A Thermo-mechanical gradient enhanced damage method for fracture
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ORIGINAL PAPER
A Thermo-mechanical gradient enhanced damage method for fracture Subrato Sarkar1 · I. V. Singh1 · B. K. Mishra1 Received: 29 February 2020 / Accepted: 17 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work, a new thermo-mechanical formulation for the conventional and localizing gradient damage method is proposed. The proposed formulation is based on the generalized micromorphic theory, which accounts for the underlying fracture processes at the micro-level. The thermal and mechanical effects on the fracture response are incorporated in the formulation through three primary variables. These variables are displacement (u), micro-equivalent strain (¯e) and temperature (θ ), which are strongly/weakly coupled. In addition to mechanical loading, steady-state and transient heat transfers are considered in the formulation. Several 1D and 2D numerical examples are solved using the formulation to demonstrate its accuracy and effectiveness in simulating thermo-mechanical fracture. In the numerical examples, different types of thermal and mechanical loads are considered to study various effects on the fracture response of the components. Moreover, a detailed description of the formulation and its numerical implementation is presented for a better understanding. Keywords Finite element method · Thermo-mechanical · Coupled field · Gradient damage · Staggered algorithm · Thermal strain
1 Introduction In actual engineering applications, various components are frequently exposed to multiple physical phenomena involving mechanical, thermal, electrical and chemical effects. In applications such as automobiles, aerospace, electronics, manufacturing, etc., thermo-mechanical effects are one of the leading causes of mechanical failure. The study of thermo-mechanical failures through simulation dates back to the work of Wilson and Nickell [44], who applied the finite element method (FEM) for heat conduction analysis. Subsequently, Oden [21] applied thermo-elasticity to dynamic problems and Zienkiewicz and Parekh [48] introduced the use of the isoparametric concept for curved 2D and 3D problems. An improvement was later presented by Warzée [41], which used temporal discretization in addition to the spatial discretization. This improvement led to the simplification of the formulation. Keramidas and Ting [12] proposed the use of a new quantity called ‘heat displacement’ related to the tem-
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I. V. Singh [email protected] Computational Mechanics and Multiscale Modelling Lab, Mechanical and Industrial Engineering Department, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, India
perature, which was analogous to mechanical displacement related to mechanical strain. Further, Bathe and Khoshgoftaar [4] presented a formulation and implementation methodology for nonlinear heat transfer problems. In the following paragraphs, a review of the thermo-mechanical fracture modeling is presented, followed by a summary of various fracture modeling methods. The work on
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