In this study a FETI: Finite Element Tearing and Interconnecting [1] technique is adopted and exp... more In this study a FETI: Finite Element Tearing and Interconnecting [1] technique is adopted and exploited for the efficient and accurate modeling of softening materials such as concrete and rock. A fie scale analysis in which concrete is modelled as a three-phase material is used. Special attention is given to the treatment of linear and non-linear domains during the analysis. Several optimization enhancements are introduced in order to identify the active non-linear domains and selectively use computational effort. The effect of different decomposition criteria is analyzed in this study. The brittle constitutive behaviour of the above mentioned material is simulated by means of a Gradient Enhanced Damage model.
We focus on the analysis of fracture in quasi-brittle materials by exploiting the potential of do... more We focus on the analysis of fracture in quasi-brittle materials by exploiting the potential of domain decomposition techniques. More specifically, we restrict our attention to the FETI (Finite Element Tearing and Interconnecting) method which is used as a solver in our non-linear solution scheme. We develop criteria to anticipate the linear/non-linear character of different regions in the structure according to a damage constitutive model. A first application of our scheme focuses on the efficiency increase of a monoscale analysis by simplifying the computations in those areas that remain linear. The second application treats the problem in a multiscale fashion where the resolution of the non-linear domains is increased in order to describe failure phenomena with a higher degree of accuracy. Both applications represent a significant improvement from a computational standpoint when the main non-linear regions are small compared to the size of the whole specimen. This is often the cas...
On the microlevel, cusps are formed during delamination crack growth under mode II loading condit... more On the microlevel, cusps are formed during delamination crack growth under mode II loading conditions. In this work, two different approaches to simulate this process are presented. Firstly a cohesive zone method where cohesive segments are introduced between a pair of neighbouring elements when the traction between those elements exceeds the strength. And secondly the thick level set method, which allows for a staggered solution scheme. Both methods successfully predict the inclined cracks that form initially if constitutive laws are chosen carefully, but both have difficulties to simulate final failure.
Stationary and propagative instabilities have been studied in the paper. For stationary or static... more Stationary and propagative instabilities have been studied in the paper. For stationary or static instabilities the numerical simulation of a finite width and unique oriention of the shear band is essential. A gradient viscoplasticity model has been used to analyse shear banding. The role of the two length scale parameters that are introduced in the model has been investigated in
Computer Methods in Applied Mechanics and Engineering
Abstract Using a path-following algorithm to analyze a quasi-static nonlinear structural problem ... more Abstract Using a path-following algorithm to analyze a quasi-static nonlinear structural problem involves selecting an appropriate constraint function. This function should improve the desired performance targets of the path-following algorithm such as robustness, speed, accuracy, and smoothness. In order to be able to draw a fair objective selection of a constraint function, it is necessary to collect adequate constraint equations as well as to define the performance of nonlinear methods. In this paper, three new path-following constraints applicable for damage analysis of quasi-brittle materials are proposed. Additionally, performance criteria and their numerical measures for a posteriori assessment of robustness, smoothness, accuracy, and speed of solving nonlinear problems by a path-following method are proposed. Based on the proposed criteria, the performance of the three new constraints and two existing ones is compared for two example problems. As a result, the performance measures are shown to possess an ability to clearly explore the strengths of each constraint. They establish a firm basis for the assessment of not only path-following methods but also other methods for solving nonlinear structural problems.
In this study, three different soft pneumatic actuators (SPA) are designed and directly fabricate... more In this study, three different soft pneumatic actuators (SPA) are designed and directly fabricated through additive manufacturing using thermoplastic polyurethane (TPU) filaments. The equal total inner volume size is used in the three varied designs to compare their effect on the bending response. A material model is selected and implemented according to the uniaxial tensile test parameters. The experimental results obtained from three different soft pneumatic actuators are compared with numerical model results. Especially, the experimentally measured bending forces are compared with the numerical model counterparts. The highest continuous bending deformation is determined among the three different soft pneumatic actua-tors. Additionally, a new integrated design and manufacturing approach is presented aiming to maximize the potential bending capability of the actuator through additive manufacturing.
