Modeling fracture in polymeric material using phase field method based on critical stretch criterion

In this work, the phase field method (PFM) is applied for modeling fracture in the polymeric type of materials. Considering the large extensibility of polymer chains before fracture, a crack initiation criteria based on a critical stretch value is proposed. The tensile stretches in the material contribute to the active strain energy, which is responsible for driving fracture. Additive decomposition of strain energy into active and passive parts is adopted based on the critical stretch value of polymer chains in a phase-field setting. This critical value is determined by assuming an equivalent uniaxial tensile state of stress in front of the crack tip at the onset of fracture. The stretch of individual polymeric chains is determined by using a polymer network model. The critical fracture toughness of the polymer is kept constant up to the onset of fracture and a gradually reducing value of it is adopted in front of the crack tip beyond the critical stretch. A hybrid phase-field formulation with a staggered solver is used owing to its numerical efficiency and robustness. The effectiveness and applicability of the present model are demonstrated through various numerical examples

IIT Hyderabad invites applications for short term course on Nonlocal Mechanics Approaches for Modelling Localized Deformations

Indian Institute of Technology, Hyderabad has invited applications for a short term course on ‘Nonlocal Mechanics Approaches for Modeling Localized Deformations’ to be held from February 19 to 21, 2020. Candidates interested and eligible for this course can apply via email on or before December 15, 201

Computational Homogenisation and Failure Modelling Of Periodic Composites

Masonry and composite laminates are periodic in nature in their own plane. Masonry is a composite material made of units and mortar, normally arranged periodically. The combined action of brick and mortar will exhibit different directional properties. Finding the orthotropic properties or effective material properties from the individual material constituents is called the homogenisation. Less computational cost, user friendly mesh, and flexible to apply for large structures are advantages while using the homogenised properties. In this study we find the homogenised properties for unstrengthen masonry and also strengthened masonry using CFRP (inserted in bed joints). For composite laminates, homogenised properties can be found from modified rule of mixture

IIT Hyderabad Invites Applications For Short Term Course

The Indian Institute of Technology-Hyderabad (IIT-H) is inviting applications for a short-term course on ‘Nonlocal Mechanics Approaches for Modeling Localised Deformations’ to be conducted from February 19-2

Peridynamic solutions to micropolar beam

Peridynamics (PD) is a non local continuum mechanics theory developed by Silling in 2000. The inception of peridynamics can be dated back to the works of Piola according to dell’Isola et al. [1]. Classical continuum theory (CCM) was there to study the materials response to deformation and loading conditions deformation response of materials and structures subjected to external loading conditions without taking into effect the atomistic structure. Classical continuum theory can be applied to various challenging problems but its governing equation have a limitation that it cannot be applied on any discontinuity such as a crack, as the partial derivatives with respect to space are not defined at a crack. To overcome this limitation , a new non local continuum approach i.e Peridynamics (PD) was developed.It was introduced as it governing equations donot contain any partial derivative with respect to space so it can be applied at cracks also. We can also think of Peridynamics as the continuum version of molecular dynamics. This behaviour of peridynamics makes it handy for multi-scale analysis of materials. Peridynamics finds it usefulness in other fields also such as moisture, thermal, fracture, aerospace etc., so that multiscale analysis can be done . The analysis of structure due to progressive failure is challenge. These challenges can be overcome by techniques such as using both nonlocal and classical (local) theories. But Peridynamic theory is computationally costly compared to the finite element method. While analyzing structures with compelxity , utilize structural idealizations is to be done to make computations feasible. Peridynamics has been catching the eyes of the researchers as its formulation include integral equations , unlike the partial differential equations in classical continuum theory. This method is still in early stages, a lot of research work is to be done to make it feasible for a large no. of problems

IIT Hyderabad Invites applications for Short Term Course on ‘Nonlocal Mechanics Approaches for Modelling Localized Deformations’

The Indian Institute of Technology-Hyderabad (IIT-H) is inviting applications for a short-term course on ‘Nonlocal Mechanics Approaches for Modeling Localised Deformations’ to be conducted from February 19-2

A strain gradient plasticity based damage model for quasibrittle materials

Boundary value problems for a softening material suer from loss of uniqueness in the post-peak regime. Numerical solutions to such problems shows mesh dependency due to lack of internal length scale in the formulation. A regularization method which introduces a characteristic length is required to get mesh independent results. A second gradient model introduces a characteristic length by taking into account the second gradient of the displacement in the principle of virtual work and thus regularizing the solution of the boundary value problem. In this work a second gradient nite element model has been developed. The regularization property of the method has been studied for elastoplastic and damage constitutive laws. It has been shown that mesh independent results can be achieved in this model. Even though unique solution is not achieved a nite number of solutions have been obtained from the proposed model

Applications invited for short-term course at IIT-H

The Indian Institute of Technology-Hyderabad (IIT-H) is inviting applications for a short-term course on ‘Nonlocal Mechanics Approaches for Modeling Localised Deformations’ to be conducted from February 19-2

Adaptive n-Sided Polygonal Finite Element Method for Analysis of Plane Problems

In this work we present an adaptive polygonal nite element method for analysis of two dimensional plane problems. The generation of n sided polygonal nite element mesh is based on generation of a centroidal Vorononi tessellation (CVT). By this method an unstructured tessellation of a scattered point set, that minimally covers the proximal space around each point in the point set can be generated. The method has also been extended to include tessellation for non convex domains. For the numerical integration of Galerkin weak form over polygonal nite element domains we resort to classical Gaussian quadrature applied on triangular sub domains of each polygonal element. An adaptive nite element analysis strategy is proposed and implemented in the present work. A patch recovery type of stress smoothing technique that utilizes polygonal element patches for obtaining smooth stresses has been proposed for obtaining the smoothed nite element stresses. A classical z2 type a - posteriori error estimator that estimates the energy norm of the error from the recovered solution is then implemented. The renement of the polygonal elements is made on an element by element basis through a renement index. Numerical examples of two dimensional plane problems are presented to demonstrate the eciency of the proposed adaptive polygonal nite element method

The Use of Contravariant Tensors to Model Anisotropic Soft Tissues

Biological tissues have been shown to behave isotropically at lower strain values, while at higher strains the fibers embedded in the tissue straighten and tend to take up the load. Thus, the anisotropy induced at higher loads can be mathematically modeled by incorporating the strains experienced by the fibers. From histological studies on soft tissues it is evident that for a wide range of tissues the fibers have an oblique mean orientation about the physiological loading directions. Thus, we require a mathematical framework of tensors defined in nonorthogonal basis to capture the direction-dependent response of fibers under high induced loads. In this work, we propose a novel approach to determine the fiber strains with the aid of the contravariant tensors defined in an oblique coordinate system. To determine the fiber strains, we introduce a fourth-order contravariant fiber orientation transformation tensor. The approach helps us successfully in determining the fiber strains, for a family of symmetrically and asymmetrically oriented fibers, with the aid of a single anisotropic invariant. The proposed model was fitted with the experimental data from literature to determine the corresponding material parameters