Colloquiam: Computational Solids and Structural Mechanics

Combination of the critical displacement method with a damage model for structural instability analysis

María Jesús Samper — Fri, 04 Jan 2019 12:07:16 +0100

The paper describes the extension of the critical
displacement method (CDM), presented by Oñate and Matias in 1996,
to the instability analysis of structures with non-linear material
behaviour using a simple damage model. The extended CDM is useful
to detect instability points using a prediction of the critical
displacement field and a secant load-displacement relationship
accounting for material non-linearities. Examples of application
of CDM to the instability analysis of structures using bar and
solid finite elements are presented.

A scalar damage model with a shear retention factor for the analysis of reinforced concrete structures: theory and validation

María Jesús Samper — Mon, 07 Jan 2019 13:57:07 +0100

A local isotropic single parameter scalar model that can simulate the mechanical behaviour of quasi-brittle materials, such as concrete, is described. The constitutive law needs the mechanical characteristics and the fracture energy of concrete to be completely defined. The damage parameter is obtained directly from the value of an equivalent effective stress in order to reduce the computing effort. Due to the unique damage parameter, this model is suitable for the study of quasi-static problems involving monotonically increasing loads. The problem of localisation and mesh dependency have been partially overcome by using an enhanced local method in which a characteristic internal length related to the mesh dimension is employed instead of the characteristic fracture length. In this work, the model was enriched further with the introduction of a shear retention factor that accounts for the friction between the two surfaces of a crack. These new features assure a real improvement of the damage model, maintaining nevertheless its simplicity and low computing cost and making it suitable for the practical solution of large scale problems. Several numerical simulations of experimental tests, concerning fracture tests on concrete specimens and beams failing in shear, have been performed for the validation of the model. The main results from the numerical analyses are described and compared with the experimental ones.

A finite point method for elasticity problems

María Jesús Samper — Mon, 07 Jan 2019 13:45:56 +0100

The basis of the finite point method (FPM) for the fully meshless solution of elasticity problems in structural mechanics is described. A stabilization technique based on a finite calculus procedure is used to improve the quality of the numerical solution. The efficiency and accuracy of the stabilized FPM in the meshless analysis of simple linear elastic structural problems is shown in some examples of applications.

Rotation‐free triangular plate and shell elements

María Jesús Samper — Wed, 12 Dec 2018 12:50:18 +0100

The paper describes how the finite element method and the finite volume method can be successfully combined to derive two new families of thin plate and shell triangles with translational degrees of freedom as the only nodal variables. The simplest elements of the two families based on combining a linear interpolation of displacements with cell centred and cell vertex finite volume schemes are presented in detail. Examples of the good performance of the new rotation‐free plate and shell triangles are given.

An anisotropic elastoplastic constitutive model for large deformation analysis of fibre reinforced composites

María Jesús Samper — Tue, 20 Nov 2018 13:32:06 +0100

In this work a generalized anisotropic elastoplastic constitutive model in large deformation is presented. It is used for the analysis of fiber-reinforced composite materials in the frame of the finite element method. Mixing theory is applied to simulate the behavior of the composite material. The elastic anisotropic behavior is simulated with classical elasticity theory, while that of a non-proportional anisotropic solid is simulated by means of the proposed generalized anisotropic elastoplastic model. The approach assumes the existence of a real anisotropic space and of a fictitious isotropic space where a mapped fictitious problem is solved. Both spaces are related by means of a linear transformation using a fourth order tensor incorporating complete information on the real anisotropic material. Details of the numerical implementations of the model into a non-linear, large deformations finite element solution scheme are provided. Examples of application showing the performance of the model for the analysis of fiber-reinforced composite materials are given.

Desarrollos y aplicaciones de modelos de fractura en la escuela de ingenieros de caminos de Barcelona

María Jesús Samper — Wed, 20 Nov 2019 11:44:53 +0100

El artículo es una panorámica de los aspectos teóricos y algunas aplicaciones prácticas de los modelos de fractura desarrollados por diversos grupos en la Escuela de Ingenieros de Caminos de Barcelona (EICB) durante los últimos quince años para el análisis no lineal de estructuras. La motivación fundamental para el desarrollo de estos modelos se centra en el análisis de la seguridad de estructuras de hormigón en masa y armado. La mayor parte de los modelos se basan en la teoría de daño continuo y utilizan el método de los elementos finitos para la solución numérica. Los modelos de daño se han extendido y aplicado también con éxito al análisis de diversas estructuras de edificios históricos. Los desarrollos más recientes de estos modelos en la EICB incluyen la predicción de fenómenos de localización en estructuras de hormigón y el análisis del comportamiento no lineal de estructuras con materiales compuestos. De todos estos modelos se presentan en el artículo unas breves pinceladas, las aplicaciones más relevantes y las referencias donde pueden encontrarse los detalles sobre cada caso.