Within the framework of additive plasticity, an objective stress update algorithm has been propos... more Within the framework of additive plasticity, an objective stress update algorithm has been proposed. The procedure is implemented in such way that the extension from a standard small strain FE code to the finite strain range is straightforward, and objectivity can be retained for any choice of the intermediate configuration. The additional computational cost only includes some geometrical manipulations. For
Computer Methods in Applied Mechanics and Engineering
ABSTRACT The Thick Level Set method (TLS) is a new approach to the modeling of damage growth. In ... more ABSTRACT The Thick Level Set method (TLS) is a new approach to the modeling of damage growth. In the TLS, damage is defined as a function of the distance to a moving front. The level set method with signed distance function is used to keep track of the front location and to evaluate the distance to the front throughout the domain. The update of damage is done indirectly by moving the damage front based on integration of the configurational force across the damaged band. In this paper, the TLS is applied to shear failure of a sandwich structure. Two problems with the TLS are encountered in this study and solutions are proposed. Firstly, it is found that sliding deformations across a crack lead to unrealistic activation of stiffness recovery that is included for modeling damage under compression. In order to allow for free sliding, a special interphase constitutive law is proposed that takes the direction of the material interface into account when it comes to stiffness recovery. Secondly, it is found that in the TLS the crack propagation stress is lower than the damage initiation stress, which is in many cases unrealistic. It is proposed to use two values instead of one for the material resistance against damage growth, one related to initiation and the other related to propagation. The resistance changes from the first to the second value as the damaged zone grows. With the two innovations presented in this paper, it is possible to simulate cusp formation in shear failure. It is emphasized that the robustness of the TLS is a significant advantage in the simulation of cusp formation which involves multiple merging cracks.
In this paper failure is assumed to be a discrete phenomenon. A modelling in which a crack or a s... more In this paper failure is assumed to be a discrete phenomenon. A modelling in which a crack or a shear band is incorporated in the shape functions of the finite element formulation is used. A discontinuous function of the displacement gradients acts as an additional localized mode with a length scale parameter that is independent of the element size. A
The last decade has seen a growing interest in cohesive zone models for fatigue applications. The... more The last decade has seen a growing interest in cohesive zone models for fatigue applications. These cohesive zone models often suffer from a lack of generality and applying them typically requires calibrating a large number of model-specific parameters. To improve on these issues a new method has been proposed in this paper based on the Thick Level Set approach. In this concept, material degradation due to cyclic loading is the result of interaction between damage evolution and fracture mechanics. The Thick Level Set formulation has been extended to interface elements, in order to allow for separation of strain energy in the bulk and energy required for surface creation. Global fracture parameters, derived from a free energy description governing the interface elements, are used as input for the empirical crack growth rate relation (Paris’ equation). It must be emphasized that in contrast to existing fatigue models, the Thick Level Set approach does not require the definition of a damage evolution law. Instead, damage is updated automatically by a continuously moving damage front. It is shown that applicability is not limited to fatigue behavior of linear elastic materials; elastic-plastic materials such as steels can be analysed as well. The sensitivity of model parameters is investigated and discussed and the practical relevance is explored for standard test configurations.
IOP Conference Series: Materials Science and Engineering
In this work a glass/epoxy composite commonly used in wind turbine blades is exposed to a humid e... more In this work a glass/epoxy composite commonly used in wind turbine blades is exposed to a humid environment at an elevated temperature. To research the anisotropic diffusion behaviour observed in unidirectional composite specimens, experimental results of slices cut along the three directional planes of the laminate immersed in demineralised water at 50 • C are coupled with numerical modelling. The weight of the slices was measured at regular intervals, from which the uptake behaviour could be deduced. The process was modelled using a 3-dimensional RVE of the material, where diffusion is modelled as steady-state and the diffusivity in each direction was measured by applying concentration gradients to the model. The experimental data shows similar water uptake behaviour for samples in both transverse directions, while the water uptake in the fibre direction was significantly faster. A proper fit according to Fick's law was obtained for the transverse direction, while this was not possible for the samples in fibre direction, suggesting a strong dependency of the diffusion behaviour on the fibre orientation. Results from the proposed numerical models show that the geometric effect of fibres acting as barriers for the water movement is indeed responsible for part of the observed anisotropy.
Proceedings of 10th World Congress on Computational Mechanics, 2014
A mesoscopic, geometrically and physically nonlinear finite element model based on solid-like she... more A mesoscopic, geometrically and physically nonlinear finite element model based on solid-like shell elements is presented for the simulation of impact damage in laminated composite structures. To model matrix cracking, a discontinuous solid-like shell element (DSLS) is utilized. A partition of unity approach is exploited to incorporate the discontinuity in the shell mid-surface, shell director and internal stretching field. This enables the element to model arbitrary propagating cracks through a finite element mesh. The element has only displacement degrees of freedom, thus avoid the need for a complicated update of rotation degrees of freedom in nonlinear applications. The model is also able to predict the buckling response of laminated composites. To model delamination phenomena, a shell interface model is developed. The model allows computationally efficient simulation of delamination and evaluation of the consistently linearized tangent stiffness matrix for large deformation problems, which is essential for convergence. To model the coupled response of matrix cracking and delamination under large deformations, a computational framework is developed. The combined modeling of matrix cracking and delamination is achieved without incorporating of additional degrees of freedom. A numerical example is presented to simulate failure resulting in matrix cracking and delamination in laminated composite shell structures.
