On the contact domain method: a comparison of penalty and Lagrange multiplier implementations

This work focuses on the assessment of the relative performance of the so-called contact domain method, using either the Lagrange multiplier or the penalty strategies. The mathematical formulation of the contact domain method and the imposition of the contact constraints using a stabilized Lagrange multiplier method are taken from the seminal work (as cited later), whereas the penalty based implementation is firstly described here. Although both methods result into equivalent formulations, except for the difference in the constraint imposition strategy, in the Lagrange multiplier method the constraints are enforced using a stabilized formulation based on an interior penalty method, which results into a different estimation of the contact forces compared to the penalty method. Several numerical examples are solved to assess certain numerical intricacies of the two implementations. The results show that both methods perform similarly as one increases the value of the penalty parameter or decreases the value of the stabilization factor (in case of the Lagrange multiplier method). However there seems to exist a clear advantage in using the Lagrange multiplier based strategy in a few critical situations, where the penalty method fails to produce convincing results due to excessive penetration

A micromorphic model for steel fiber reinforced concrete

A new formulation to model the mechanical behavior of high performance fiber reinforced cement composites with arbitrarily oriented short fibers is presented. The formulation can be considered as a two scale approach, in which the macroscopic model, at the structural level, takes into account the mesostructural phenomenon associated with the fiber-matrix interface bond/slip process. This phenomenon is contemplated by including, in the macroscopic description, a micromorphic field representing the relative fiber-cement displacement. Then, the theoretical framework, from which the governing equations of the problem are derived, can be assimilated to a specific case of the Material Multifield Theory. The balance equation derived for this model, connecting the micro stresses with the micromorphic forces, has a physical meaning related with the fiber-matrix bond slip mechanism. Differently to previous procedures in the literature, addressed to model fiber reinforced composites, where this equation has been added as an additional independent ingredient of the methodology, in the present approach it arises as a natural result derived from the multifield theory. Every component of the composite is defined with a specific free energy and constitutive relation. The mixture theory is adopted to define the overall free energy of the composite, which is assumed to be homogeneously constituted, in the sense that every infinitesimal volume is occupied by all the components in a proportion given by the corresponding volume fraction. The numerical model is assessed by means of a selected set of experiments that prove the viability of the present approach. A new formulation to model the mechanical behavior of high performance fiber reinforced cement composites with arbitrarily oriented short fibers is presented. The formulation can be considered as a two scale approach, in which the macroscopic model, at the structural level, takes into account the mesostructural phenomenon associated with the fiber–matrix interface bond/slip process. This phenomenon is contemplated by including, in the macroscopic description, a micromorphic field representing the relative fiber–cement displacement. Then, the theoretical framework, from which the governing equations of the problem are derived, can be assimilated to a specific case of the material multifield theory. The balance equation derived for this model, connecting the micro stresses with the micromorphic forces, has a physical meaning related with the fiber–matrix bond slip mechanism. Differently to previous procedures in the literature, addressed to model fiber reinforced composites, where this equation has been added as an additional independent ingredient of the methodology, in the present approach it arises as a natural result derived from the multifield theory. Every component of the composite is defined with a specific free energy and constitutive relation. The mixture theory is adopted to define the overall free energy of the composite, which is assumed to be homogeneously constituted, in the sense that every infinitesimal volume is occupied by all the components in a proportion given by the corresponding volume fraction. The numerical model is assessed by means of a selected set of experiments that prove the viability of the present approac

