SearcharxivSearch

arXiv · 2005.04965

A finite-strain model for incomplete damage in elastoplastic materials

Abstract

We address a three-dimensional model capable of describing coupled damage and plastic effects in solids at finite strains. Formulated within the variational setting of {\it generalized standard materials}, the constitutive model results from the balance of conservative and dissipative forces. Material response is rate-independent and associative and damage evolution is unidirectional. We assess the model features and performance on both uniaxial and non-proportional biaxial tests. The constitutive model is then complemented with the quasistatic equilibrium system and initial and boundary conditions. We produce numerical simulations with the help of the powerful multiphysics finite element software NETGEN/NGSolve. We show the flexibility of the implementation and run simulations for various 2D and 3D settings under different choices of boundary conditions and possibly in presence of pre-damaged regions.

Explore related subjects

Keep this discovery

BibTeXRIS

David Melching, Michael Neunteufel, Joachim Schöberl, Ulisse Stefanelli. 2020-05-11. A finite-strain model for incomplete damage in elastoplastic materials. https://doi.org/10.1016/j.cma.2020.113571

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Well-posedness of the two-dimensional unsteady Prandtl system in Sobolev space with degenerate critical points

This paper is devoted to the well-posedness of classical Prandtl equations in a finite order Sobolev space. For a initial data with degenerate critical points and general outflow, we obtain the local-in-time existence and uniqueness of the solution to the Prandtl equations in a Sobolev space, by introducing a new iteration scheme and linear cancelation. This result shows that Oleinik's monotonicity condition is not a necessary condition for the Prandtl equations to be well-posed in Sobolev spaces and provides evidence to demonstrate that zero shear stress does not necessarily lead to boundary layer separation in two-dimensional unsteady boundary layers.

math.AP

Global existence and time decay for a bipolar Euler-Poisson system with one pressureless and undamped fluid

We study the Cauchy problem for a three-dimensional bipolar Euler--Poisson system in which one fluid is pressureless and undamped, while the other is subject to momentum relaxation. For sufficiently small smooth perturbations of a constant equilibrium, we prove the global existence and uniqueness of smooth solutions under an irrotationality assumption on the initial velocity of the pressureless fluid, together with algebraic time-decay estimates. The main difficulty is that the velocity of the pressureless fluid is dissipated only indirectly through the Poisson coupling, and this mechanism degenerates strongly at high frequencies, leading to a regularity-loss structure. We overcome this difficulty by combining refined Green-function estimates, a low--middle--high frequency decomposition, and high-order nonlinear energy estimates adapted to the asymmetric regularity hierarchy. The result establishes a global small-data theory for this asymmetric regime, in which pressure and damping are simultaneously absent from the same fluid.

math.AP

Boundary layer of 2D Chemotaxis Navier-Stokes equations with logarithmic Sensitivity. II. viscous vanishing limit

This is the second part of a two-part work concerning boundary layer solutions to the coupled Chemotaxis-Navier-Stokes system in the two-dimensional half-space. In the present work, we address the convergence of boundary layer solutions to singular chemotaxis-fluid equations under slip boundary conditions with respect to the chemical diffusion-viscosity parameter $\varepsilon$ in the two-dimensional half-plane. More precisely, we show that the boundary layer for $\varepsilon>0$ (viscous convection coefficient) converges to the superposition of the outer layer (solution with $\varepsilon=0$) and the inner layer as $\varepsilon\rightarrow0$. The outer and inner profiles are explicitly derived as in the first part\cite{WWZ}. Furthermore, the well-posedness results of the coupled Chemotaxis-Navier-Stokes system in conormal Sobolev spaces will be presented in Appendix. They answer the question mentioned in the first part of the two-part work. This study could help the understanding of the chemotactic movement of aerobic bacteria to the water-air surface observed experimentally in fluids, and enrich the theoretical results of boundary layer in chemotactic fluid models.

math.AP