Rubber-like materials exhibit a strongly non-linear behaviour characterised by large strains and ... more Rubber-like materials exhibit a strongly non-linear behaviour characterised by large strains and a non-linear stress-strain response. When a rubber specimen is subjected to cyclic loading, stress-softening phenomena (the Mullins effect) are also observed. Moreover, carbon-filled rubber specimens, in general, do not return to their initial state after loading and subsequent unloading, but exhibit a residual strain or permanent deformation. The permanent deformation combined with stress-softening effects in rubber-like materials results in complex mechanical behaviour and modelling is still in an initial stage.
In the paper a number of computational issues related to the continuum modelling of dynamic failu... more In the paper a number of computational issues related to the continuum modelling of dynamic failure will be addressed. Attention is focused on the influence of the crack concept. A comparison is made between the standard, the rate-dependent and the gradient-dependent crack concept. The effect of the inclusion of an internal length scale for the latter two models and it’s influence on the failure mechanism is discussed. The computational analysis of a reinforced beam under impact loading is treated as an example.
International Journal of Numerical Methods for Heat & Fluid Flow, 2013
Purpose – This paper aims to present a computationally efficient finite element model for the sim... more Purpose – This paper aims to present a computationally efficient finite element model for the simulation of isothermal immiscible two-phase flow in a rigid porous media with a particular application to CO2 sequestration in underground formations. Focus is placed on developing a numerical procedure, which is effectively mesh-independent and suitable to problems at regional scales. Design/methodology/approach – The averaging theory is utilized to describe the governing equations of the involved unsaturated multiphase flow. The level-set (LS) method and the extended finite element method (XFEM) are utilized to simulate flow of the CO2 plume. The LS is employed to trace the plume front. A streamline upwind Petrov-Galerkin method is adopted to stabilize possible occurrence of spurious oscillations due to advection. The XFEM is utilized to model the high gradient in the saturation field front, where the LS function is used for enhancing the weighting and the shape functions. Findings – The capability of the pro...
In this study a FETI: Finite Element Tearing and Interconnecting [1] technique is adopted and exp... more In this study a FETI: Finite Element Tearing and Interconnecting [1] technique is adopted and exploited for the efficient and accurate modeling of softening materials such as concrete and rock. A fie scale analysis in which concrete is modelled as a three-phase material is used. Special attention is given to the treatment of linear and non-linear domains during the analysis. Several optimization enhancements are introduced in order to identify the active non-linear domains and selectively use computational effort. The effect of different decomposition criteria is analyzed in this study. The brittle constitutive behaviour of the above mentioned material is simulated by means of a Gradient Enhanced Damage model.
We focus on the analysis of fracture in quasi-brittle materials by exploiting the potential of do... more We focus on the analysis of fracture in quasi-brittle materials by exploiting the potential of domain decomposition techniques. More specifically, we restrict our attention to the FETI (Finite Element Tearing and Interconnecting) method which is used as a solver in our non-linear solution scheme. We develop criteria to anticipate the linear/non-linear character of different regions in the structure according to a damage constitutive model. A first application of our scheme focuses on the efficiency increase of a monoscale analysis by simplifying the computations in those areas that remain linear. The second application treats the problem in a multiscale fashion where the resolution of the non-linear domains is increased in order to describe failure phenomena with a higher degree of accuracy. Both applications represent a significant improvement from a computational standpoint when the main non-linear regions are small compared to the size of the whole specimen. This is often the cas...
On the microlevel, cusps are formed during delamination crack growth under mode II loading condit... more On the microlevel, cusps are formed during delamination crack growth under mode II loading conditions. In this work, two different approaches to simulate this process are presented. Firstly a cohesive zone method where cohesive segments are introduced between a pair of neighbouring elements when the traction between those elements exceeds the strength. And secondly the thick level set method, which allows for a staggered solution scheme. Both methods successfully predict the inclined cracks that form initially if constitutive laws are chosen carefully, but both have difficulties to simulate final failure.
