A gradient-enhanced continuum damage model for fibre-reinforced materials

Modelo de daño no local definido a materiales fibrados. Este modelo se aplica al estudio de problemas típicos en la biomecánica de los tejidos blandos, como las paredes arteriales.

Discontinuous solutions and boundary value problems for non-linearly elastic fibre-reinforced materials

En este trabajo se han analizado varios problemas en el contexto de la elasticidad no lineal basándose en modelos constitutivos representativos. En particular, se han analizado problemas relacionados con el fenómeno de perdida de estabilidad asociada con condiciones de contorno en el caso de material reforzados con fibras. Cada problema se ha formulado y se ha analizado por separado en diferentes capítulos. En primer lugar se ha mostrado el análisis del gradiente de deformación discontinuo para un material transversalmente isótropo, en particular, el modelo del material considerado consiste de una base neo-Hookeana isótropa incrustada con fibras de refuerzo direccional caracterizadas con un solo parámetro. La solución de este problema se vincula con instabilidades que dan lugar al mecanismo de fallo conocido como banda de cortante. La perdida de elipticidad de las ecuaciones diferenciales de equilibrio es una condición necesaria para que aparezca este tipo de soluciones y por tanto las inestabilidades asociadas. En segundo lugar se ha analizado una deformación combinada de extensión, inación y torsión de un tubo cilíndrico grueso donde se ha encontrado que la deformación citada anteriormente puede ser controlada solo para determinadas direcciones de las fibras refuerzo. Para entender el comportamiento elástico del tubo considerado se ha ilustrado numéricamente los resultados obtenidos para las direcciones admisibles de las fibras de refuerzo bajo la deformación considerada. En tercer lugar se ha estudiado el caso de un tubo cilíndrico grueso reforzado con dos familias de fibras sometido a cortante en la dirección azimutal para un modelo de refuerzo especial. En este problema se ha encontrado que las inestabilidades que aparecen en el material considerado están asociadas con lo que se llama soluciones múltiples de la ecuación diferencial de equilibrio. Se ha encontrado que el fenómeno de instabilidad ocurre en un estado de deformación previo al estado de deformación donde se pierde la elipticidad de la ecuación diferencial de equilibrio. También se ha demostrado que la condición de perdida de elipticidad y ^W=2 = 0 (la segunda derivada de la función de energía con respecto a la deformación) son dos condiciones necesarias para la existencia de soluciones múltiples. Finalmente, se ha analizado detalladamente en el contexto de elipticidad un problema de un tubo cilíndrico grueso sometido a una deformación combinada en las direcciones helicoidal, axial y radial para distintas geotermias de las fibras de refuerzo . In the present work four main problems have been addressed within the framework of non-linear elasticity based on representative constitutive models. Namely, problems related to the loss of stability phenomena associated with boundary value problems for fibre-reinforced materials. Each of the considered problems is formulated and analysed separately in different chapters. We first start with the analysis of discontinuous deformation gradients for a transversely isotropic material under plane deformation. In particular, the material model is an augmented neo-Hookean base with a simple unidirectional reinforcement characterised by a single parameter. The solution of this problem is related to material instabilities and it is associated with a shear band-type failure mode. The loss of ellipticity of the governing differential equations is a necessary condition for the existence of these material instabilities. The second problem involves a detailed analysis of the combined non-linear extension, inflation and torsion of a thick-walled circular cylindrical tube where it has been found that the aforementioned deformation is controllable only for certain preferred directions of transverse isotropy. Numerical results have been illustrated to understand the elastic behaviour of the tube for the admissible preferred directions under the considered deformation. The third problem deals with the analysis of a doubly fibre-reinforced thickwalled circular cylindrical tube undergoing pure azimuthal shear for a special class of the reinforcing model where multiple non-smooth solutions emerge. The associated instability phenomena are found to occur prior to the point where the nominal stress tensor changes monotonicity in a particular direction. It has been also shown that the loss of ellipticity condition that arises from the equilibrium equation and ^W=2 = 0 (the second derivative of the strain-energy function with respect to the deformation) are equivalent necessary conditions for the emergence of multiple solutions for the considered material. Finally, a detailed analysis in the basis of the loss of ellipticity of the governing differential equations for a combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube is carried out.

