Quasistatic normal-compliance contact problem of visco-elastic bodies with Coulomb friction implemented by QP and SGBEM

Vodička, Roman; Mantič, V.; Roubíček, Tomáš

doi:10.1016/j.cam.2016.10.010

Cited by 11 publications

(8 citation statements)

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“…Such an approach assumes contact surface exhibiting certain elastic response also under compression, e.g., due to its roughness, which is macroscopically seen as a small interpenetration [21,46], or due to the presence of a thin adhesive layer. This approach is also well amenable for mathematical analysis [44,46].…”

Section: Roman Vodička and Vladislav Mantičmentioning

confidence: 99%

“…Also important features of the computational implementation are summarized, for further implementation details see [40]. The computational implementation is based on the vanishing-viscosity concept of the weak solution introduced in [30,33], with spatial discretization by the Symmetric Galerkin Boundary Element Method (SGBEM) [34,41,42] combined with visco-elastic solution transformation according to [25], and with Quadratic Programming (QP) [10] or sequential QP (SQP) [28], depending on the actual form of the arising functionals, as it was also done in [40,43,44].…”

Section: Roman Vodička and Vladislav Mantičmentioning

confidence: 99%

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An energy based formulation of a quasi-static interface damage model with a multilinear cohesive law

Vodička¹,

Mantič²

2017

Discrete &Amp; Continuous Dynamical Systems - S

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A new quasi-static and energy based formulation of an interface damage model which provides interface traction-relative displacement laws like in traditional trilinear (with bilinear softening) or generally multilinear cohesive zone models frequently used by engineers is presented. This cohesive type response of the interface may represent the behaviour of a thin adhesive layer. The level of interface adhesion or damage is defined by several scalar variables suitably defined to obtain the required traction-relative displacement laws. The weak solution of the problem is sought numerically by a semi-implicit timestepping procedure which uses recursive double minimization in displacements and damage variables separately. The symmetric Galerkin boundary-element method is applied for the spatial discretization. Sequential quadratic programming is implemented to resolve each partial minimization in the recursive scheme applied to compute the time-space discretized solutions. Sample 2D numerical examples demonstrate applicability of the proposed model.

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Section: Roman Vodička and Vladislav Mantičmentioning

confidence: 99%

Section: Roman Vodička and Vladislav Mantičmentioning

confidence: 99%

An energy based formulation of a quasi-static interface damage model with a multilinear cohesive law

Vodička¹,

Mantič²

2017

Discrete &Amp; Continuous Dynamical Systems - S

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“…damage or delamination problems with healing in arbitrary space dimension. Another application can be frictional contact [46] or adhesive contact with an interfacial plasticity [37] allowing to distinguish less dissipative mode I (opening) from more dissipative mode II (shear) in two-dimensional cases. Another, rather academical, application is the bulk plasticity with kinematic hardening in one dimension.…”

Section: Notation and Selected Notions Of Variational Analysismentioning

confidence: 99%

Identification of some nonsmooth evolution systems with illustration on adhesive contacts at small strains

2015

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A class of evolution quasistatic systems which leads, after a suitable time discretization, to recursive nonlinear programs, is considered and optimal control or identification problems governed by such systems are investigated. The resulting problem is an evolutionary Mathematical Programs with Equilibrium Constraints (MPEC). A subgradient information of the (in general nonsmooth) composite objective function is evaluated and the problem is solved by the Implicit programming approach. The abstract theory is illustrated on an identification problem governed by delamination of a unilateral adhesive contact of elastic bodies discretized by finite-element method in space and a semi-implicit formula in time. Being motivated by practical tasks, an identification problem of the fracture toughness and of the elasticity moduli of the adhesive is computationally implemented and tested numerically on a two-dimensional example. Other applications including frictional contacts or bulk damage, plasticity, or phase transformations are outlined.

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“…due to its roughness, or due to the presence of a thin layer of an adhesive. This approach is also suitable for mathematical analysis, even if friction is present [19,20].…”

Section: Introductionmentioning

confidence: 99%

A quasi-static interface damage model with frictional contact – applications to steel reinforced concrete structures

Vodička¹,

Kšiňan²

2018

Int. J. CMEM

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A model for numerical analysis of compound structures made of various materials is presented. The mathematical concept of solution is based on quasi-static evolution of debonding processes occurring along the interface. It is formulated in terms of energies considering the stored energy represented by the elastic energy of the structures and dissipation due to damage processes, plastic slip at the interface or friction. The numerical solution includes a semi-implicit time stepping procedure, relying on splitting of the whole problem at a current time step into two problems of variational nature solved recursively. The space discretisation includes Symmetric Galerkin Boundary Element Method used to obtain the stored energies, and, in combination with the variational character of the recursive problems, also to calculate its gradients to be utilized in non-linear programming algorithms for finding the timeevolving solution. Numerical results are demonstrated for a steel-concrete interface frequently met in civil engineering applications to assess the model applicability in engineering practice.

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Quasistatic normal-compliance contact problem of visco-elastic bodies with Coulomb friction implemented by QP and SGBEM

Cited by 11 publications

References 50 publications

An energy based formulation of a quasi-static interface damage model with a multilinear cohesive law

An energy based formulation of a quasi-static interface damage model with a multilinear cohesive law

Identification of some nonsmooth evolution systems with illustration on adhesive contacts at small strains

A quasi-static interface damage model with frictional contact – applications to steel reinforced concrete structures

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