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- Grymer, Mikkel, 1980, et al.
(författare)
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Modeling the Grain Size Effect using Gradient Hardening and Damage in Crystal (Visco) Plasticity
- 2006
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Ingår i: III European Conference on Computational Mechanics, Solids, Structures and Coupled Problems in Engineering, June 5-8 2006, Lisbon, Portugal, C.A. Mota Soares et.al. (eds.). - 1402049943 ; , s. 69-
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The macroscopic behavior of a polycrystalline material (metal) depends on the characteristicsof the grain structure. Among the important properties are the size and morphologyof the grains, volume fraction of different phases, and the subgrain material modeling. In thiscontribution we put emphasis on the modeling and numerical simulation of the grain size dependenceon the macroscopic response.Within the framework of continuum thermodynamics and finite strains, we formulate a subgrainmaterial model that comprises crystal (visco)plasticity and gradient hardening. The gradienthardening gives a contribution from each slip system which is added to the well establishedlocal hardening. The grain interaction in a Representative Volume Element is resolvedusing finite elements. In order to solve the arising coupled field equations (for the displacementsand the gradient hardening in the slip systems) a so-called dual mixed FE algorithm isadopted. Linear displacements and gradients are assumed in a basic set-up. As an alternative,quadratic displacements are introduced, while the linear gradient approximation is retained.Dirichlet boundary conditions on the RVE (corresponding to a given macro-scale deformationgradient) are adopted, and various prolongation conditions inside the RVE are investigated:The Classical Taylor assumption, Relaxed Taylor assumption (to grain boundaries only) anda fully unconstrained local displacement field. In particular, the two first approaches may beused to provide a good start solution for the fully unconstrained (most general) approach. Allcomputations are restricted to 2D.
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- Hansbo, Peter, et al.
(författare)
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Nitsche's method combined with space-time finite elements for ALE fluid-structure interaction problems
- 2004
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 193:39-41, s. 4195-4206
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Tidskriftsartikel (refereegranskat)abstract
- We propose a weak method for handling the fluid-structure interface in finite element fluid-structure interaction based on Nitsche's method [Abh. Math. Univ. Hamburg 36 (1971) 9]. We assume transient incompressible Newtonian flow and, for the structure, undamped linear elasticity. For the time-discretization, we use the time-continuous (energy conserving) Galerkin method for the structure, and for the fluid we employ the time-discontinuous Galerkin method. This means that the velocity becomes piecewise constant on each timestep for the fluid, matching the time-derivative of the displacements in the solid which is also piecewise constant over a time step. We formulate the method and report some numerical examples using space-time oriented elements for the fluid in order to mimic Lagrangian or ALE-type simulations.
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- Svedberg, Thomas, 1968
(författare)
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On the Modelling and Numerics of Gradient-Regularized Plasticity Coupled to Damage
- 1999
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is primarily concerned with issues that arise in conjunction with the modelling of localization phenomena in solids using gradient-regularized plasticity with coupling to damage. The thermodynamic framework for a larger class of models is established, whereby gradients of the internal variables are included as arguments of the free energy. Small as well as large deformation formulations are discussed. In particular, the dissipation inequality provides constraints on the choice of boundary conditions for the gradient-regularized variables. A perturbation analysisis is presented that establishes the localization condition for a homogeneous thermodynamic state. For the numerical investigations a prototype model is chosen that is characterized by nonlinear local hardening, linear gradient hardening and (local) scalar damage, while the local format of the von Mises yield criterion is adopted. The incremental format of the constitutive equations is obtained upon using the implicit (exponential) Backward Euler algorithm to integrate the evolution equations in a fashion that is similar to that of local theory. The appropriate mixed variational format of the constitutive problem, which is a full-fledged boundary value problem, is proposed. The corresponding mixed finite element algorithm is discussed in some detail. An adaptive finite element strategy is also developed (in the small deformation setting), > whereby the underlying a > posteriori error computation is carried out in the energy norm, that is naturally associated with the mixed variational format of the constitutive problem. A brief comparison of the nonlocal (averaging) and gradient theories of plasticity is presented, whereby a thermodynamically consistent theory of the nonlocal format is developed in the same spirit as for gradient theory. The comparison concerns both formulation and numerics. Numerical examples of a one-dimensional tension bar and a two-dimensional plate in plane stress or plane strain are examined to show the performance of the proposed models and algorithm(s). The results are found to be insensitive to the mesh design, even for unstructured meshes, and some analytical predictions of the shear band orientation are confirmed.
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