Shantanu S. Mulay

A detailed study on micromechanical constitutive modelling of unidirectional fiber reinforced and plain woven textile composites (PWTC) is performed. The primary objective is to compute the equivalent homogenized effective properties of PWTC through its mesoscale model. A novel parallel-series model is proposed, to compute the engineering constants in transverse plane of unidirectional composite, and validated against Chamis approaches, Mori–Tanaka and finite element method results for glass/epoxy composite. Computational homogenization of representative volume element (RVE) of transverse direction unidirectional composite is performed satisfying the periodicity of RVE. The RVE of PWTC is then approximated as cross-ply laminate consisting warp and fill plies, whose averaged properties are computed considering fiber undulations by micromechanics-based models. The bounds of the effective material properties of PWTC are determined employing Voigt and Reuss approximation. The effective engineering constants of glass/epoxy PWTC computed are compared with in-house experiments and found to be closely matching with Voigt model.

This work deals with the existence of representative volume element (RVE) for unidirectional laminated composites (with and without preexisting cracks). The RVE existence in elastic regime is studied employing periodic boundary conditions for uniaxial and shear loadings separately. RVE does exist in elastic regime for materials having discrete cracking. The numerical simulations for different sizes of RVE are performed keeping the fiber volume and crack volume fractions constant. It is observed that the elastic response is independent of RVE dimension. The RVE validity in softening regime is studied by Lemaitre ductile damage model within matrix phase.

Pagano’s flexural theory is extended in this work proposing two homogenization theories of flexure for laminated beams. The proposed homogenization approaches convert a given laminated beam configuration under transverse loading into a mechanically equivalent homogenized configuration resulting in a homogenized flexural rigidity or a flexural modulus. The theory thus developed converts a two-dimensional (2D) problem into an equivalent one-dimensional (1D) problem of transverse deflection of a macro-scale homogenized beam. The proposed homogenization approaches can be employed for a laminated beam with randomly oriented fiber directions having an asymmetric configuration, thereby eliminating the need to solve coupled partial differential equations by classical laminate theory. The proposed approaches thus extend the applicability of Pagano’s theory from being applied to [0,90] laminates to a more general laminate. The applicability of the proposed homogenization approaches has also been discussed, and a comparison has been drawn with classical laminate theory. The proposed homogenization approaches are further successfully coupled with a progressive failure analysis framework based on anisotropic damage mechanics to demonstrate their applicability in meso-macro-coupling in laminated beam homogenization, which is highly appealing to the aeronautical field.

A study on the fracture and damage-healing behavior of plain woven textile composite (PWTC) is performed in the present work. The primary objective is to conduct 2D progressive failure analysis (PFA) under static in-plane loading conditions, progressive damage-healing analysis for different cyclic strain histories, and experimental fracture studies of PWTC material. A chain of equivalent cross-ply laminates (ECPL) consisting of warp and fill plies is considered as the modified representative volume element (RVE) of PWTC distributing matrix phase within warp and fill yarns. The 2D PFA, based on classical laminate theory (diffused cracking) by eliminating stiffness terms, is performed applying maximum stress theory to predict the macro-scale stress-strain behavior of PWTC. The 2D PFA of PWTC material behavior is implemented as ABAQUS® user material subroutines (UMAT and VUMAT), and the fracturing of PWTC notched bar is demonstrated for an illustration purpose. The novel multi-scale progressive damage-healing analysis is subsequently performed, by (Formula presented.) -order damage-healing effect tensor, applying Voigt approximation on ECPL model (self-healing in warp ply for an illustration purpose). The failure modes identified in numerical PFA are verified performing in-house experiments (through fractography).

A micro-electro-mechanical (MEM) beam and column structures are analysed in details in the present work containing fixed charge (+ve or −ve). The transverse deflection of this column, due to the presence of fixed-charge concentration and axial compressive force, is firstly studied (linear elastic and viscoelastic cases). An analytical solution of critical buckling load P supported by MEM column, with initial imperfections due to the presence of fixed-charge in the column (simply-supported), is derived. The variation of P with fixed-charge concentration is finally obtained. A pull-in instability of MEM beam is secondly studied under the influence of external electric field, and a critical voltage V without any instability is obtained varying fixed-charge concentration inside beam. All the presented formulations are extended incorporating finite deformation (von Kármán strain field) setting, as the beam rotation becomes significant at higher fixed-charge values. All the presented results are also verified with the published literature wherever it was possible. The presented work thus can be reasonably employed in the design of MEM micro-switches.

