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- Heintz, Per, 1975, et al.
(författare)
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Adaptive strategies and error control for computing material forces in fracture mechanics
- 2004
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 60:7, s. 1287-1299
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Tidskriftsartikel (refereegranskat)abstract
- The concept of material forces pertains to a variation of the inverse motion map while the placement field is kept fixed. From the weak formulation of the self-equilibrating Eshelby (material) stress tensor it turns out that the classical J-integral formulations in fracture mechanics are just special cases due to the choice of particular weight functions. In this contribution, we discuss a posteriori error control of the material forces as part of an adaptive strategy to reduce the discretization error to an acceptable level. The data of the dual problem involves the quite non-conventional tangent stiffness of the (material) Eshelby stress tensor with respect to a variation of the (physical) strain field. The suggested strategy is applied to the common fracture mechanics problem of a single-edged crack, whereby different strategies for computing the J-integral are compared. We also consider the case in which the crack edges are not parallel, i.e. a notch.
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- Heintz, Per, 1975
(författare)
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Finite Element Procedures for the Numerical Simulation of CRack Propagation and Bilateral Contact
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis concerns finite element methods for the numerical simulation of crack propagation including contact formulations for the contact between deformable bodies. The classical integral formulations for theenergy release rate at crack growth are considered and adaptive algorithms are developed. In addition, we derive three different strategies for computing the material forces at a cracktip and the different strategies are compared. A new stabilized Lagrange multipliermethod is presented where the multipliers are discretized with global polynomials. The method allows for non-matching meshes at the contact interface and the delicate problem of integrating products of basisfunctions between the master and slave body is alleviated. A discontinuous Galerkin method for cutting elements independent of the mesh structure is extended to the problem of a propagating crack whereby different strategies for computing the crack driving force areconsidered.
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- Heintz, Per, 1975, et al.
(författare)
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Stabilized Lagrange multiplier methods for elastic contact with friction
- 2006
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 195:33-36, s. 4323-4333
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Tidskriftsartikel (refereegranskat)abstract
- In most finite element (FE) codes contact is checked only at the nodes, corresponding to the use of pointwise constraints. However, this approach might not be stable in case the bodies coming into contact have non-matching grids at the contact interface. To alleviate this problem, we propose a stabilized Lagrange multiplier method, based on a global polynomial multiplier, for the finite element solution of (non)linear elastic contact problems with non-matching grids. In particular, our approach allows us to avoid integrating products of different finite element basis functions on the surface meshes at the contact zone.
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