Multiscale Modeling of Multiphase Materials

Aim: Development of computationally cost effective and efficient technique for the prediction of failure of heterogenous materials.

Elaboração: The behavior of the composite material can be determined by analyzing the representative section of the composite microstructure which is named as representative volume element (RVE). RVE based analysis for effective property determination involves two different scales i.e. the macroscopic scale where the domain is regarded as homogeneous and heterogeneities are not visible, second is microscopic scale which is called as scale of heterogeneity. The effective macroscopic properties can be calculated using multiscale modeling approaches. A reduced order asymptotic homogenization based multiscale technique which can capture damage and inelastic effects in composite materials is proposed. Macroscale stress is derived by calculating the influence tensors from the analysis of representative volume element (RVE). To solve the problem of strain localization a method of the alteration of stress-strain relation of micro constituents based on the dissipated fracture energy in a crack band is implemented. Under transient loads, when the wavelength of loading function and microstructure size are of same order, the composite material response become extremely complex due to wave interactions at the interfaces of different phases. Local waves may generate at microscale with micro-reflections and micro-refractions, leading to dispersion of global wave under impact load. Investigation of material microstructure relationship with energy dissipation of composite material for impact and blast applications is the future goal of my research.

Impact Modeling of Composite Materials

Aim: Damage and inelastic behavior of composite material under extreme transient loading conditions and development of impact resistant materials for desirable properties i.e. energy dissipation, localization and damage mitigation.

Elaboração: On the basis of their applications, the fiber reinforced polymer matrix composites can be divided “structural grade composites” and “armor grade composites”. The “armor grade composites” are mainly used for blast and ballistic-protection systems in military and civilian applications and aircraft structures are made predominantly from “structural grade composites”. For these composites high energy absorbing capability or high ballistic-impact protection resistance is required. If the impact response of the target is dominated by flexural response without any penetration of impactor, the impact phenomenon is classified as “Low Velocity Impact (LVI)” and response mainly depends upon the bending stiffness of the target and failure occurs due to matrix cracking. In second category, called as “High Velocity Impact (HVI)”, the impactor causes the penetration of the plate and the failure occurs due to fiber breakage in tension or due to shear punching of fibers. I proposed an elasto plastic damage model to simulate the progressive damage and damaged induced inelastic deformation and a methodology to calculate the material softening parameter for a particular mesh size to eliminate the strain softening effect. An improved analytical model to predict the response of composite laminate under low velocity large mass impact. A spring–mass system is used to represent the contact, bending, shear and membrane stiffnesses for the laminate system. The present research efforts include the extension of the proposed formulation to high pressure and high strain rate conditions by including viscous and shock wave dominated effects.

Geometric Modeling of Thin Materials

Aim: Can the shapes of thin laminae present in nature be explained based on the principles of mechanics. Using the underlying physics of those shapes in design of thin structures.

Elaboração: Thin materials comprise an important and growing proportion of engineering construction with areas of application becoming increasingly diverse, ranging from aircraft, bridges, ships, and oil rigs to storage vessels. We consider one phenomenon of our interest: thin-sheet crumpling. If we compress a thin sheet, or a piece of paper, along its boundaries, the sheet begins to buckle. However, instead of exhibiting large wavelength deformations, the material develops highly connected networks of vertices and ridges spanning its entire extent. In the asymptotic limit where the sheet thickness goes to zero, it becomes impossible to stretch the zero-thickness sheet due to the underlying mechanics and are hence referred to as isometric sheets. This flat isometric sheet will have zero Gaussian curvature (k=0) everywhere after it is deformed. Since the Gaussian curvature is the product of the principal surface curvatures (k= k1.k2), there must be a principal direction of zero curvature at each point in the material. These directions are known as generators, and a surface described by these generators is known as a developable surface. Further, the isometric deformation of the flat sheet leads to the imposition of constraints: Compatibility constraint and Developability constraint. In this study, we apply these constraints to construct a developable surface.