Large deformation analysis of functionally graded elastoplastic materials via solid tetrahedral finite elements

Pascon, João Paulo; Coda, Humberto Breves

doi:10.1016/j.compstruc.2014.09.005

Cited by 17 publications

(6 citation statements)

References 27 publications

(44 reference statements)

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“…Expression (28) is determined only for the released degrees of freedom. Similar finite element formulations based on the positional version can be found, for instance, in: Pascon and Coda (2012, 2013, 2015).…”

Section: Numerical Algorithmmentioning

confidence: 92%

Finite element analysis of flexible functionally graded beams with variable Poisson’s ratio

Pascon

2016

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Purpose The purpose of this paper is to deal with large deformation analysis of plane beams composed of functionally graded (FG) elastic material with a variable Poisson’s ratio. Design/methodology/approach The material is assumed to be linear elastic, with a Poisson’s ratio varying according to a power law along the thickness direction. The finite element used is a plane beam of any-order of approximation along the axis, and with four transverse enrichment schemes, which can describe constant, linear, quadratic and cubic variation of the strain along the thickness direction. Regarding the constitutive law, five materials are adopted: two homogeneous limiting cases, and three intermediate FG cases. The effect of both finite element kinematics and distribution of Poisson’s ratio on the mechanical response of a cantilever is investigated. Findings In accordance with the scientific literature, the second scheme, in which the transverse strain is linearly variable, is sufficient for homogeneous long (or thin) beams under bending. However, for FG short (or moderate thick) beams, the third scheme, in which the transverse strain variation is quadratic, is needed for a reliable strain or stress distribution. Originality/value In the scientific literature, there are several studies regarding nonlinear analysis of functionally graded materials (FGMs) via finite elements, analysis of FGMs with constant Poisson’s ratio, and geometrically linear problems with gradually variable Poisson’s ratio. However, very few deal with finite element analysis of flexible beams with gradually variable Poisson’s ratio. In the present study, a reliable formulation for such beams is presented.

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Section: Numerical Algorithmmentioning

confidence: 92%

Finite element analysis of flexible functionally graded beams with variable Poisson’s ratio

Pascon

2016

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“…in which k F β is the external force applied in k direction at node β . For strain energy one uses the energy conjugate concept among internal force and position (Coda 2018, Soares et al 2019, Coda 2015, Pascon and Coda 2015, Pascon and Coda 2013…”

Section: Motion Equationmentioning

confidence: 99%

Alternative active nonlinear total Lagrangian truss finite element applied to the analysis of cable nets and long span suspension bridges

Coda

Silva

Paccola

2020

Lat. Am. j. solids struct.

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An alternative geometrically nonlinear total Lagrangian finite element is presented and applied to solve cable, cable nets and a very long suspended bridge in both three and two-dimensional spaces from its setting-up through its response to earthquake. It includes dynamics, pseudo-dynamics regularization, elastic actuators and automatic stress calibration. Dynamics and pseudo-dynamics are used to perform transient structural analysis and the setting-up of very unstable structures. Elastic actuators allow pre-stressing structural members for the iterative structural design and cables natural length definition. Automatic stress calibration comprises continuous cables in complicated structures without sliding contact devices. The formulation is applied to model main cables of suspended bridges passing through saddle points. Inertial terms are introduced by an alternative mathematical way. Two simple examples are used to validate all aspects of the proposed formulation. Finally, a representative application is performed, i.e., the numerical design and analysis of a very long span suspension bridge by the proposed strategy.

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“…Some interesting FEM applications using plastic potentials, as metal forming and stamping, can be seen for example in Chung et al (1998) and Schwarze et al (2011). The same Kröner-Lee multiplicative decomposition is also used to describe finite viscoelasticity or viscoplasticity (Pascon and Coda (2015) and Pascon and Coda (2017)). Although considering large strain viscoplasticity, none of the above mentioned works extended their formulation to model fluids, as it will be done originally here.…”

Section: Introductionmentioning

confidence: 99%

Large strain Flory’s decomposition for Lagrangian modeling of viscoleastic solids and compressive fluids

Kishino

Sanches

et al. 2022

Lat. Am. j. solids struct.

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The fundamental difference in the solution of solids and fluids relies on the respective constitutive laws. Based on the Rivlin-Saunders-Düster-Hartmann hyperelastic model and using the Flory's strain decomposition, we present a new total Lagrangian viscoelastic constitutive model for both Kelvin-Voigt viscoelastic solids and free-surface compressive viscous isothermal fluids. A dissipative viscous virtual work is written as a function of the time rate of isochoric invariants and its relation with the viscous stress is derived. Local time derivatives are solved by backward finite difference, allowing a consistent tangent viscoelastic constitutive tensor. The virtual work principle is used to write the weak equilibrium equation and its position-based finite element counterpart. Dynamic time integration is carried out by the Newmark β method and the Newton-Raphson procedure is used to solve time steps. The formulation is validated against experimental and numerical literature results revealing good precision. Additional examples are shown in order to demonstrate the applicability and future possibilities of the technique.

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Large deformation analysis of functionally graded elastoplastic materials via solid tetrahedral finite elements

Cited by 17 publications

References 27 publications

Finite element analysis of flexible functionally graded beams with variable Poisson’s ratio

Finite element analysis of flexible functionally graded beams with variable Poisson’s ratio

Alternative active nonlinear total Lagrangian truss finite element applied to the analysis of cable nets and long span suspension bridges

Large strain Flory’s decomposition for Lagrangian modeling of viscoleastic solids and compressive fluids

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