Computational Solid and Structural Mechanics Laboratory (CSSML)

Multi-scale thermo-mechanical modeling and simulation of cellular solids at high strain rates

Cellular solids are encountered widely in nature. Most naturally occurring materials such as wood, bone, biological tissues etc. are highly porous and/or functionally anisotropic at the micron scale. This has inspired significant research in man-made cellular solids for various engineering applications such as blast / impact absorption, thermal insulation / conduction, light-weight construction, acoustic / structural damping, chemical catalysis, water filtration, waste containment etc. As the manufacturing cost of these materials comes down, the list of applications keeps growing along with the need for a better understanding of the behaviour of these materials. Researchers in various fields have conducted a wide variety of experimental and numerical studies in order to characterize the mechanical, thermal and chemical properties of cellular solids.

In this study, we present a discrete structural model for irregular open-cell metallic foams that is capable of capturing a variety of physical phenomena at multiple spatial and temporal scales ranging from local ligament damage to the global deformation response. The ligaments are modelled with geometrically non-linear, non-prismatic 3-D frame elements and the nodes are modelled as stiff spheres that represent the inertial properties of the cellular material more accurately. Similar unit-cell and representative volume element models in the literature have usually been calibrated against the static bulk moduli of the foam material while the study of the dynamic characteristics of these models has received only limited attention. We evaluate the performance of our model in terms of its ability to capture the dynamic behaviour of metallic foams under high strain rate loading conditions and present some examples from real life applications.


"Roll-up" (beyond 2π) of a 3D large deformation cantilever beam (Cosserat rod) under applied end moment.

Nonlinear crushing response (Load vs. Displacement) of a cylindrical sample of aluminium foam under uniaxial compression.

Coupled Meshfree and Finite Element simulations for Structural and Material behavior under Extreme Loads

In recent years, several meshfree methods have been proposed to overcome some of the difficulties encountered with finite element methods for problems involving large deformations and/or fracture. However, depending upon the implementation, meshfree methods also suffer from some drawbacks such as greater computational cost, inconsistent enforcement of essential boundary conditions and errors in the integration of the discretized weak form.

In order to alleviate some of these difficulties, researchers have proposed coupled meshfree and finite element methods to capitalize on the best attributes of both methods. In such an approach, large parts of the problem domain are solved with finite elements and a meshfree discretization is used only in small regions of interest where finite elements may be insufficient to capture the desired response. These are usually regions with high spatial and/or temporal gradients. Significant effort has been devoted to the resolution of multiple scales in space through techniques such as domain decomposition and multi-scale methods but a commensurate effort to capture multiple scales in time is lacking in the current literature.

We present an accurate multi-time-step integration method that enables one to decompose a large spatial domain into smaller subdomains and solve each subdomain with its requisite spatial and temporal resolution. This method can be used effectively to augment existing methods for spatial coupling of meshfree and finite element methods, such as blending functions and/or Lagrange multipliers, with an appropriate time integration using multiple time-steps. In the present study, we evaluate the computational performance of this method in terms of the stability and accuracy of the spatial and temporal coupling. We also investigate the effect of various coupling parameters on the rate of convergence of this method for highly non-linear problems and present results from several example problems that we used for verification and validation.
Axial Stress wave in Meshfree-FEM Beam with different Meshfree-FE interfaces and time-steps

Response of a fixed-free cracked Meshfree-FEM beam to a horizontal traction load applied at the free end.

Multi-time-step Domain Decomposition and Coupling Methods for Non-linear Structural Dynamics

Developing efficient and accurate computational methods for solving coupled multi-physics problems is the primary goal of my research. The disparity in the length and time scales usually involved in these problems makes them extremely challenging. Researchers have devoted significant effort to address the coupling of multi-physics phenomena in space through techniques such as domain decomposition and multi-scale methods but a commensurate effort to couple multiple scales in time is lacking in the current literature.

Consider the problem of coupling multiple time scales for non-linear dynamic analysis of large structures with complex geometries efficiently. Such problems have been solved, in the past, by discretizing the structural domain in space with finite elements and using a time-stepping scheme for numerical time integration. However, using a uniform time step for the entire mesh that meets that stability and accuracy requirements of all the elements is computationally very inefficient.

The present multi-time-step coupling method is based on a dual Schur domain decomposition method (FETI finite element tearing and interconnecting) that uses Lagrange multipliers to enforce the continuity of the solution across the interfaces between the subdomains. The subdomains can be integrated with different time steps and/or time stepping schemes. The method has been shown to be unconditionally stable, energy preserving and computationally very efficient. The multi-time-step method has also been extended for problems with geometric and material non-linearities. Multiple subdomains with multiple levels of time steps are coupled using a hierarchical recursive coupling method. An efficient parallelization based on message passing interface (MPI) that uses a recursive tree topology for distributing subdomains between processors has also been developed.
Axial Stress wave in Notched Beam
Rocket case with cracks subject to sudden head end pressure

Axial Stress Response of a rocket casing with cracks to sudden head-end pressure; Analyzed with 32 subdomains partitioned with METIS; Coupled with Recursive Multi-time-step method with a time step ratio 10.

Other Research Interests
  • Non-linear Computational Structural Dynamics
  • Coupled Multi-physics and Multi-scale Problems
  • Contact, Impact, Blast, Fluid-Structure interaction
  • Material modeling: Plasticity, Damage, Fracture
  • Inverse Problems in Engineering