A frictional mortar contact approach for the analysis of large inelastic deformation problems

Doca, T.; Pires, F.M. Andrade; de, Jose Cesar

doi:10.1016/j.ijsolstr.2014.01.013

Cited by 28 publications

(27 citation statements)

References 32 publications

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“…The nonlinear contact behaviors are governed by the contact constraints, ie, contact constitutive law. Although the contact constraints between solids provide a good reference, the porous media contact constraints require further discussion for both the solid and fluid phases. These contact constraints are presented next as two individual subsections.…”

Section: Porous Media Dual Mortar Contact Methodsmentioning

confidence: 99%

“…We can directly replace the dual variables with their corresponding multipliers. Therefore, only the terms that include primal variables require weak form representations:

δ {\overset{true˜}{g}}_{u} = - \int_{{{}^{t}Γ}_{C}^{s}} {δλ}_{u}^{n} g_{u} dΓ \geq 0,

\int_{{{}^{t}Γ}_{C}^{s}} δ λ_{u}^{τ} \cdot ((), {\overset{true¯}{boldv}}_{τ} + β λ_{u}^{τ}) dΓ = 0 .

Then, the contact constraints are rewritten in the following weak forms:

λ_{u}^{n} + italicα italicp \geq 0, normalδ {\overset{true~}{italicg}}_{u} \geq 0, ((), λ_{u}^{n} + italicα italicp) {\overset{true~}{italicg}}_{u} = 0,

\begin{matrix} centertrue \\ ‖λ_{u}^{τ}‖ - μ |λ_{u}^{n} + αp| \leq 0, & β \geq 0, & (‖λ_{u}^{τ}‖ - μ |λ_{u}^{n} + αp|) β = 0 \end{matrix} .

…”

Section: Porous Media Dual Mortar Contact Methodsmentioning

confidence: 99%

“…However, with the use of the penalty method or Lagrange multiplier method to enforce contact constraints, the resultant global matrix is either ill‐conditioned or nonpositive definite, leading to a significant increase in time for solving the matrix system. The recently developed dual mortar approach provides an alternative for modeling contact problems with high accuracy at low computational cost. This approach allows for local condensing of the additional Lagrange multiplier degrees of freedom by interpolating the multipliers with biorthogonal dual basis functions.…”

Section: Introductionmentioning

confidence: 99%

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A dual mortar contact method for porous media and its application to clay‐core rockfill dams

Wang

Zhou

Zhang

et al. 2019

Num Anal Meth Geomechanics

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Summary The clay‐core rockfill dam is a multibody contact system in which the hydromechanical response of the clay core plays a crucial role. This complex problem is highly challenging to model numerically. We present a numerical approach that considers the multibody contact, consolidation, and strong geometric and material nonlinearities for the modeling of clay‐core rockfill dams. Within the framework of the dual mortar finite element method, the presented approach considers the contact bodies as independent porous media continuums. The nonlinear contact conditions are derived based on the effective contact traction on contact interfaces and pore pressure continuity. The weak forms are obtained by introducing Lagrange multipliers as additional unknowns, which are then condensed through an extended general transformation. The presented method is first validated with a patch test considering the contact between two porous media. Then, a three‐dimensional analysis of the Rumei clay‐core rockfill dam is performed. The main numerical analysis concerns are the two observation galleries planned for construction inside the clay core. The galleries consist of dozens of tunnel‐like concrete blocks, giving rise to complex concrete‐concrete and concrete‐clay contacts. The discontinuous separation and sliding between concrete blocks are investigated. For the concrete‐concrete contact, both hard and soft joint approaches are evaluated and compared. The pore pressure results of the concrete structures are also analyzed.

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Section: Porous Media Dual Mortar Contact Methodsmentioning

confidence: 99%

“…We can directly replace the dual variables with their corresponding multipliers. Therefore, only the terms that include primal variables require weak form representations:

δ {\overset{true˜}{g}}_{u} = - \int_{{{}^{t}Γ}_{C}^{s}} {δλ}_{u}^{n} g_{u} dΓ \geq 0,

\int_{{{}^{t}Γ}_{C}^{s}} δ λ_{u}^{τ} \cdot ((), {\overset{true¯}{boldv}}_{τ} + β λ_{u}^{τ}) dΓ = 0 .

