arXiv subjects

Sandipan Paul

Publications and source records attributed to Sandipan Paul.

3 recordsLinked to original sources

arXiv2025

A novel large-strain kinematic framework for fiber-reinforced laminated composites and its application in the characterization of damage

In this paper, a novel kinematic framework for fiber-reinforced composite materials is presented. For this purpose, we use the multiple natural configurations in conjunction with the multi-continuum theory of Bedford and Stern~(1972). Keeping the underlying physics of the proposed kinematics consistent. The proposed kinematics results in a three-term decomposition of the deformation gradient i.e. $\mathbf{F}=\mathbf{F}^e\mathbf{F}^r_\alpha\mathbf{F}^d_\alpha$, where $\alpha$ represents either the matrix or the fiber. After discussing the kinematic framework in detail, we use this new kinematic framework to characterize the damage contents associated with four damage mechanisms. These damage mechanisms are matrix cracking, fiber breakage, interfacial slip or debonding, and delamination. While the first two are derived by measuring the incompatibility of the pertinent configuration occupied by individual constituents, the latter two involve a relative displacement between either the constituents or the lamin\ae. The geometric interpretation corresponding to these damage mechanisms is also presented using tools from differential geometry. The derived damage contents can be used in developing an appropriate constitutive model for laminated composites undergoing damage.

physics.class-ph↗

arXiv2025

Constitutive modeling of viscoelastic solids at large strains based on the theory of evolving natural configurations

The theory of evolving natural configurations is an effective technique to model dissipative processes. In this paper, we use this theory to revisit nonlinear constitutive models of viscoelastic solids. Particularly, a Maxwell and a Kelvin-Voigt model and their associated standard solids, viz., a Zener and a Poynting-Thompson solids respectively, have been modeled within a Lagrangian framework. We show that while a strain-space formulation of the evolving natural configurations is useful in modeling Maxwell-type materials, a stress-space formulation that incorporates a rate of dissipation function in terms of the relevant configurational forces is required for modeling the Kelvin-Voigt type materials. Furthermore, we also show that the basic Maxwell and Kelvin-Voigt models can be obtained as limiting cases from the derived standard solid models. Integration algorithms for the proposed models have been developed and numerical solutions for a relevant boundary value problem are obtained. The response of the developed models have been compared and benchmarked with experimental data. Specifically, the response of the novel Poynting-Thompson model is studied in details. This model shows a very good match with the existing experimental data obtained from a uniaxial stretching of polymers over a large extent of strain. The relaxation behavior and rate effects for the developed models have been studied.

cond-mat.soft↗

arXiv2025

On the extension of the concept of rheological connections to a finite deformation framework using multiple natural configurations

The constitutive behaviors of materials are often modeled using a network of different rheological elements. These rheological models are mostly developed within a one-dimensional small strain framework. One of the key impediments of extending these models to a three-dimensional finite deformation setting is to determine how the different types of connections, i.e., a series and a parallel connection, are incorporated into the material models. The primary objective of this article is to develop an appropriate strategy to address this issue. We show that both the series and the parallel connection between two rheological elements can be modeled within a multiple natural configurations framework without changing or introducing new configurations. The difference in a series and a parallel connection is manifested in the ratio of the stress powers expended during the deformations of the associated rheological elements. Finite deformation version of some well-known rheological models have been used to demonstrate the utility of the proposed theory.

cond-mat.mtrl-sci↗