Adaptivity based on error estimation for viscoplastic softening materials

María Jesús Samper — Thu, 24 Oct 2019 13:27:02 +0200

This paper focuses on the numerical simulation of strain softening mechanical problems. Two problems arise: (1) the constitutive model has to be regular and (2) the numerical technique must be able to capture the two scales of the problem (the macroscopic geometrical representation and the microscopic behavior in the localization bands). The Perzyna viscoplastic model is used in order to obtain a regularized softening model allowing to simulate strain localization phenomena.
This model is applied to quasistatic examples. The viscous regularization of quasistatic processes is also discussed: in quasistatics, the internal length associated with the obtained band width is no longer only a function of the material parameters but also depends on the boundary value problem (geometry and loads, specially loading velocity). An adaptive computation is applied to softening viscoplastic materials showing strain localization. As the key ingredient of the adaptive strategy, a residual type error estimator is generalized to deal with such highly nonlinear material model. In several numerical examples the adaptive process is able to detect complex collapse modes that are not captured by a first, even if fine, mesh. Consequently, adaptive strategies are found to be essential to detect the collapse mechanism and to assess the optimal location of the elements in the mesh.

Error estimation for adaptive computations on shell structures

María Jesús Samper — Thu, 24 Oct 2019 11:33:01 +0200

The finite element discretization of a shell structure introduces two kinds of
errors: the error in the functional approximation and the error in the geometry
approximation. The first is associated with the finite dimensional interpolation
space and it is present in any finite element computation. The latter is associated
with the piecewise polynomial approximation of a curved surface and is much more
relevant in shell problems than in any other standard 2D or 3D computation. In
the shells framework, formerly the quality control of the finite element solution
has been carried out using flux projection a posteriori error estimators. This
technique exhibits two main drawbacks: 1) the flux smoothing averages stress components
over different elements that may have different physical meaning if the tangent
planes are different and 2) the error estimation process uses only the approximate
solution and hence, the discretized forces and the computational mesh: the data
describing the real geometry and load is therefore not accounted for. In this
work, a residual type error estimator introduced for standard 2D finite element
analysis is generalized to shell problems. This allows to easily account for the
real original geometry of the problem in the error estimation procedure and precludes
the necessity of comparing generalized stress components between non coplanar
elements. This estimator is based on approximating a reference error associated
with a refined reference mesh. In order to build up the residual error equation
the computed solution must be represented (projected) on the reference mesh. The
use of thin shell finite elements requires a proper formulation in order to preclude
shear locking. Following an idea of Donea and Lamain, the interpolation of the
rotations is not unique and requires a particular technique to transfer the information
from the computational mesh to the reference mesh. This technique is also developed
in this work and may be used in any adaptive evolution problem where the solution
must be transferred from one mesh to another.

Simulation of Construction of RCC Dams. II: Stress and Damage

María Jesús Samper — Wed, 03 Apr 2019 10:47:13 +0200

The increasing number of roller compacted concrete (RCC) dams being built around the world demands accurate methodologies for the realistic short- and long-term evaluations of the risk of thermally induced cracking in these constructions. In this work a numerical procedure for the simulation of the construction process of RCC dams is presented. It takes into account the more relevant features of the behavior of concrete at early ages, such as hydration, aging, creep, and damage. A 2D model of the Urugua-;aaı RCC Dam, built in Argentina, is used to perform the corresponding analyses. In this second part of the paper, the mechanical aspects of the simulation are presented; long-term effects are included by incorporating a creep model that naturally accounts for the aging effects, and the risk of tensile damage is also considered. The methodology determines the stress field inside the dam at any time during the construction and in the following years. Results for the reference case assess the suitability of the adopted design. This is compared to alternative studies considering different construction schedules to conclude that for these cases changes should be introduced in the dam design.