Stationary and propagative instabilities have been studied in the paper. For stationary or static... more Stationary and propagative instabilities have been studied in the paper. For stationary or static instabilities the numerical simulation of a finite width and unique oriention of the shear band is essential. A gradient viscoplasticity model has been used to analyse shear banding. The role of the two length scale parameters that are introduced in the model has been investigated in
Computer Methods in Applied Mechanics and Engineering
Abstract Using a path-following algorithm to analyze a quasi-static nonlinear structural problem ... more Abstract Using a path-following algorithm to analyze a quasi-static nonlinear structural problem involves selecting an appropriate constraint function. This function should improve the desired performance targets of the path-following algorithm such as robustness, speed, accuracy, and smoothness. In order to be able to draw a fair objective selection of a constraint function, it is necessary to collect adequate constraint equations as well as to define the performance of nonlinear methods. In this paper, three new path-following constraints applicable for damage analysis of quasi-brittle materials are proposed. Additionally, performance criteria and their numerical measures for a posteriori assessment of robustness, smoothness, accuracy, and speed of solving nonlinear problems by a path-following method are proposed. Based on the proposed criteria, the performance of the three new constraints and two existing ones is compared for two example problems. As a result, the performance measures are shown to possess an ability to clearly explore the strengths of each constraint. They establish a firm basis for the assessment of not only path-following methods but also other methods for solving nonlinear structural problems.
In this study, three different soft pneumatic actuators (SPA) are designed and directly fabricate... more In this study, three different soft pneumatic actuators (SPA) are designed and directly fabricated through additive manufacturing using thermoplastic polyurethane (TPU) filaments. The equal total inner volume size is used in the three varied designs to compare their effect on the bending response. A material model is selected and implemented according to the uniaxial tensile test parameters. The experimental results obtained from three different soft pneumatic actuators are compared with numerical model results. Especially, the experimentally measured bending forces are compared with the numerical model counterparts. The highest continuous bending deformation is determined among the three different soft pneumatic actua-tors. Additionally, a new integrated design and manufacturing approach is presented aiming to maximize the potential bending capability of the actuator through additive manufacturing.
Within the framework of additive plasticity, an objective stress update algorithm has been propos... more Within the framework of additive plasticity, an objective stress update algorithm has been proposed. The procedure is implemented in such way that the extension from a standard small strain FE code to the finite strain range is straightforward, and objectivity can be retained for any choice of the intermediate configuration. The additional computational cost only includes some geometrical manipulations. For
Computer Methods in Applied Mechanics and Engineering
ABSTRACT The Thick Level Set method (TLS) is a new approach to the modeling of damage growth. In ... more ABSTRACT The Thick Level Set method (TLS) is a new approach to the modeling of damage growth. In the TLS, damage is defined as a function of the distance to a moving front. The level set method with signed distance function is used to keep track of the front location and to evaluate the distance to the front throughout the domain. The update of damage is done indirectly by moving the damage front based on integration of the configurational force across the damaged band. In this paper, the TLS is applied to shear failure of a sandwich structure. Two problems with the TLS are encountered in this study and solutions are proposed. Firstly, it is found that sliding deformations across a crack lead to unrealistic activation of stiffness recovery that is included for modeling damage under compression. In order to allow for free sliding, a special interphase constitutive law is proposed that takes the direction of the material interface into account when it comes to stiffness recovery. Secondly, it is found that in the TLS the crack propagation stress is lower than the damage initiation stress, which is in many cases unrealistic. It is proposed to use two values instead of one for the material resistance against damage growth, one related to initiation and the other related to propagation. The resistance changes from the first to the second value as the damaged zone grows. With the two innovations presented in this paper, it is possible to simulate cusp formation in shear failure. It is emphasized that the robustness of the TLS is a significant advantage in the simulation of cusp formation which involves multiple merging cracks.
In this paper failure is assumed to be a discrete phenomenon. A modelling in which a crack or a s... more In this paper failure is assumed to be a discrete phenomenon. A modelling in which a crack or a shear band is incorporated in the shape functions of the finite element formulation is used. A discontinuous function of the displacement gradients acts as an additional localized mode with a length scale parameter that is independent of the element size. A
The last decade has seen a growing interest in cohesive zone models for fatigue applications. The... more The last decade has seen a growing interest in cohesive zone models for fatigue applications. These cohesive zone models often suffer from a lack of generality and applying them typically requires calibrating a large number of model-specific parameters. To improve on these issues a new method has been proposed in this paper based on the Thick Level Set approach. In this concept, material degradation due to cyclic loading is the result of interaction between damage evolution and fracture mechanics. The Thick Level Set formulation has been extended to interface elements, in order to allow for separation of strain energy in the bulk and energy required for surface creation. Global fracture parameters, derived from a free energy description governing the interface elements, are used as input for the empirical crack growth rate relation (Paris’ equation). It must be emphasized that in contrast to existing fatigue models, the Thick Level Set approach does not require the definition of a damage evolution law. Instead, damage is updated automatically by a continuously moving damage front. It is shown that applicability is not limited to fatigue behavior of linear elastic materials; elastic-plastic materials such as steels can be analysed as well. The sensitivity of model parameters is investigated and discussed and the practical relevance is explored for standard test configurations.