The present work deals with the constitutive modelling and progressive failure analysis (PFA) of plain woven textile composites (PWTC). Two novel approaches, equivalent cross ply laminate (ECPL) coupled with classical laminate theory and Mori–Tanaka theory, are developed to compute homogenized properties of PWTC lamina. The PFA of PWTC lamina is performed coupling isotropic damage mechanics with ECPL theory, and meso-scale failure modes are identified. The novelty in the proposed PFA is that, the stress-based failure is detected, and the strain-based damage evolution is computed. A user-defined material subroutine of PFA of PWTC lamina is finally developed and test problems are solved in ABAQUS. All the simulation results of the proposed approaches are finally compared with experiments and found to be closely matching.

A novel three-dimensional elasto-plastic damage-healing (EPDH) model, based on continuum damage mechanics, is proposed capturing the self-healing phenomenon occurring in plastically deforming materials. A novel secondary damage variable, with separate evolution law, is introduced removing an assumption in the existing literature that the healed area cannot undergo damage again or healed area undergoes damage only once. The implicit damage-healing formulation, based on the irreversible thermodynamics, is developed detailing evolution equations of all internal variables. A novel pressure-dependent yield surface (qualitatively behaving like Gurson model) is developed by damage-healing equivalent stress modifying von Mises yield surface. The physical interpretation of damage and healing energy release rates are presented to elucidate their impact on the energy dissipation within the system. The proposed formulation is numerically implemented by return mapping approach employing elastic strain equivalence hypothesis. The applicability of newly proposed EPDH + secondary damage framework is successfully demonstrated considering different strain histories. The secondary damage variable is finally found crucial while obtaining the physically realistic stress–strain response of self-healing materials leading to complete failure upon exhaustion of healing capabilities.

It is critical to handle geometric and material nonlinearities in a stable manner while solving the problems from solid mechanics, such that it results in a converged solution. The present work compares the suitability of generalised displacement control (GDC) and displacement control algorithms (DCA) by solving several 1D and 2D formulations. The ability of these algorithms to handle homogeneous and inhomogeneous deformations is also studied. A novel direct displacement control method (DDCM), coupled with Newton-Raphson method, is proposed and compared with GDC and DCA approaches. Appropriate conclusions are finally drawn based on the successful demonstrations of the numerical results obtained by GDC, DCA and DDCM approaches.

A novel viscoelastic damage-healing model for self-healing materials is proposed coupling continuum damage healing mechanics (CDHM) framework with a viscoelastic constitutive model for self-healing during unloading and rest periods. The viscoelastic damage-healing model is coupled with the novel secondary damage internal variable accounting for the subsequent damage of healed material. The proposed viscoelastic damage-healing model formulation is numerically implemented by return mapping approach employing the elastic strain equivalence hypothesis from CDHM, and model response as stress update is obtained for several strain histories. Detailed parametric studies are conducted by varying the material constants appearing in the damage and healing evolution equations, and their influence on the constitutive model response is analysed. Various tangent moduli expressions are finally derived, and successfully coupled with an in-house developed plane strain nonlinear finite element code while solving different boundary value problems.

A three-dimensional anisotropic damage model, based on continuum damage mechanics, is presented capturing the damage induced anisotropy in the initially isotropic, viscoelastic (VE) solid. The second order tensor damage variable, conceived as an evolving structural tensor, is coupled with linear VE model at the finite as well as infinitesimal strains. A dissipation potential, based on a novel damage interaction tensor (fourth order tensor), is proposed from which the damage tensor evolution happens in an associative manner. The newly proposed model is numerically implemented as an implicit stress update algorithm, and the infinitesimal part of the formulation is validated against the available experimental results in the literature. A parametric study of the newly developed finite strain formulation is presented employing three different deformation histories demonstrating further the utility of the proposed anisotropic damage model. The successful experimental validation of the proposed model demonstrates its applicability and utility in the existing finite element codes.