4 research outputs found
An Eulerian hybrid WENO centered-difference solver for elastic-plastic solids
We present a finite-difference based solver for hyper-elastic and viscoplastic systems using a hybrid of the weighted essentially non-oscillatory (WENO) schemes combined with explicit centered difference to solve the equations of motion expressed in an Eulerian formulation. By construction our approach minimizes both numerical dissipation errors and the creation of curl-constraint violating errors away from discontinuities while avoiding
the calculation of hyperbolic characteristics often needed in general finite-volume schemes. As a result of the latter feature, the formulation allows for a wide range of
constitutive relations and only an upper-bound on the speed of sound at each time is required to ensure a stable timestep is chosen. Several one- and two-dimensional examples are presented using a range of constitutive laws with and without additional plastic modeling. In addition we extend the reflection technique combined with ghost-cells to enforce fixed boundaries with a zero tangential stress condition (i.e. free-slip)
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Finite volume modelling of low speed structural impact problems
Two investigations are described in this thesis on the common theme of applying finite volume methods to simulate structural impact problems. The first investigation is the application of the Eulerian Finite Volume Method (EFVM) to simulate the low-speed impact of ductile materials. Simulation results are validated against experiment showing that it is possible to accurately predict crater deformation profiles over the low speed speed impact regime for different projectile and substrate materials. We demonstrate how the rate dependent Johnson-Cook plasticity model is crucial to ensure correspondence to experiment.
The second investigation is concerned with the application of EFVM to simulate impact damage to thin polymeric coatings applied to the surface of metals. The aim of this work is to demonstrate how new simulation methods can help understand coating damage due stone impact. We simulate the debonding phenomenon of single layer coatings under impact by setting boundary conditions at the plate and paint interface. We show how EFVM can capture two limits of interface behaviour, sliding and separation 'slip' at one extreme and zero sliding 'welded' at the other. Results compare well to previously published experimental and simulation work, and our own finite element simulations in Abaqus. We also demonstrate how EFVM brings greater robustness and stability compared to FEM when modelling adhesive failure and higher energy impact penetration
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On the Equivalence between the Additive Hypo-Elasto-Plasticity and Multiplicative Hyper-Elasto-Plasticity Models and Adaptive Propagation of Discontinuities
Ductile and brittle failure of solids are closely related to their plastic and fracture behavior, respectively. The two most common energy dissipation mechanisms in solids possess distinct kinematic characteristics, i.e. large strain and discontinuous displacement, both of which pose challenges to reliable, efficient numerical simulation of material failure in engineering structures. This dissertation addresses the reliability and efficiency issues associated with the kinematic characteristics of plasticity and fracture.
At first, studies are conducted to understand the relation between two well recognized large strain plasticity models that enjoy widespread popularity in numerical simulation of plastic behavior of solids. These two models, termed the additive hypo-elasto-plasticity and multiplicative hyper-elasto-plasticity models, respectively, are regarded as two distinct strategies for extending the classical infinitesimal deformation plasticity theory into the large strain regime. One of the most recent variants of the additive models, which features the logarithmic stress rate, is shown to give rise to nonphysical energy dissipation during elastic unloading. A simple modification to the logarithmic stress rate is accordingly made to resolve such a physical inconsistency. This results in the additive hypo-elasto-plasticity models based on the kinetic logarithmic stress rate in which energy dissipation-free elastic response is produced whenever plastic flow is absent. It is then proved that for isotropic materials the multiplicative hyper-elasto-plasticity models coincide with the additive ones if a newly discovered objective stress rate is adopted. Such an objective stress
rate, termed the modified kinetic logarithmic rate, reduces to the kinetic logarithmic rate in the absence of strain-induced anisotropy which is characterized as kinematic hardening in the present dissertation.
In the second part of the dissertation, the computational complexity of finite element analysis of the onset and propagation of interface cracks in layered materials is addressed. The study is conducted in the context of laminated composites in which interface fracture (delamination) is a dominant failure mode. In order to eliminate the complexities of remeshing for constant initiation and propagation of delamination, two hierarchical approaches, the extended finite element method (XFEM) and the s-version of the finite element method (s-method) are studied in terms of their effectiveness in representing displacement discontinuity across delaminated interfaces. With one single layer of 20-node serendipity solid elements resolving delamination-free response of the layered materials, it is proved that the delamination representations based on the s-method and the XFEM result in the same discretization space as the conventional non-hierarchical ply-by-ply approach which employs one layer of solid elements for each ply as well as double nodes on delaminated interfaces. Delamination indicators based on the s-method representation of delamination are then proposed to detect the onset and propagation of delamination. An adaptive methodology is accordingly developed in which the s-method displacement field enrichment for delamination is adaptively added to interface areas with high likelihood of delamination. Numerical examples show that the computational cost of the adaptive s-method is significantly lower than that incurred by the conventional ply-by-ply approach despite the fact that the two approaches produce practically identical results
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The Particle Based Moving Interface Method for Soft Matter Mechanics and Fluid/membrane Interactions with Applications to Biological Cells
The mechanics of the interaction between a fluid and a soft interface (such as an elastic membrane or shell) undergoing large deformations appears in many places, such as in biological systems or industrial processes. We present here an Eulerian approach that describes the mechanics of an interface and its interactions with a surrounding fluid via the so-called Navier boundary condition. The interface is modeled as a curvilinear surface with arbitrary mechanical properties across which discontinuities in pressure and tangential fluid velocity can naturally be enforced using a modified version of the extended finite element method. The tracking and evolution of the membrane is then handled with the Grid Based Particle method, and the handling of complex singular boundary conditions around sharp corner is accounted for with the use of an asymptotic/numerical matching method. We show that this method is ideal to describe large membrane deformations, enforce volume constraints, and Navier boundary conditions on the interface with velocity/pressure discontinuities. The method is applied to the study of the filtration of deformable particles through a fibrous network, and an the equivalent permeabilities with respect to the fluid and particles are estimated. The method is then adapted to the study of an elastic material in an Eulerian framework and is shown to be capable of handling arbitrarily large deformations, which is ideal for the study of biological problems