Then, the contact constraints are rewritten in the following weak forms:

λ_{u}^{n} + italicα italicp \geq 0, normalδ {\overset{true~}{italicg}}_{u} \geq 0, ((), λ_{u}^{n} + italicα italicp) {\overset{true~}{italicg}}_{u} = 0,

\begin{matrix} centertrue \\ ‖λ_{u}^{τ}‖ - μ |λ_{u}^{n} + αp| \leq 0, & β \geq 0, & (‖λ_{u}^{τ}‖ - μ |λ_{u}^{n} + αp|) β = 0 \end{matrix} .

…”

Section: Porous Media Dual Mortar Contact Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A dual mortar contact method for porous media and its application to clay‐core rockfill dams

Wang

Zhou

Zhang

et al. 2019

Num Anal Meth Geomechanics

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“…The whole concept of virtual work for a single solid can be found in [72] and for solids in contact using mortar formulation can be found in [73], however, discretized equilibrium equation can be written as [61]:…”

Section: Discretized Equilibrium Equation and Matrix Representation Omentioning

confidence: 99%

“…The proposed model is applicibale in the analysis of any problem like metal forming problems; however, here just the efficiency of the model for prediction of ratcheting in double shear lap joints is examined, especially near the hole and notch zone. The similar work was conducted [61] for frictional mortar contact formulation with large inelastic deformations based on hyper-elastic and multiplicative plasticity, the main focus of which was dealing with contact nonlinearities and implementing dual Lagrange multipliers and PDASS (Primal Dual Active set strategy) which only treats contact nonlinearities and accuracy is not dealt. Consequently, due to the need for prolonged discussion and also because it has no effect on the accuracy, these two strategies are not discussed here.…”

Section: Introductionmentioning

confidence: 99%

Numerical and experimental study of an interference fitted joint using a large deformation Chaboche type combined isotropic–kinematic hardening law and mortar contact method

Mohammadpour

Chakherlou

2016

International Journal of Mechanical Sciences

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Three‐dimensional numerical analysis of concrete‐faced rockfill dam using dual‐mortar finite element method with mixed tangential contact constraints

Zhou

Zhang

Peng³

et al. 2016

Num Anal Meth Geomechanics

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SUMMARYConcrete-faced rockfill dam (CFRD) is a popular alternative to traditional dam types in the last two decades. The modelling of CFRD involves complex multi-body contact and strong geometry and material nonlinearities. We present a numerical approach for the modelling of CFRDs in this paper. Based on the dual-mortar finite element method, the presented approach considers different parts of rockfill and all concrete slabs as independent deformable continuum. The multi-body contacts are modelled using Lagrange multipliers with a weak form segment-to-segment contact strategy. To alleviate instability induced by strong geometry nonlinearity in the slab-slab contact, we propose a mixed type of constraints for the tangential contact. A general transformation scheme is introduced to simplify the implementation of contact constraints. Three-dimensional analysis of Tianshengqiao-1 CFRD is performed. The nonlinear and time-dependent deformation of the rockfill is considered. We study the influence of the rockfill deformation on the reliability of the concrete face. Three major concerns of the face, that is, the axial compression, the slab-slab separation and the face-rockfill separation, are discussed in detail. The numerical results are compared with data from in-situ observation.

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A frictional mortar contact approach for the analysis of large inelastic deformation problems

Cited by 28 publications

References 32 publications

A dual mortar contact method for porous media and its application to clay‐core rockfill dams

A dual mortar contact method for porous media and its application to clay‐core rockfill dams

Numerical and experimental study of an interference fitted joint using a large deformation Chaboche type combined isotropic–kinematic hardening law and mortar contact method

Three‐dimensional numerical analysis of concrete‐faced rockfill dam using dual‐mortar finite element method with mixed tangential contact constraints

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