Alternative multiscale material and structures modeling by the finite-element method

Coda, Humberto Breves; Sanches, Rodolfo André Kuche; Paccola, Rodrigo Ribeiro

doi:10.1007/s00366-020-01148-y

Cited by 3 publications

(1 citation statement)

References 32 publications

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“…A summary of the evolution of this subject in the scientific literature (linked to numerical methods) can be extracted from the work of Zhang and Montán (2019) that specifies two main approaches for modeling plasticity. The first is called multiscale and is important to improve the understanding of the microscopic behavior of materials, but its computational cost makes prohibitive its implementation in current commercial softwares (Coda et al, 2020;Abraham et al, 2002;Buehler et al, 2004). The second plasticity approach (based on continuum mechanics) has a relative low computational cost and, as a consequence, is the most used in the development of engineering softwares.…”

Section: Introductionmentioning

confidence: 99%

An alternative finite strain elastoplastic model applied to soft core sandwich panels simulation

Coda

2021

Lat. Am. j. solids struct.

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An alternative elastoplastic model based on the Flory's right Cauchy-Green stretch tensor decomposition is proposed and applied to model soft cores of sandwich panels. It does not follow usual methodologies as the additive decomposition or the Kröner-Lee multiplicative decomposition of strains. It is based on an important hyperelastic relation, Flory's decomposition, from which the total strain is separated in two isochoric and one volumetric parts. Using this decomposition, the volumetric strain energy continues to be elastic during all elastoplastic analysis and the isochoric parts are managed to produce the plastic evolution. As a consequence of Flory's decomposition, the plastic flow direction is known and independent of the yielding surfaces. Moreover, it provides the well known deviatoric nature of plastic strains. For validation purposes, the resulting formulation is implemented using a special 3D prismatic element in a geometrical nonlinear positional FEM computational code. The achieved numerical results are compared with literature experimental data of soft core laminated structural elements.

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Section: Introductionmentioning

confidence: 99%

An alternative finite strain elastoplastic model applied to soft core sandwich panels simulation

Coda

2021

Lat. Am. j. solids struct.

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A finite strain elastoplastic model based on Flory’s decomposition and 3D FEM applications

Coda

2021

Comput Mech

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Symmetric stiffness matrices for isoparametric finite elements in nonlinear elasticity

Valvo

2024

Comput Mech

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The article illustrates a position-based finite element formulation, which greatly simplifies the statement of nonlinear elasticity problems. The formulation adopts as main unknowns the nodal positions in the current configuration instead of the nodal displacements. As a result, simple analytical expressions are obtained of the secant and tangent stiffness matrices for general isoparametric finite elements. Contrary to most formulations of the literature, the secant stiffness matrices turn out to be symmetric. Furthermore, any hyperelastic constitutive law can be easily implemented. Specialised expressions are deduced for the stiffness matrices of a two-node truss bar element and a three-node planar triangular element. The validity of the proposed approach is illustrated through the analysis of a steep von Mises truss and Cook’s membrane. For illustration, the de Saint Venant–Kirchhoff and neo-Hookean material models are considered.

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Alternative multiscale material and structures modeling by the finite-element method

Cited by 3 publications

References 32 publications

An alternative finite strain elastoplastic model applied to soft core sandwich panels simulation

An alternative finite strain elastoplastic model applied to soft core sandwich panels simulation

A finite strain elastoplastic model based on Flory’s decomposition and 3D FEM applications

Symmetric stiffness matrices for isoparametric finite elements in nonlinear elasticity

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