Fully coupled peridynamic thermomechanics

This study concerns the derivation of the coupled peridynamic (PD) thermomechanics equations based on thermodynamic considerations. The generalized peridynamic model for fully coupled thermomechanics is derived using the conservation of energy and the free-energy function. Subsequently, the bond-based coupled PD thermomechanics equations are obtained by reducing the generalized formulation. These equations are also cast into their nondimensional forms. After describing the numerical solution scheme, solutions to certain coupled thermomechanical problems with known previous solutions are presented.

[1]  M. R. Eslami,et al.  BEM analysis of thermal and mechanical shock in a two-dimensional finite domain considering coupled thermoelasticity , 2000 .

[2]  P. Chadwick,et al.  Plane waves in an elastic solid conducting heat , 1958 .

[3]  Gunadhar Paria,et al.  Coupling of elastic and thermal deformations I , 1958 .

[4]  Florin Bobaru,et al.  The peridynamic formulation for transient heat conduction , 2010 .

[5]  H. Deresiewicz,et al.  Plane Waves in a Thermoelastic Solid , 1957 .

[6]  William Thomson,et al.  On the Dynamical Theory of Heat , 1853 .

[7]  Francisco Armero,et al.  A new unconditionally stable fractional step method for non‐linear coupled thermomechanical problems , 1992 .

[8]  J. L. Nowinski,et al.  Theory of thermoelasticity with applications , 1978 .

[9]  Propagation of Discontinuities in Coupled Thermoelastic Problems , 1968 .

[10]  P Stanley,et al.  Beginnings and Early Development of Thermoelastic Stress Analysis , 2008 .

[11]  M. Biot.  Thermoelasticity and Irreversible Thermodynamics , 1956 .

[12]  J. T. Oden.  Finite element analysis of nonlinear problems in the dynamical theory of coupled thermoelasticity , 1969 .

[13]  Dan Givoli,et al.  Dynamic thermoelastic coupling effects in a rod , 1995 .

[14]  Daniel Rittel,et al.  Experimental investigation of transient thermoplastic effects in dynamic fracture , 1998 .

[15]  M. Brünig,et al.  Numerical Analyses of Stress-triaxiality-dependent Inelastic Deformation Behavior of Aluminum Alloys , 2011 .

[16]  Charbel Farhat,et al.  An unconditionally stable staggered algorithm for transient finite element analysis of coupled thermoelastic problems , 1991 .

[17]  P. Chadwick,et al.  On the propagation of thermoelastic disturbances in thin plates and rods , 1962 .

[18]  Stewart Andrew Silling,et al.  Linearized Theory of Peridynamic States , 2010 .

[19]  W. Cheng-I,et al.  Coupled transient thermoelastic response in an axi-symmetric circular cylinder by Laplace transform-finite element method , 1989 .

[20]  A. Cemal Eringen,et al.  On the Problem of Crack Tip in Nonlocal Elasticity , 1974 .

[21]  Edward C. Ting,et al.  A unified numerical approach for thermal stress waves , 1982 .

[22]  A. V. Manzhirov,et al.  Closed solutions of boundary-value problems of coupled thermoelasticity , 2010 .

[23]  S. Silling.  Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces , 2000 .

[24]  H. Zaixing.  New points of view on the nonlocal field theory and their applications to the fracture mechanics(II)—re-discuss nonlinear constitutive equations of nonlocal thermoelastic bodies , 1999 .

[25]  Florin Bobaru,et al.  A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities , 2012, J. Comput. Phys..

[26]  Y. Fung.  Foundations of solid mechanics , 1965 .

[27]  R. E. Nickell,et al.  Approximate Solutions in Linear, Coupled Thermoelasticity , 1968 .

[28]  C. Comi,et al.  Nonlocal Thermoelastic Damping in Microelectromechanical Resonators , 2009 .

[29]  Yi Fei Zhang,et al.  Unconditionally stable implicit-explicit algorithms for coupled thermal stress waves , 1983 .

[30]  S. Silling,et al.  Peridynamics via finite element analysis , 2007 .

[31]  Erdogan Madenci,et al.  An adaptive dynamic relaxation method for quasi-static simulations using the peridynamic theory , 2010 .

[32]  W. L. Wood.  Practical Time-Stepping Schemes , 1990 .

[33]  Wing Kam Liu,et al.  A Note on Numerical Analysis of Dynamic Coupled Thermoelasticity , 1985 .

[34]  S. Silling,et al.  A meshfree method based on the peridynamic model of solid mechanics , 2005 .

[35]  B. Kilic,et al.  Peridynamic Theory for Thermomechanical Analysis , 2010, IEEE Transactions on Advanced Packaging.

[36]  C. Weng,et al.  Generalized coupled transient thermoelastic plane problems by laplace transform/finite element method , 1988 .

[37]  C. Weng,et al.  GENERALIZED COUPLED TRANSIENT THERMOELASTIC PROBLEM OF A SQUARE CYLINDER WITH ELLIPTICAL HOLE BY LAPLACE TRANSFORM/FINITE-ELEMENT METHOD , 1989 .

[38]  A. Agwai,et al.  A Peridynamic Approach for Coupled Fields , 2011 .

[39]  S. Silling,et al.  Peridynamic States and Constitutive Modeling , 2007 .

[40]  A. T. Hoop.  On the plane-wave extinction cross-section of an obstacle , 1959 .

[41]  A. Cemal Eringen,et al.  Stress concentration at the tip of crack , 1974 .

[42]  R. Lehoucq,et al.  Peridynamic Theory of Solid Mechanics , 2010 .

[43]  B. Boley,et al.  Transient Coupled Thermoelastic Boundary Value Problems in the Half-Space , 1962 .