A gradient-enhanced large-deformation continuum damage model for fibre-reinforced materials

A non-local gradient-based damage formulation within a geometrically non-linear setting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre-reinforced material, respectively. The inelastic constitutive response is governed by a scalar [1–d]-type damage formulation, where only the anisotropic elastic part is assumed to be affected by the damage. Following the concept in Dimitrijević and Hackl [28], the local free energy function is enhanced by a gradient-term. This term essentially contains the gradient of the non-local damage variable which, itself, is introduced as an additional independent variable. In order to guarantee the equivalence between the local and non-local damage variable, a penalisation term is incorporated within the free energy function. Based on the principle of minimum total potential energy, a coupled system of Euler–Lagrange equations, i.e., the balance of linear momentum and the balance of the non-local damage field, is obtained and solved in weak form. The resulting coupled, highly non-linear system of equations is symmetric and can conveniently be solved by a standard incremental-iterative Newton–Raphson-type solution scheme. Several three-dimensional displacement- and force-driven boundary value problems—partially motivated by biomechanical application—highlight the mesh-objective characteristics and constitutive properties of the model and illustratively underline the capabilities of the formulation proposed

Implementation of a bond model, including dilation, for reinforced materials in a finite element analysis /

Cover title.

Biaxial failure model for fiber reinforced concrete

Steel fiber reinforced concrete (SFRC) is widely applied in the construction industry. Numerical elastoplastic analysis of the macroscopic behavior is complex. This typically involves a piecewise linear failure curve including corner singularities. This paper presents a single smooth biaxial failure curve for SFRC based on a semianalytical approximation. Convexity of the proposed model is guaranteed so that numerical problems are avoided. The model has sufficient flexibility to closely match experimental results. The failure curve is also suitable for modeling plain concrete under biaxial loading. Since this model is capable of simulating the failure states in all stress regimes with a single envelope, the elastoplastic formulation is very concise and simple. The finite element implementation is developed to demonstrate the conciseness and the effectiveness of the model. The computed results display good agreement with published experimental data.

Thermoplastic Starch-based Composites Reinforced with Rape Fibers: Water Uptake and Thermomechanical Properties

Fully biodegradable composite materials were obtained through reinforcement of a commercially available thermoplastic starch (TPS) matrix with rapeseed fibers (RSF). The influence of reinforcement content on the water sorption capacity, as well as thermal and thermo-mechanical properties of composites were evaluated. Even though the hydrophilic character of natural fibers tends to favor the absorption of water, results demonstrated that the incorporation of RSF did not have a significant effect on the water uptake of the composites. DSC experiments showed that fibers restricted the mobility of the starch macromolecules from the TPS matrix, hence reducing their capacity to crystallize. The viscoelastic behaviour of TPS was also affected, and reinforced materials presented lower viscous deformation and recovery capacity. In addition, the elasticity of materials was considerably diminished when increasing fiber content, as evidenced in the TMA and DMTA measurements

A robust numerical framework for the analysis of material failure of fibre reinforced soft tissue

In this work, robustness and stability of continuum damage models applied to material failure in soft tissues are addressed. In the implicit damage models equipped with softening, the presence of negative eigenvalues in the tangent elemental matrix degrades the condition number of the global matrix, leading to a reduction of the computational performance of the numerical model. Two strategies have been adapted from literature to improve the aforementioned computational performance degradation: the IMPL-EX integration scheme [Oliver,2006], which renders the elemental matrix contribution definite positive, and arclength-type continuation methods [Carrera,1994], which allow to capture the unstable softening branch in brittle ruptures. The IMPL-EX integration scheme has as a major drawback the need to use small time steps to keep numerical error below an acceptable value. A convergence study, limiting the maximum allowed increment of internal variables in the damage model, is presented. Finally, numerical simulation of failure problems with fibre reinforced materials illustrates the performance of the adopted methodology.