Numerical modeling of crack formation in powder forming processes

This paper presents a constitutive model describing the mechanical behavior of metal powders during (uniaxial) cold die compaction processes, placing special emphasis on the modeling of cracks formed during the ejection stage. The constitutive relationships are derived within the general framework of rate-independent, isotropic, finite strain elastoplasticity. The yield condition is determined by three surfaces intersecting non-smoothly in stress space, namely, an elliptical cap and the classical Von Mises and Drucker–Prager yield surfaces. The distinct irreversible processes are described in terms of two internal variables: an internal hardening variable, associated with accumulated compressive (plastic) strains, and an internal softening variable, linked with accumulated (plastic) shear strains. Motivated by both numerical and physical reasons, a parabolic plastic potential function is introduced to characterize the plastic flow on the linear Drucker–Prager failure surface. A thermodynamically consistent calibration procedure is employed to relate the softening modulus to fracture energy values obtained experimentally on Distaloy AE powder specimens. The predictive capability of the constitutive model is checked by simulating three representative cases: a diametral compression test, the ejection of an over-densified thin cylindrical part and the compaction of an axially symmetric multilevel part in an advanced CNC press machine. These simulations demonstrate the ability of the model to detect evidence of macroscopic cracks, clarify and provide reasons for the formation of such cracks, and evaluate, at least qualitatively, the influence of variations in the input variables on their propagation through the green compac

A 3D Frictionless Contact Domain Method for Large Deformation Problems

This work describes a three-dimensional contact domain method for large deformation frictionless contact problems. Theoretical basis and numerical aspects of this specific contact method are given in [Oliver, Hartmann, Cante, Weyler and Hernández (2009)] and [Hartmann, Oliver, Weyler, Cante and Hernández (2009)] for two-dimensional, large deformation frictional contact problems. In this method, in contrast to many other contact formulations, the necessary contact constraints are formulated on a so-called contact domain, which can be interpreted as a fictive intermediate region connecting the potential contact surfaces of the deformable bodies. This contact domain has the same dimension as the contacting bodies. It will be endowed with a displacement field, interpolated from the displacements at the contact surfaces and will be subdivided into a non-overlapping set of contact patches, where the contact constraints will be applied. For the enforcement of these contact constraints a stabilized Lagrange multiplier method is used, which allows the condensation of the introduced Lagrange multipliers, leading to a purely displacement driven problem

A new approach in computational contact mechanics: The contact domain method

This first part of the work presents the theoretical aspects of a new approach to solve two-dimensional large-strain problems in computational contact mechanics. The basic elements of the proposed metod are: 1) the use of an updated Lagrangean approach to describe the motion of the contacting bodies, 2) consideration of a two-dimensional aontact domain, where the contact/friction restrictions are imposed, and construction of a one layer triangulation in this domain, 3) resorting to a Lagrange multiplier method to impose the contact/friction contraints, 4) an interior penaltyprocedure, allowing condensation of the Lagrange multipliers, ensuring the stability of the discretized problem and 5) an active set strategy, for determining the subsets of the contact domain were contact/friction conditions have to be applied, based on the concept domain were contact/friction conditions have to be aaplied, based on the concept of effective gaps as suitable entities for extrapolation and prediction purposes

A contact domain method for large deformation frictional contact problems. Part 1: Theoretical basis

In the first part of this work, the theoretical basis of a frictional contact domain method for two-dimensional large deformation problems is presented. Most of the existing contact formulations impose the contact constraints on the boundary of one of the contacting bodies, which necessitates the projection of certain quantities from one contacting surface onto the other. In this work, the contact constraints are formulated on a so-called contact domain, which has the same dimension as the contacting bodies. This contact domain can be interpreted as a fictive intermediate region connecting the potential contact surfaces of the deformable bodies. The introduced contact domain is subdivided into a non-overlapping set of patches and is endowed with a displacement field, interpolated from the displacements at the contact surfaces. This leads to a contact formulation that is based on dimensionless, strain-like measures for the normal and tangential gaps and that exactly passes the contact patch test. In addition, the contact constraints are enforced using a stabilized Lagrange multiplier formulation based on an interior penalty method (Nitsche method). This allows the condensation of the introduced Lagrange multipliers and leads to a purely displacement driven problem. An active set strategy, based on the concept of effective gaps as entities suitable for smooth extrapolation, is used for determining the active normal stick and slip patches of the contact domain

A contact domain method for large deformation frictional contact problems. Part 2: Numerical aspects

This second part of the work describes the numerical aspects of the developed contact domain method for large deformation frictional contact problems. The theoretical basis of this contact method is detailed in the first part of this work. Starting from this, the present contribution focuses on describing important algorithmic details that go along with the finite element implementation for two-dimensional problems. Important aspects are the construction of the contact domain mesh, via a constraint Delaunay triangulation, the linearization of the discretized contact contributions and some important technical aspects about the extrapolation procedure used for the predictive active set strategy. Finally a set of numerical examples is presented to demonstrate the performance of the developed contact strategy. Demanding static and dynamic contact problems in the context of large deformations, including frictional effects as well as self contact, show the wide applicability and the robustness of the proposed metho

