
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| 7. |
- Englund, Jonas
(författare)
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Stable algorithm for the stress field around a multiply branched crack
- 2005
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 1097-0207 .- 0029-5981. ; 63:6, s. 926-946
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Tidskriftsartikel (refereegranskat)abstract
- We present an algorithm for the computation of the stress field around a branched crack. The algorithm is based on an integral equation with good numerical properties. Our equation is obtained through a left regularization of an integral equation of Fredholm's first kind. Complex valued functions involving repeated products of square roots appear in the regularization. A new and effective scheme for correct evaluation of these functions is described. For validation, mode I and II stress intensity factors are computed for simple branched geometries. The relative errors in the stress intensity factors are typically as low as 10(-12). A large scale example is also presented, where a crack with 176 branching points is studied.
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| 8. |
- Esen, Sedat, et al.
(författare)
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Prediction of the non-ideal detonation performance of commercial explosives using the DeNE and JWL++ codes
- 2005
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 64:14, s. 1889-1914
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Tidskriftsartikel (refereegranskat)abstract
- The non-ideal detonation performance of two commercial explosives is determined using the DeNE and JWL++ codes. These two codes differ in that DeNE is based on a pseudo-one-dimensional theory which is valid on the central stream-tube and capable of predicting the non-ideal detonation characteristics of commercial explosives as a function of the explosive type, rock properties and blasthole diameter. On the other hand, JWL++ is a hydrocode running in a 2-D arbitrary Lagrangian-Eulerian code with CALE-like properties and can determine the flow properties in all stream lines within the reaction zone. The key flow properties (detonation velocity, pressure, specific volume, extent of reaction and reaction zone length) at the sonic locus on the charge axis have been compared. In general, it is shown that the flow parameters determined using both codes agree well. The pressure contours determined using the JWL++ are analysed in detail for two explosives at 165 mm blastholes confined in limestone and kimberlite with a view to further investigate the explosive/rock interface. The DeNE and JWL++ codes have been validated using the measured in-hole detonation velocity data.
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| 10. |
- Fagerström, Martin, 1979, et al.
(författare)
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Theory and numerics for finite deformation fracture modelling using strong discontinuities
- 2006
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 66:6, s. 911-948
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Tidskriftsartikel (refereegranskat)abstract
- A general finite element approach for the modelling of fracture is presented for the geometrically nonlinear case. The kinematical representation is based on a strong discontinuity formulation in line with the concept of partition of unity for finite elements. Thus, the deformation map is defined in terms of one continuous and one discontinuous portion, considered as mutually independent, giving rise to a weak formulation of the equilibrium consisting of two coupled equations. In addition, two different fracture criteria are considered. Firstly, a principle stress criterion in terms of the material Mandel stress in conjunction with a material cohesive zone law, relating the cohesive Mandel traction to a material displacement 'jump' associated with the direct discontinuity. Secondly, a criterion of Griffith type is formulated in terms of the material-crack-driving force (MCDF) with the crack propagation direction determined by the direction of the force, corresponding to the direction of maximum energy release. Apart from the material modelling, the numerical treatment and aspects of computational implementation of the proposed approach is also thoroughly discussed and the paper is concluded with a few numerical examples illustrating the capabilities of the proposed approach and the connection between the two fracture criteria. Copyright © 2005 John Wiley & Sons, Ltd.
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