In this study, we present the steps taken for analyzing and simulating a particular type of metamaterial composed of a pantographic substructure which is periodic in space-it is simply a grid. Detailed simulations of a metamaterial is challenging but accurately possible by means of the elasticity theory. These kinds of materials which are ‘substructure depending’ are called metamaterials. Indeed, the main structure can be obtained by means of periodically (or quasi-periodically) arranged substructures which are properly conceived to provide unconventional deformation patterns. The development of additive manufacturing methods, such as 3D printing, allows the design of more complex architectured materials. Significantly less computational cost than the direct numerical simulations. The homogenized model is capable of describing materials response at a This reduced-order model represents a homogenized material on macro-scale with Of the reduced-order model, we utilize a numerical inverse analysis and make use of ad hoc computationalĮxperiments performed by a direct numerical simulation on the microscale with detailed modeling of the
For determining the coefficients in the elastic energy Twisted and bent fibers in plane as well as out of plane. The properties of this reduced-order model are characterized by an elasticĮnergy density that involves second space derivatives of the displacement for capturing the resistance of In order to predict the behavior of such a system in three-dimensionalĬontinuum, a reduced-order model is introduced by means of a bi-dimensional elastic surface accuratelyĭescribing large deformations. Specifically, we consider a composite material with orthogonal, mutually interconnected fibersīuilding a pantographic substructure.
Mechanical properties are investigated for a class of microstructured materials with promisingĪpplications. The numerical analysis is then carried out using the practically important properties of ultra-thin-film materials. Finally, the solution of boundary value problem is obtained in terms of Fourier series. Using Goursat–Kolosov complex potentials, the system of boundary equations is reduced to a system of the integral equations via first-order boundary perturbation method. Kinematic boundary conditions describe the continuous of displacements across the surface and interphase regions. Static boundary conditions are formulated in the form of generalized Young–Laplace equations. In the case of plane strain conditions, the boundary value problem is formulated for a four-phase system involving two-dimensional constitutive equations for bulk materials and one-dimensional equations of Gurtin–Murdoch model for surface and interface. The boundary perturbation method combined with the superposition principle is used to calculate the stress concentration along the arbitrary curved interface of an isotropic thin film coherently bonded to a substrate. Through numerical examples, various applications of the bulk–boundary coupled formulation which require further investigation are highlighted. Non-equilibrium counterpart of surface tension is introduced and its effects are elucidated via examples. Equipped with the theoretical and computational framework, the influence of boundary viscoelasticity on the material response is illustrated. A geometrically exact computational framework using isogeometric analysis inherently suited to account for boundaries is developed. The boundary constitutive models are formulated such that fluid-like and solid-like viscoelastic behavior of boundaries are considered. Boundary contributions include both surface and curve effects wherein boundary elasticity as well as boundary tension are accounted for.
We present a model that utilizes a nonlinear evolution law and thus is not restricted to the states that are close to the thermodynamic equilibrium. The main objective of this contribution is to formulate a finite deformation theory for boundary viscoelasticity in principal stretches by accounting for strain-dependent boundary stresses. Various extensions of surface elasticity theory have been proposed. Use of surface elasticity theory has experienced a prolific growth recently due to its utility in understanding the mechanics of nanomaterials and soft solids at small scales.
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