Anàlisi biomecànic d'un implant intervertebral mitjançant el mètode dels elements finits

Sovint la fusió intervertebral és l'única opció efectiva en pacients que pateixen lesions importants de disc. És necessari conèixer de quina manera es comporta el conjunt vertebral sota aquesta nova configuració. En l'estudi que es presenta s'ha elaborat un model numèric que a partir d'una malla d'elements prismàtics en el teixit cortical, és capaç de calcular els esforços de làmina associats al comportament de flexió

Stress-driven integration strategies and m-AGC tangent operator for Perzyna viscoplasticity and viscoplastic relaxation: application to geomechanical interfaces

This is the peer reviewed version of the following article: [Aliguer, I., Carol, I., and Sture, S. (2017) Stress-driven integration strategies and m-AGC tangent operator for Perzyna viscoplasticity and viscoplastic relaxation: application to geomechanical interfaces. Int. J. Numer. Anal. Meth. Geomech., 41: 918–939. doi: 10.1002/nag.2654.], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nag.2654/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The paper proposes a stress-driven integration strategy for Perzyna-type viscoplastic constitutive models, which leads also to a convenient algorithm for viscoplastic relaxation schemes. A generalized trapezoidal rule for the strain increment, combined with a linearized form of the yield function and flow rules, leads to a plasticity-like compliance operator that can be explicitly inverted to give an algorithmic tangent stiffness tensor also denoted as the m-AGC tangent operator. This operator is combined with the stress-prescribed integration scheme, to obtain a natural error indicator that can be used as a convergence criterion of the intra-step iterations (in physical viscoplasticity), or to a variable time-step size in viscoplastic relaxation schemes based on a single linear calculation per time step. The proposed schemes have been implemented for an existing zero-thickness interface constitutive model. Some numerical application examples are presented to illustrate the advantages of the new schemes proposed.Peer ReviewedPostprint (author's final draft

On integration strategies for perzyna-type viscoplasticity, and application to zero-thickness interface elements

In this paper, Perzyna-type viscoplastic rate equations are integrated for a time step by considering the step as stress-driven. Depending on how the increment is imposed (constant, linear etc.), different strategies arise. The secant compliance is obtained by truncated expansion of the yield function. The viscoplastic model can be applied to materials exhibiting rate-dependent behavior, but it can also be used to recover an inviscid elastoplasticity solution when stationary conditions are reached. Within this framework, a viscoplastic relaxation iterative strategy is developed, relating the iterations with the fictitious time steps. Some examples of application are presented in the context of the Finite Element Method with zero-thickness interface elements for slope and stability problems with discontinuities

Numerical analysis and safety evaluation of a large arch dam founded on fractured rock, using zero-thickness interface elements and a c-φ reduction method

A 140m high arch dam in the Pyrenees, built in the 50s, is founded on fractured limestone rock. Since the beginning of the design process, two main families of discontinuities were identified. The dam was built very close to the end of the narrow part of the valley, which raised stability concerns early on. In the late 80s - early 90s, a numerical study of the dam was developed at the Dept of Geotechnical Engineering and Geo-Sciences UPC (School of Civil Engineering) UPC, using a progressively more realistic series of models and approaches, culminating with a 3D discretization of the dam plus rock mass, in which discontinuities were explicitly represented using zero-thickness interface elements with frictional constitutive laws in terms of stress tractions and the corresponding normal and shear relative displacements. In the present study, that dam and its foundation are revisited and reanalyzed with current, more advanced numerical tools and a third family of rock joints which has been identified more recently. The same mesh is used as a departure point, although a much more detailed description is now possible. The analysis is also approached in a different way, now using the traditional c-φ reduction method developed and implemented specifically for non-linear zero-thickness interfaces

Evaluación de la seguridad en problemas de mecánica de rocas mediante el método c-Φ reduction

En este documento de detalla de forma sintética el trabajo realizado hasta la fecha en la realización por parte del primer autor de la tesis doctoral que lleva por título: “Métodos Numéricos Avanzados para Evaluar la Estabilidad en Problemas de Mecánica de Rocas”, dirigida y tutelada por I. Carol y co-dirigida por E.E. Alonso. El trabajo se enmarca dentro el amplio campo de la mecánica de rocas tratando aspectos de modelos constitutivos e ingeniería computacional. Se presenta a continuación la formulación de un método para la evaluación de la seguridad en macizos rocosos fracturados mediante la reducción de los parámetros resistentes de la ley de comportamiento de las juntes de roca. Éste método se codificó y se implementó en el código por el Método de los Elementos Finitos DRAC, desarrollado por el grupo de investigación MECMAT. Finalmente se presentan algunos ejemplos

Further developments in stress initialization in geomechanics via FEM and a two-step procedure involving airy functions

The in-situ stress field in rock masses is a key aspect when a numerical analysis of a rock mass is carried out in any area of geo-engineering, such as civil, mining, or Oil & Gas. A method for the numerical generation of the in-situ stress state in the FE context, based on Airy stress functions was previously introduced. It involves two steps: 1) an estimate of the stress state at each Gauss point is generated, and 2) global equilibrium is verified and re-balancing nodal forces are applied as needed. In this paper, new developments towards improving the accuracy of the stress proposal are discussed. A real application example has been used to illustrate the results achieved with the new implementation

Zero-thickness interface elements with h-m coupling, formulation and applications in geomechanics

Previous developments on zero-thickness interface elements for coupled Hydro-Mechanics problems are briefly described, followed by some new geomechanical applications, particularly to hydraulic fracture in rock. The results are compared satisfactorily to approximate formulas and previously published numerical results. Once verified, the model is applied to new cases to show the capabilities of the approach

Further developments in stress initialization in geomechanics via FEM and a two-step procedure involving Airy functions

The in-situ stress field in rock masses is a key aspect when a numerical analysis of a rock mass is carried out in any area of geo-engineering, such as civil, mining, or Oil & Gas. A method for the numerical generation of the in-situ stress state in the FE context, based on Airy stress functions was previously introduced. It involves two steps: 1) an estimate of the stress state at each Gauss point is generated, and 2) global equilibrium is verified and re-balancing nodal forces are applied as needed. In this paper, new developments towards improving the accuracy of the stress proposal are discussed. A real application example has been used to illustrate the results achieved with the new implementation.Postprint (published version

Numerical stress initialization in geomechanics via the FEM and a two-step procedure

The knowledge of the in-situ stress field in rock masses is crucial in different areas of geo-engineering, such as mining or civil underground excavations, hydrocarbon extraction, CO2 storage, hydraulic fracture operations, etc. A method for the numerical generation of the in-situ stress state is described in this paper, which involves two steps: 1) an estimate of the stress state at each Gauss point is generated, and 2) global equilibrium is verified and re-balancing nodal forces are applied as needed. While the re-equilibration step is a closed procedure based only on statics, the first estimate of the stress state can be done in a variety of ways to incorporate all the information available. In this paper, the various options available are discussed and compared, and a new alternative procedure is presented which is based on the Airy stress function. The performance of the various procedures is illustrated with a real application example

Anàlisi biomecànic d'un implant intervertebral mitjançant el mètode dels elements finits

Sovint la fusió intervertebral és l'única opció efectiva en pacients que pateixen lesions importants de disc. És necessari conèixer de quina manera es comporta el conjunt vertebral sota aquesta nova configuració. En l'estudi que es presenta s'ha elaborat un model numèric que a partir d'una malla d'elements prismàtics en el teixit cortical, és capaç de calcular els esforços de làmina associats al comportament de flexió