Author
Alexander Janz
Bio: Alexander Janz is an academic researcher from Karlsruhe Institute of Technology. The author has contributed to research in topics: Discretization & Finite element method. The author has an hindex of 5, co-authored 15 publications receiving 127 citations.
Papers
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TL;DR: A novel formulation for finite strain polyconvex elasticity is presented by introducing a new anisotropic split based on the principal invariants of the right Cauchy–Green tensor, which always ensures polyconcexity of the resulting strain energy function.
57 citations
TL;DR: In this paper, a mixed variational formulation for the development of energy-momentum consistent (EMC) time-stepping schemes is proposed, which accommodates mixed finite elements based on a Hu-Washizu-type variational approach in terms of displacements, Green-Lagrangian strains, and conjugated stresses.
Abstract: Summary
In this paper, a mixed variational formulation for the development of energy–momentum consistent (EMC) time-stepping schemes is proposed. The approach accommodates mixed finite elements based on a Hu–Washizu-type variational formulation in terms of displacements, Green–Lagrangian strains, and conjugated stresses. The proposed discretization in time of the mixed variational formulation under consideration yields an EMC scheme in a natural way. The newly developed methodology is applied to a high-performance mixed shell finite element. The previously observed robustness of the mixed finite element formulation in equilibrium iterations extends to the transient regime because of the EMC discretization in time. Copyright © 2016 John Wiley & Sons, Ltd.
34 citations
TL;DR: A new approach to the design of energy–momentum consistent algorithms for nonlinear elastodynamics is proposed, which yields an EM consistent semi-discrete formulation in the special case of a purely displacement-based method.
24 citations
TL;DR: A new one-step second order accurate energy–momentum (EM) preserving time integrator for reversible electro-elastodynamics is shown to be extremely useful for the long-term simulation of electroactive polymers (EAPs) undergoing massive strains and/or electric fields.
20 citations
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01 Jan 2020
TL;DR: This chapter provides an extensive overview of the literature on the so-called phase-field fracture/damage models (PFMs), particularly, for quasi-static and dynamic fracture of brittle and quasi-brittle materials, from the points of view of a computational mechanician.
Abstract: Fracture is one of the most commonly encountered failure modes of engineering materials and structures. Prevention of cracking-induced failure is, therefore, a major concern in structural designs. Computational modeling of fracture constitutes an indispensable tool not only to predict the failure of cracking structures but also to shed insights into understanding the fracture processes of many materials such as concrete, rock, ceramic, metals, and biological soft tissues. This chapter provides an extensive overview of the literature on the so-called phase-field fracture/damage models (PFMs), particularly, for quasi-static and dynamic fracture of brittle and quasi-brittle materials, from the points of view of a computational mechanician. PFMs are the regularized versions of the variational approach to fracture which generalizes Griffith's theory for brittle fracture. They can handle topologically complex fractures such as initiation, intersecting, and branching cracks in both two and three dimensions with a quite straightforward implementation. One of our aims is to justify the gaining popularity of PFMs. To this end, both theoretical and computational aspects are discussed and extensive benchmark problems (for quasi-static and dynamic brittle/cohesive fracture) that are successfully and unsuccessfully solved with PFMs are presented. Unresolved issues for further investigations are also documented.
290 citations
TL;DR: In this article, a modified Newton solver for phase-field fracture propagation with Jacobian matrix modification is presented, which switches smoothly between full Newton and Newton-like steps to solve the nonlinear flow problem.
120 citations
TL;DR: In this article, the authors present a computational framework to account for three-dimensional fracture in ductile solids undergoing large elastic and plastic deformations, based on a triple multiplicative decomposition of the deformation gradient and an exponential update scheme for the return map in the time discrete setting.
93 citations
TL;DR: In this paper, it was shown that for a practical setting, where the internal length scale and the spacing of the discretisation are small but finite, the observed discrepancy partially stems from the fact that numerical studies consider specimens of a finite length, and partially relates to the irreversibility introduced when casting the variational theory for brittle fracture in a damage-like format.
69 citations
TL;DR: In this article, the authors investigated the effect of plasticity on dynamic fracture propagation and observed the increment of the instantaneous dynamic stress intensity factor during the acceleration stage of the crack without introducing a rate dependent critical fracture energy.
60 citations