Simulation of Construction of RCC Dams. I: Temperature and Aging

María Jesús Samper — Wed, 03 Apr 2019 10:41:06 +0200

The increasing number of roller compacted concrete (RCC) dams being built around the world demands accurate methodologies for the realistic short- and long-term evaluations of the risk of thermally induced cracking in these constructions. In this work a numerical procedure for the simulation of the construction process of RCC dams is presented. It takes into account the more relevant features of the behavior of concrete at early ages, such as hydration, aging, creep, and damage. A 2D model of the Urugua-í RCC Dam, built in Argentina, is used to perform the corresponding analyses. In this first part only the thermochemical aspects of the simulation of the construction process are presented. The temperature distribution and evolution inside the dam are obtained before and after the completion of the dam. The evolution of the compressive and tensile strengths and elastic moduli and their final distribution inside the dam can also be predicted. Results from 2D and simplified vertical 1D models are compared to assess the validity of the latter, and several parametric studies are carried out. The simulation and discussion of the mechanical aspects of the construction process are relegated to a companion paper that follows.

A finite point method for incompressible flow problems

María Jesús Samper — Tue, 22 Jan 2019 11:47:07 +0100

A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite increment calculus (FIC) procedure developed by Oñate [14]. An enhanced fractional step procedure allowing the semi-implicit numerical solution of incompressible fluids using the FPM is described. Examples of application of the stabilized FPM to the solution of two incompressible flow problems are presented.

Solving structural optimization problems with genetic algorithms and simulated annealing

María Jesús Samper — Wed, 12 Dec 2018 12:24:32 +0100

In this paper we study the performance of two stochastic search methods: Genetic Algorithms and Simulated Annealing, applied to the optimization of pin‐jointed steel bar structures. We show that it is possible to embed these two schemes into a single parametric family of algorithms, and that optimal performance (in a parallel machine) is obtained by a hybrid scheme. Examples of applications to the optimization of several real steel bar structures are presented.

A homogeneous constitutive model for masonry

María Jesús Samper — Wed, 12 Dec 2018 12:14:16 +0100

Masonry has been a broadly used material since the beginning of human life. Despite its popularity, the analysis of masonry structures is a complex task due to the heterogeneity and the non‐linear material behaviour. The need for reliable analysis procedures capable of predicting damage evolution and failure in historical structures in order to design efficient repair and maintenance has motivated the work of many structural analysts in this field. Here the finite element method has emerged as one of the most powerful procedures for linear and non‐linear analysis of masonry structures. The main problem pending is the development of accurate and efficient constitutive models capable of predicting the behaviour of masonry in the non‐linear range and this has been the motivation of this work.

The constitutive model presented is based on the homogenized anisotropic elastoplasticity previously developed by the authors. The effect of anisotropy is introduced by means of fictitious isotropic stress and strain spaces. The material properties in the fictitious isotropic spaces are mapped into the actual anisotropic space by means of a consistent fourth‐order tensor. The advantage of the model is that the classical theory of plasticity can be used to model the non‐linear behaviour in the isotropic spaces.

Details of the model for masonry structures and its implementation in a general non‐linear finite element code are given. Examples of application to the analysis of some masonry structures are presented, showing the efficiency of the model.

A large strain explicit formulation for composites

María Jesús Samper — Wed, 12 Dec 2018 11:58:30 +0100

A geometrically non‐linear formulation for composites and the resulting explicit dynamic finite element algorithm are presented. The proposed formulation assumes that small elastic and large plastic strains, being the anisotropy considered using tensors which map the model variables at each time step into an equivalent isotropic space, where the integration of the rate constitutive equations is performed. The evolution of the internal variables is calculated in the auxiliary spaces, taking into account the material non‐linear behaviour, and the results mapped back to the real stress space. The updating of the mapping tensors for each new spatial configuration allows the treatment of general anisotropic materials under large strain and can be extended to treat multiphase composite materials using the mixing theory. The behaviour of the composite is dictated by the mechanical response of each substance, and the resultant model allows a fully non‐linear analysis combining different material models, such as damage in one compounding substance, elastoplastic behaviour in the other, while a third substance behaves elastically.

