Browsing by Subject "Large deformations"

Now showing 1 - 3 of 3

Open Access
A geometrically exact formulation of peridynamics
(Elsevier BV, 2021-02) Javili, Ali; McBride, A. T.; Steinmann, P.
The main objective of this contribution is to develop a geometrically exact peridynamics (PD) formulation wherein the basic elements of continuum kinematics are preserved. The proposed formulation accounts for large deformations and is variationally consistent. We distinguish between one-, two- and three-neighbour interactions. One-neighbour interactions recover the original (bond-based) PD formalism. Two- and three-neighbour interactions are fundamentally different to state-based PD. We account for material frame indifference and provide a set of appropriate arguments for objective interaction potentials accordingly. This contribution is presented in a manner such that the established theory is immediately suitable for computational implementation. From a computational perspective, the proposed strategy is fully implicit and the quadratic rate of convergence associated with the Newton–Raphson scheme is observed. Finally, we demonstrate the capability of our proposed framework via a series of numerical examples at large deformations.
Open Access
A mixed formulation of mortar-based contact with friction
(Elsevier, 2013) Temizer, I.
A classical three-field mixed variational formulation of frictionless contact is extended to the frictional regime. The construction of the variational framework with respect to a curvilinear coordinate system naturally induces projected mortar counterparts of tangential kinetic and kinematic quantities while automatically satisfying incremental objectivity of the associated discrete penalty-regularized mortar constraints. Mixed contact variables that contribute to the boundary value problem are then obtained through unconstrained, lumped or constrained recovery approaches, complemented by Uzawa augmentations. Patch tests and surface locking studies are presented together with local and global quality monitors of the contact interactions in two- and three-dimensional settings at the infinitesimal and finite deformation regimes. © 2012 Elsevier B.V.
Open Access
A unifying approach towards the geometrical instabilities of compressible, multilayer domains
(2022-07) Bakiler, Ayşe Derya
Instabilities that arise in layered systems have been a riveting course of study for the past few decades, having found utility in various fields, while also being frequently observed in biological systems. However, the large deformation bifurcation analysis of compressible domains remains vastly understudied compared to the incompressible case. In this work, we present a unifying approach for the instability analysis of multilayer compressible elastic domains under plane deformations, also extending the approach to include the general interface model and to capture growth-induced instabilities. First, a linear elastic, displacement-based approach to capture bilayer wrinkling is taken, outlining the basics of such an approach. Then, the large-deformation incremental analysis for a rectangular, compressible, hyperelastic domain under plane deformations is developed, which serves as a generic framework for other geometries. This framework is applied to beam, half-space, bilayer and trilayer structures. Next, the framework is extended to account for the general interface model, looking into coated half-spaces, coated beams, and bilayers with interfaces. Finally, the framework is derived to account for both compression and growth. Obtained analytical results for the onset of wrinkling are compared with computational simulations using the finite element method (FEM) enhanced with eigenvalue analysis, cultivating excellent agreements between analytical and numerical results all across the material and geometrical parameter spectrum, and portraying clearly the significant effect of compressibility on bifurcation behavior. The analytical framework presented here provides grounds for further works on other modes of instabilities and more complex geometries.