Peridynamic Theory for Thermomechanical Analysis

Thermomechanical modeling for interconnects and electronic packages is a difficult challenge, especially for material interfaces and films under 1 ¿m dimension. Understanding and prediction of their mechanical failure require the simulation of material behavior in the presence of multiple length scales. However, the classical continuum theory is not capable of predicting failure without a posterior analysis with an external crack growth criteria and treats the interfaces having zero thickness. A new nonlocal continuum theory referred to as peridynamic theory offers the ability to predict failure at these length scales. This study presents a new response function as part of the peridynamic theory to include thermal loading. After validating this response function by comparing against the displacement predictions in benchmark problems against those of finite element method, the peridynamic theory is used to predict damage initiation and propagation in regions having dissimilar materials due to thermomechanical loading.

[1]  Shahid H. Bokhari,et al.  A Partitioning Strategy for Nonuniform Problems on Multiprocessors , 1987, IEEE Transactions on Computers.

[2]  A. Cemal Eringen,et al.  Nonlocal Stress Field at Griffith Crack. , 1980 .

[3]  H. Elliott.  An analysis of the conditions for rupture due to griffith cracks , 1947 .

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

[5]  Erdogan Madenci,et al.  Effects of Nanoparticles on Stiffness and Impact Strength of Composites , 2007 .

[6]  S. Silling,et al.  Deformation of a Peridynamic Bar , 2003 .

[7]  A. Eringen,et al.  On nonlocal elasticity , 1972 .

[8]  Olaf Weckner,et al.  The effect of long-range forces on the dynamics of a bar , 2005 .

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

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

[11]  E. Kröner,et al.  Elasticity theory of materials with long range cohesive forces , 1967 .

[12]  Bahattin Kilic,et al.  Peridynamic theory for progressive failure prediction in homogeneous and heterogeneous materials , 2008 .

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

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

[15]  S. Silling,et al.  Peridynamic modeling of membranes and fibers , 2004 .

[16]  I. Kunin,et al.  Elastic Media with Microstructure I: One-Dimensional Models , 1982 .

[17]  N. Cristescu,et al.  On dynamic relaxation , 1967 .

[18]  Peridynamic theory for failure prediction in multilayer thin-film structures of electronic packages , 2008, 2008 58th Electronic Components and Technology Conference.

[19]  Dominik Rogula,et al.  Nonlocal theory of material media , 1982 .