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Alberty, Jochen; Carstensen, Carsten; Funken, Stefan A.; Klose, Roland

doi:10.1007/s00607-002-1459-8

Cited by 102 publications

(29 citation statements)

References 8 publications

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“…To investigate stress field at divergent plate boundaries, we applied a finite element method (FEM) for elastostatic problems [Alberty et al, 2002]. We considered a two-dimensional cross section and model the brittle crust as a rectangular slab of elastic material.…”

Section: Appendix A: Density Modelmentioning

confidence: 99%

Forecasting the path of a laterally propagating dike

2015

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An important aspect of eruption forecasting is predicting the path of propagating dikes. We show how lateral dike propagation can be forecast using the minimum potential energy principle. We compare theory to observed propagation paths of dikes originating at the Bárðarbunga volcano, Iceland, in 2014 and 1996, by developing a probability distribution for the most likely propagation path. The observed propagation paths agree well with the model prediction. We find that topography is very important for the model, and our preferred forecasting model considers its influence on the potential energy change of the crust and magma. We tested the influence of topography by running the model assuming no topography and found that the path of the 2014 dike could not be hindcasted. The results suggest that lateral dike propagation is governed not only by deviatoric stresses but also by pressure gradients and gravitational potential energy. Furthermore, the model predicts the formation of curved dikes around cone‐shaped structures without the assumption of a local deviatoric stress field. We suggest that a likely eruption site for a laterally propagating dike is in topographic lows. The method presented here is simple and computationally feasible. Our results indicate that this kind of a model can be applied to mitigate volcanic hazards in regions where the tectonic setting promotes formation of laterally propagating vertical intrusive sheets.

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Section: Appendix A: Density Modelmentioning

confidence: 99%

Forecasting the path of a laterally propagating dike

2015

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“…If the reader is interested in reproduce the results, the code is also available to download at the link https://github.com/ diogocecilio/FEM. 1…”

Section: Examplesmentioning

confidence: 99%

“…For each gauss point the routine Contribute is called and the matrix form B T CB is computed, and the final stiffness matrix (39) is the sum of the nine contributions. 1 The code was written the Wolfram Mathematica 11.0.1.0 version.…”

Section: Examplementioning

confidence: 99%

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A finite element elasticity programming in Mathematica software

Cecílio

Santos

2018

Comp Applic In Engineering

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Modern software's allow computers to perform symbolic calculations in addition to simple numerical computations for which they were originally designed. This fact opens new possibilities in numerical simulation. In this paper a finite element implementation using the commercial software Wolfram Mathematica is used to solve a plane stress elasticity problem. The code adaptability from the provided examples to more challenging problems can easily be performed using the present code. Numerical examples with post‐processing illustrates the new tool and its flexibility. It has been proven in this study the feasibility of Wolfram Mathematica in learning and programming finite element methods for the solution of two‐dimensional problems in elasticity.

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“…Following [15] and [6] a common way to formulate linearized elastoplasticity leads to the relations − div σ = f, σ = C(ε(u) − p), . P ∈ ∂I S (Σ) (1) for the displacement u, stresses σ and plastic strain p, complemented by boundary and initial conditions. The fields Σ and P are generalized versions of σ and p respectively, that also include inner variables to control hardening;…”

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confidence: 99%

Adaptive time stepping in elastoplasticity

Bartels¹,

Keck²

2021

Discrete &Amp; Continuous Dynamical Systems - S

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Using rate-independent evolutions as a framework for elastoplasticity, an a posteriori bound for the error introduced by time stepping is established. A time adaptive algorithm is devised and tested in comparison to a method with constant time steps. Experiments show that a significant error reduction can be obtained using variable time steps.2010 Mathematics Subject Classification. Primary: 65N12, 74C05.

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Cited by 102 publications

References 8 publications

Forecasting the path of a laterally propagating dike

Forecasting the path of a laterally propagating dike

A finite element elasticity programming in Mathematica software

Adaptive time stepping in elastoplasticity

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