A robust numerical framework to the analysis of material failure of fibre reinforced soft tissue

In this work, robustness and stability of continuum damage models applied to material failure in soft tissues are addressed. In the implicit damage models equipped with softening, the presence of negative eigenvalues in the tangent elemental matrix degrades the condition number of the global matrix, leading to a reduction of the computational performance of the numerical model. Two strategies have been adapted from literature to improve the aforementioned computational performance degradation: the IMPL-EX integration scheme [Oliver,2006], which renders the elemental matrix contribution definite positive, and arclength-type continuation methods [Carrera,1994], which allow to capture the unstable softening branch in brittle ruptures. The IMPL-EX integration scheme has as a major drawback the need to use small time steps to keep numerical error below an acceptable value. A convergence study, limiting the maximum allowed increment of internal variables in the damage model, is presented. Finally, numerical simulation of failure problems with fibre reinforced materials illustrates the performance of the adopted methodology.

Fiberglass reinforced polymer composite bridge deck construction in Illinois /

"Report no. FHWA/IL/PRR-145"--Technical rept. documentation p.

Influencia del proceso de reciclado sobre las propiedades de los materiales compuestos obtenidos por inyección de poliestireno reforzado con fibras lignocelulósicas

The objective of this research is to study the influence of several recycling cycles on the mechanical properties of four different materials made by the injection of polystyrene. The four materials studied have different characteristics. The first one is polystyrene (PS), the second one is polystyrene reinforced with hemp fibers (PSf), the third one is polystyrene reinforced with hemp fibers modified with AKD (PSft) and the last one is polystyrene reinforced with fiberglass (PSfv). With all these materials tensile strength, bending, hardness and impact is measured. After the measurement of these physical properties, materials are recycled to obtain new injection samples, and its physical properties are measured again. This process is repeated during 24 cycles. After each recycling cycle material physical properties are related with polystyrene molecular weight, melt flow, FTIR spectra and DSC. From reinforced materials, fibers are recovered and through microscopy and image analysis they are characterized to study the influence that recycling has on its structure.

Fadiga em dormentes de concreto reforçados com fibras de aço

A prestressed concrete monoblock railroad tie was designed to attend the characteristics of a Brazilian railroad track with 1,600 mm gauge and 320 kN axle load. Concrete ties specimens were manufactured without and with steel fibers in a volume fraction of 60 kg/m3 (0.76 % by volume), and three different initial prestress forces. Static and fatigue tests were carried out on the ties. Static tests showed that steel fibers increase the first crack and ultimate bending moments, increase significantly the slip force of the prestressing tendons, reduce crack width, add higher ductility to the ties and decrease the stress in the prestressing tendons. Under dynamic loading the steel fibers decreased the stress in the prestressing tendons by about 50%, which improved significantly the fatigue strength of the tie. A tie without fibers failed after only 150,000 cycles. However, a similar tie, with fibers, resisted 3,000,000 cycles without suffering fatigue failure.

Remarks on orthotropic elastic models applied to wood

Wood is generally considered an anisotropic material. In terms of engineering elastic models, wood is usually treated as an orthotropic material. This paper presents an analysis of two principal anisotropic elastic models that are usually applied to wood. The first one, the linear orthotropic model, where the material axes L (Longitudinal), R(radial) and T(tangential) are coincident with the Cartesian axes (x, y, z), is more accepted as wood elastic model. The other one, the cylindrical orthotropic model is more adequate of the growth caracteristics of wood but more mathematically complex to be adopted in practical terms. Specifically due to its importance in wood elastic parameters, this paper deals with the fiber orientation influence in these models through adequate transformation of coordinates. As a final result, some examples of the linear model, which show the variation of elastic moduli, i.e., Young's modulus and shear modulus, with fiber orientation are presented.

Stacking faults in SiCf/SiC composite obtained by chemical vapor reaction process

SiC fiber-reinforced SiC matrix composite (SiCf/SiC) is one of the leading candidates in ceramic materials for engineering applications due to its unique combination of properties such as high thermal conductivity, high resistance to corrosion and working conditions. Fiber-reinforced composites are materials which exhibit a significant improvement in properties like ductility in comparison to the monolithic SiC ceramic. The SiCf/SiC composite was obtained from a C/C composite precursor using convertion reaction under high temperature and controlled atmosphere. In this work, SiC phase presented the stacking faults in the structure, being not possible to calculate the unit cell size, symmetry and bond lengths but it seem equal card number 29-1129 of JCPDS.