Structural shape sensitivity analysis for nonlinear material models with strain softening

María Jesús Samper — Fri, 26 Apr 2019 11:54:51 +0200

This paper describes some considerations around the analytical structural shape sensitivity analysis when the structural behaviour is computed using the finite element method with a nonlinear constitutive material model. Traditionally, the structural sensitivity analysis is computed using an incremental approach based on the incremental procedures for the solution of the structural equilibrium problem. In this work, a direct (nonincremental) formulation for computing these structural sensitivities, that is valid for some specific nonlinear material models, is proposed. The material models for which the presented approach is valid are characterized by the fact that the stresses at any timet can be expressed in terms of the strains at the timet and, in some cases, the strains at a specific past timet u (t u<t). This is the case of elasticity (linear as well as nonlinear), perfect plasticity and damage models. A special strategy is also proposed for material models with strain softening.

For the cases where it is applicable, the sensitivity analysis proposed here allows us to compute the structural sensitivities around any structural equilibrium point after finishing the solution process and it is completely independent of the numerical scheme used to solve the structural equilibrium problem. This possibility is particularized for the case of a damage model considering a strain-softening behaviour. Finally, the quality and reliability of the proposed approach is assessed through its application to some example

Thermo-Chemo-Mechanical Model for Concrete. II: Damage and Creep

María Jesús Samper — Tue, 02 Apr 2019 13:13:26 +0200

In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. This paper presents the formulation and assessment of the mechanical aspects of the model. Short- and long-term mechanical behaviors are modeled via a viscoelastic damage model that accounts for the aging effects. The short-term model is based on the framework of the continuum damage mechanics theory. A novel normalized format of the damage model is proposed, so that the phenomenon of aging is accounted for in a natural fashion. Long-term effects are included by incorporating a creep model inspired in the microprestress-solidification theory.

Thermo-chemo-mechanical model for concrete. I: Hydration and aging

María Jesús Samper — Tue, 02 Apr 2019 13:09:18 +0200

In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. The model allows simulation of the observed phenomena of hydration, aging, damage, and creep. It is formulated within an appropriate thermodynamic framework, from which the state equations are derived. In this first part, the formulation and assessment of the thermochemical aspects of the model are presented. It is based on the reactive porous media theory, and it can accurately predict the evolution in time of the hydration degree and the hydration heat production. The evolution of the compressive and tensile strengths and elastic moduli is related to the aging degree, a concept introduced to account for the effect of the curing temperature in the evolution of the mechanical properties. The short- and long-term mechanical behavior is modeled by means of a viscoelastic damage model that accounts for the aging effects. The formulation and assessment of the mechanical part of the model are relegated to a companion paper.

Strong discontinuities and continuum plasticity models: the strong discontinuity approach

María Jesús Samper — Tue, 02 Apr 2019 12:37:54 +0200

The paper presents the Strong Discontinuity Approach for the analysis and simulation of strong discontinuities in solids using continuum plasticity models. Kinematics of weak and strong discontinuities are discussed, and a regularized kinematic state of discontinuity is proposed as a mean to model the formation of a strong discontinuity as the collapsed state of a weak discontinuity (with a characteristic bandwidth) induced by a bifurcation of the stress–strain field, which propagates in the solid domain. The analysis of the conditions to induce the bifurcation provides a critical value for the bandwidth at the onset of the weak discontinuity and the direction of propagation. Then a variable bandwidth model is proposed to characterize the transition between the weak and strong discontinuity regimes. Several aspects related to the continuum and, their associated, discrete constitutive equations, the expended power in the formation of the discontinuity and relevant computational details related to the finite element simulations are also discussed. Finally, some representative numerical simulations are shown to illustrate the proposed approach.

A layer-wise triangle for analysis of laminated composite plates and shells

María Jesús Samper — Mon, 07 Jan 2019 13:32:03 +0100

The paper presents a new triangle for analysis of laminate plates and shells. The in-plane degrees of freedom are interpolated quadratically whereas a linear layer-wise approximation is chosen for the normal displacement. A substructuring technique is used to eliminate the in-plane degrees of freedom during the assembly process thus reducing substantially the computationed costs. The element performance is evaluated in the static and dynamic analysis of dierent laminate plate and shell structures

A general procedure for deriving symmetric expressions for the secant and tangent stiffness matrices in finite element analysis

María Jesús Samper — Wed, 12 Dec 2018 11:29:15 +0100

The paper presents a general and straightforward procedure based on the use of the strain energy density for deriving symmetric expressions of the secant and tangent stiffness matrices for finite element analysis of geometrically non‐linear structural problems. The analogy with previously proposed methods for deriving secant and tangent matrices is detailed. The simplicity of the approach is shown in an example of application