IOP Conference Series: Materials Science and Engineering
In this work a glass/epoxy composite commonly used in wind turbine blades is exposed to a humid e... more In this work a glass/epoxy composite commonly used in wind turbine blades is exposed to a humid environment at an elevated temperature. To research the anisotropic diffusion behaviour observed in unidirectional composite specimens, experimental results of slices cut along the three directional planes of the laminate immersed in demineralised water at 50 • C are coupled with numerical modelling. The weight of the slices was measured at regular intervals, from which the uptake behaviour could be deduced. The process was modelled using a 3-dimensional RVE of the material, where diffusion is modelled as steady-state and the diffusivity in each direction was measured by applying concentration gradients to the model. The experimental data shows similar water uptake behaviour for samples in both transverse directions, while the water uptake in the fibre direction was significantly faster. A proper fit according to Fick's law was obtained for the transverse direction, while this was not possible for the samples in fibre direction, suggesting a strong dependency of the diffusion behaviour on the fibre orientation. Results from the proposed numerical models show that the geometric effect of fibres acting as barriers for the water movement is indeed responsible for part of the observed anisotropy.
Proceedings of 10th World Congress on Computational Mechanics, 2014
A mesoscopic, geometrically and physically nonlinear finite element model based on solid-like she... more A mesoscopic, geometrically and physically nonlinear finite element model based on solid-like shell elements is presented for the simulation of impact damage in laminated composite structures. To model matrix cracking, a discontinuous solid-like shell element (DSLS) is utilized. A partition of unity approach is exploited to incorporate the discontinuity in the shell mid-surface, shell director and internal stretching field. This enables the element to model arbitrary propagating cracks through a finite element mesh. The element has only displacement degrees of freedom, thus avoid the need for a complicated update of rotation degrees of freedom in nonlinear applications. The model is also able to predict the buckling response of laminated composites. To model delamination phenomena, a shell interface model is developed. The model allows computationally efficient simulation of delamination and evaluation of the consistently linearized tangent stiffness matrix for large deformation problems, which is essential for convergence. To model the coupled response of matrix cracking and delamination under large deformations, a computational framework is developed. The combined modeling of matrix cracking and delamination is achieved without incorporating of additional degrees of freedom. A numerical example is presented to simulate failure resulting in matrix cracking and delamination in laminated composite shell structures.
Rubber-like materials exhibit a strongly non-linear behaviour characterised by large strains and ... more Rubber-like materials exhibit a strongly non-linear behaviour characterised by large strains and a non-linear stress-strain response. When a rubber specimen is subjected to cyclic loading, stress-softening phenomena (the Mullins effect) are also observed. Moreover, carbon-filled rubber specimens, in general, do not return to their initial state after loading and subsequent unloading, but exhibit a residual strain or permanent deformation. The permanent deformation combined with stress-softening effects in rubber-like materials results in complex mechanical behaviour and modelling is still in an initial stage.
In the paper a number of computational issues related to the continuum modelling of dynamic failu... more In the paper a number of computational issues related to the continuum modelling of dynamic failure will be addressed. Attention is focused on the influence of the crack concept. A comparison is made between the standard, the rate-dependent and the gradient-dependent crack concept. The effect of the inclusion of an internal length scale for the latter two models and it’s influence on the failure mechanism is discussed. The computational analysis of a reinforced beam under impact loading is treated as an example.
International Journal of Numerical Methods for Heat & Fluid Flow, 2013
Purpose – This paper aims to present a computationally efficient finite element model for the sim... more Purpose – This paper aims to present a computationally efficient finite element model for the simulation of isothermal immiscible two-phase flow in a rigid porous media with a particular application to CO2 sequestration in underground formations. Focus is placed on developing a numerical procedure, which is effectively mesh-independent and suitable to problems at regional scales. Design/methodology/approach – The averaging theory is utilized to describe the governing equations of the involved unsaturated multiphase flow. The level-set (LS) method and the extended finite element method (XFEM) are utilized to simulate flow of the CO2 plume. The LS is employed to trace the plume front. A streamline upwind Petrov-Galerkin method is adopted to stabilize possible occurrence of spurious oscillations due to advection. The XFEM is utilized to model the high gradient in the saturation field front, where the LS function is used for enhancing the weighting and the shape functions. Findings – The capability of the pro...
Uploads
Papers by L. Sluys