A multiscale numerical approach for the finite strains analysis of materials reinforced with helical fibers

Carniel, Thiago André; Klahr, Bruno; Fancello, Eduardo Alberto

doi:10.1016/j.mechmat.2018.07.014

Cited by 13 publications

(13 citation statements)

References 34 publications

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“…Following the incremental numerical approach described in Carniel et al [7], the current microscopic displacements field u μ n+1 is solution of the minimum principle…”

Section: Computational Homogenization At Finite Strainsmentioning

confidence: 99%

“…Aiming at multiscale analyses of soft fibrous materials, the numerical investigation reported in Carniel et al [7] points out that the classical boundary conditions, namely, the linear boundary displacements model, the periodic boundary displacements model and the minimally constrained model are not convenient choices for wavy-like RVEs reinforced with helical fibers (similar to that shown in Fig. 2c).…”

Section: Proposed Multiscale Boundary Conditionmentioning

confidence: 99%

“…For example, van Dijk [12] presents a stress-strain driven multiscale approach based on the Hill-Mandel principle, but only the periodic boundary condition was investigated. On the other hand, the classical multiscale boundary conditions, i.e., the Taylor, linear, periodic, and minimal models, seem not to be suitable choices for the multiscale analyses of materials reinforced with wavy fibers (a detailed discussion on this topic is provided in Carniel et al [7]).…”

Section: Introductionmentioning

confidence: 99%

“…A computational homogenization approach driven by stress and strain is proposed to account for the macroscopic constraints resulting from the uniaxial stress state assumption. Moreover, aiming further investigation of fibrous materials, a mixed boundary condition allying characteristics of both, linear and minimal models-previously reported in Carniel et al [7] and extensively investigated in Carniel et al [8] and Carniel and Fancello [6]-is included within the present approach. A verification strategy is performed in order to assess the soundness of the proposed homogenization procedure.…”

Section: Introductionmentioning

confidence: 99%

“…The numerical approach presented in this manuscript is consistently grounded within a mathematically elegant and numerically robust RVE-based variational multiscale theory formulated at finite strains [3,7,11,24,30]. In this case, the microscopic equilibrium of the RVE is retrieved from a minimum principle, where the multiscale constraints are enforced with the aid of the Lagrange multipliers method [7,23]. In addition, the present approach is suitable for considering dissipative material effects within a variational constitutive framework [25,27].…”

Section: Introductionmentioning

confidence: 99%

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A computational homogenization approach for uniaxial stress state analyses of wavy fibrous materials

et al. 2020

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Most of the classical computational homogenization techniques at finite strains comprise strain-driven homogenization approaches, in the sense that all the components of the macroscopic deformation gradient F are known as the input data to the homogenization procedure, being the macroscopic stress tensor computed afterwards. On the other hand, a macroscopic uniaxial stress state renders to a multiscale boundary condition driven by the knowledge of both macroscopic conditions, i.e., stress and strain. In this regard, this manuscript presents a computational homogenization approach for the analyses of such mechanical conditions. Aiming further numerical investigations of soft tissues and tissue engineering scaffolds, materials whose microstructures are composed of wavy arrangements of fibers, are investigated. The proposed numerical approach is grounded within a variational framework based on representative volume elements (RVEs) and formulated at finite strains. Tensile tests performed on numerical specimens larger than the RVEs are proposed as reference solutions. The numerical results point out that the present homogenization approach is able to predict not only the macroscopic (homogenized) quantities but also the microscopic kinematic fields investigated. One of the major contributions of the present work is the possibility to investigate how the changes of the macroscopic volume depend on the strain distribution at the microscale under macroscopic uniaxial stress states, since this behavior is intrinsically related to the microstructural material response.

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“…Following the incremental numerical approach described in Carniel et al [7], the current microscopic displacements field u μ n+1 is solution of the minimum principle…”

Section: Computational Homogenization At Finite Strainsmentioning

confidence: 99%

Section: Proposed Multiscale Boundary Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A computational homogenization approach for uniaxial stress state analyses of wavy fibrous materials

et al. 2020

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Finite strain parametric HFGMC micromechanics of soft tissues

Breiman

Meshi

Aboudi

et al. 2020

Biomech Model Mechanobiol

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Limitations of poromechanical first-order computational homogenization for the representation of micro-scale volume changes

Thiesen,

Klahr,

Carniel

et al. 2024

J Braz. Soc. Mech. Sci. Eng.

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Poromechanical computational homogenization models relate the behavior of a macro-scale poroelastic continuum to phenomena occurring at smaller (and also poroelastic) spatial scales. This paper presents a comprehensive analysis of classical micro-scale boundary conditions for the pore pressure field, namely Taylor Boundary Condition (TBC-p), Linear Boundary Condition (LBC-p), Periodic Boundary Condition (PBC-p) and Uniform Boundary Flux (UBF-p), in terms of their accuracy in representing primary (pore pressure) and dual (relative fluid velocity) fields in finite-strain multiscale poromechanical problems. A specific benchmark problem was formulated to investigate the performance of these approaches in scenarios where the rate of the volumetric Jacobian is non-zero, a condition of significant physical interest, especially in contexts such as swelling. Numerical results show that the UBF-p and PBC-p approaches effectively capture the behavior of Direct Numerical Simulation (DNS) during the early time steps. However, deviations from the expected behavior occur when the Representative Volume Element (RVE) undergoes significant volume changes. It is concluded that the observed limitations are due to the first-order nature of the multiscale model. This study highlights the need for more sophisticated computational homogenization poromechanical models that can accurately capture the complex interplay between fluid flow and deformation at different length scales. Second-order computational homogenization models can be alternatives to overcome the limitations of first-order multiscale poromechanical models by enriching the information coming from the macro-scale and relaxing the constraints on the fluid flow at the RVE boundaries.

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A multiscale numerical approach for the finite strains analysis of materials reinforced with helical fibers

Cited by 13 publications

References 34 publications

A computational homogenization approach for uniaxial stress state analyses of wavy fibrous materials

A computational homogenization approach for uniaxial stress state analyses of wavy fibrous materials

Finite strain parametric HFGMC micromechanics of soft tissues

Limitations of poromechanical first-order computational homogenization for the representation of micro-scale volume changes

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