Alagappan Ponnalagu

Fatigue and damage are the least understood phenomena in the mechanics of solids. Recently, Alagappan et al. (“On a possible methodology for identifying the initiation of damage of a class of polymeric materials”, Proc R Soc Lond A Math Phys Eng Sci 2016; 472(2192): 20160231) hypothesized a criterion for the initiation of damage for a certain class of compressible polymeric solids, namely that damage will be initiated at the location where the derivative of the norm of the stress with respect to the stretch starts to decrease. This hypothesis led to results that were in keeping with the experimental work of Gent and Lindley(“Internal rupture of bonded rubber cylinders in tension. Proc. R. Soc. Lond. A 1959; 249, 195–205 :10.1098) and agrees qualitatively with the results of Penn (“Volume changes accompanying the extension of rubber”, Trans Soc Rheol 1970; 14(4): 509–517) on compressible polymeric solids. Alagappan et al. considered a body wherein there is a localized region in which the density is less than the rest of the solid. In this study, we show that the criterion articulated by Alagappan et al. is still applicable when bodies have multiple localized regions of lower density, thereby lending credence to the notion that the criterion might be reasonable for a large class of bodies with multiple inhomogeneities. As in the previous study, it is found that damage is not initiated at the location where the stresses are the largest but instead at the location where the densities tend to the lowest value. These locations of lower densities coincide with locations in which the deformation gradient is very large, suggesting large changes in the local volume, which is usually the precursor to phenomena such as the bursting of aneurysms.

We extend the methodology introduced for the initiation of damage within the context of a class of elastic solids to a class of viscoelastic solids (Alagappan et al. 2016 Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci. 472, 20160231. (doi:10.1098/rspa.2016.0231)). In a departure from studies on damage that consider the body to be homogeneous, with initiation of damage being decided by parameters that are based on a quantity such as the strain, that requires information concerning a special reference configuration, or the use of ad hoc parameters that have no physically meaningful origins, in this study we use a physically relevant parameter that is completely determined in the current deformed state of the body to predict the initiation of damage. Damage is initiated due to the inhomogeneity of the body wherein certain regions in the body are unable to withstand the stresses, strains, etc. The specific inhomogeneity that is considered is the variation of the density in the body. We consider damage within the context of the deformation of two representative viscoelastic solids, a generalization of a model proposed by Gent (1996 Rubber Chemistry and Technology 69, 59-61. (doi:10.5254/1.3538357)) for polymeric solids and a generalization of the Kelvin-Voigt model. We find that the criterion leads to results that are in keeping with the experiments of Gent & Lindley (1959 Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci. 249, 195-205. (doi:10.1098/rspa.1959.0016)).

Bridges are key components of transportation network, especially in strategic border areas in a country, and consequently are susceptible to subversive blast attacks. Hence in this study, dynamic response of a reinforced concrete (RC) bridge (single span) consisting of a deck slab supported on longitudinal girders along with transverse ones placed symmetrically has been numerically investigated when subjected to blast loading using ABAQUS/CAE 2020. The effects of an explosive charge of 226.8 kg (TNT) at 1 m standoff distance have been analyzed using the CONWEP algorithm. Three different locations of the bursting charge along the cross section at mid span of the bridge above the deck, such as on the central girder, between two adjacent longitudinal girders, and on the cantilever part, have been considered. Concrete damage distribution in terms of concrete spalling and cracking has been studied with concrete damage plasticity (CDP) model. Also, the response in terms of damage dissipation energy, maximum displacements, and stresses has been compared for the blast scenarios. Furthermore, AASHTO: LRFD Bridge Design Specifications (2017) provisions have been used to compare obtained maximum displacement values.

In this paper, we provide a possible methodology for identifying the initiation of damage in a class of polymeric solids. Unlike most approaches to damage that introduce a damage parameter, which might be a scalar, vector or tensor, that depends on the stress or strain (that requires knowledge of an appropriate reference configuration in which the body was stress free and/or without any strain), we exploit knowledge of the fact that damage is invariably a consequence of the inhomogeneity of the body that makes the body locally 'weak' and the fact that the material properties of a body invariably depend on the density, among other variables that can be defined in the current configuration, of the body. This allows us to use density, for a class of polymeric materials, as a means to identify incipient damage in the body. The calculations that are carried out for the biaxial stretch of an inhomogeneous multi-network polymeric solid bears out the appropriateness of the thesis that the density of the body can be used to forecast the occurrence of damage, with the predictions of the theory agreeing well with experimental results. The study also suggests a meaningful damage criterion for the class of bodies being considered.

Damage in concrete has been modelled using various approaches such as fracture mechanics, continuum damage mechanics and failure envelope theories. This study proposes a new approach to model the initiation of damage in concrete that addresses some limitations associated with the existing approaches. The proposed approach defines damage in terms of changes in the density of the material at the microscopic level, where such changes are induced by mechanical loading. The suggested approach is used to simulate the response of 2D concrete bodies to uni-axial tension and uni-axial compression. The simulation results indicate that the proposed model, by means of a single constitutive function, is able to correctly predict failure patterns and aptly capture the damage mechanisms under both uni-axial tension and uni-axial compression loadings using only the information related to the microstructure, the density field and the stiffness field. As a continuation, in Part II, the ability of the D3-M approach to model fully coupled chemo-mechanical damage in concrete using a single constitutive equation will be demonstrated.