A non-randomized comparison of gemcitabine-based chemoradiation with or without induction chemotherapy for locally advanced squamous cell carcinoma of the head and neck

<p>Abstract</p> <p>Background</p> <p>Concomitant chemotherapy and radiotherapy (chemoradiation; CRT) is the standard treatment for locoregionally advanced squamous cell carcinoma of the head and neck (LA-SCCHN). CRT improves local control and overall survival (OS) when compared to radiotherapy (RT) alone. Induction chemotherapy (IC) reduces the risk of distant metastases (DM) and improves OS by 5% with the use of cisplatin/infusional 5 fluorouracil (PF) in meta-analysis. Adding a taxane to PF in the IC regimen confers a better outcome. Sequential treatment (ST) of IC followed by CRT is therefore under active investigation in multiple phase III trials.</p> <p>Methods</p> <p>We compared the outcome of two cohorts of patients (pts) with LA-SCCHN treated at our institution with CRT (n = 27) or ST (n = 31), respectively. CRT consisted of GEM 100 mg/m²weekly + conventional RT (70 Gy); ST consisted of the same CRT preceded by platinum-based IC.</p> <p>Results</p> <p>Response to IC: complete 8 (26%), partial 20 (65%), stable 1, progressive 1, not evaluable 1. Median follow up of the surviving pts: for CRT 73 months, for ST 51 months. Median time to distant metastasis (TDM) was for CRT 23.6 months, for ST not reached. Median OS was for CRT 20.2 months, for ST 40.2 months. Cox regression analysis, taking into account age, T and N stage and tumor site, showed a hazard ratio with ST of 1.190 for time to locoregional failure (p = 0.712), 0.162 for TDM (p = 0.002), and 0.441 for overall survival (OS) (p = 0.026).</p> <p>Conclusion</p> <p>TDM and OS were found significantly longer in the ST cohort without a reduced locoregional control. Notwithstanding the limitations of a non-randomized single-center comparison, the results are in line with very preliminary data of randomized comparisons suggesting an improved outcome with ST.</p

Structure-activity relationships of anthraquinone derivatives derived from bromaminic acid as inhibitors of ectonucleoside triphosphate diphosphohydrolases (E-NTPDases)

Reactive blue 2 (RB-2) had been characterized as a relatively potent ectonucleoside triphosphate diphosphohydrolase (E-NTPDase) inhibitor with some selectivity for NTPDase3. In search for the pharmacophore and to analyze structure-activity relationships we synthesized a series of truncated derivatives and analogs of RB-2, including 1-amino-2-sulfo-4-ar(alk)ylaminoanthraquinones, 1-amino-2-methyl-4-arylaminoanthraquinones, 1-amino-4-bromoanthraquinone 2-sulfonic acid esters and sulfonamides, and bis-(1-amino-4-bromoanthraquinone) sulfonamides, and investigated them in preparations of rat NTPDase1, 2, and 3 using a capillary electrophoresis assay. Several 1-amino-2-sulfo-4-ar(alk)ylaminoanthraquinone derivatives inhibited E-NTPDases in a concentration-dependent manner. The 2-sulfonate group was found to be required for inhibitory activity, since 2-methyl-substituted derivatives were inactive. 1-Amino-2-sulfo-4-p-chloroanilinoanthraquinone (18) was identified as a nonselective competitive blocker of NTPDases1, 2, and 3 (Ki 16–18 μM), while 1-amino-2-sulfo-4-(2-naphthylamino)anthraquinone (21) was a potent inhibitor with preference for NTPDase1 (Ki 0.328 μM) and NTPDase3 (Ki 2.22 μM). Its isomer, 1-amino-2-sulfo-4-(1-naphthylamino)anthraquinone (20), was a potent and selective inhibitor of rat NTPDase3 (Ki 1.5 μM)