Computational Modeling

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In our industry, there are many complex problems which cannot be solved with a high level of fidelity using classical mechanics or design-level analysis approaches. Although physical testing can produce high-quality and reliable results, we understand the costs associated with physical experiments. For this reason, PEC aims to apply computational modeling as a supplemental solution. When applied correctly, computational modeling tools can provide results that are both cost-effective and accurate.

Exceptional Versatility

Our computational modeling experience is wide-ranging, including: conventional and nuclear weapons effects; anti-terrorism and force protection threats; explosives safety applications; industrial hazards arising from process accidents and hazardous material storage; natural hazards; vibration effects associated with groundshock, wind, acoustic insults, quarry blasting, and construction activities; and multi-physics applications involving fluid-structure, soil-structure, and thermal-mechanical interaction phenomena. We have modeled a plethora of materials, from metals, concretes, and ceramics, to plastics, polymers, glass, and soils. We leverage our computational modeling capabilities to help industry combat emerging security threats, such as malicious drone attacks and active shooter/armed aggressor events.

At Protection Engineering Consultants, you will have access to a deep bench of state-of-the-art computational modeling tools and hardware resources. Our tools range from structural-level codes such as SAP2000 and OpenSees to general-purpose finite element analysis (FEA) codes like LS-DYNA to Government and open-source computational fluid dynamics (CFD) codes such as CTH and OpenFoam/BlastFoam.

Nonlinear Static and Dynamic Solid Mechanics

Nonlinear static and dynamic solid mechanics covers a wide range of problems that we tackle routinely at PEC. These types of problems typically involve continuum modeling of structures, systems, components, and equipment using Lagrangian finite element formulations and sophisticated nonlinear constitutive relationships. The time scale and response regime of interest for these types of problems can vary greatly depending on the threat/hazard, loading conditions, and materials at play. For instance, the modeling approach one would employ for a limit-state stress analysis of a detailed structural connection subject to conventional loading conditions will be necessarily different from that employed for a response analysis of critical infrastructure subject to blast, shock, or impact loading conditions.

We are well-versed in traditional Finite Element formulations, as well as particle-based formulations like Smoothed Particle Hydrodynamics (SPH) and Discrete Element Method (DEM). Our modeling tool of choice for nonlinear static and dynamic solid mechanics is the high-fidelity finite element code LS-DYNA. Our engineers offer a wealth of knowledge and experience using this tool to adequately capture the physics of your problem and help you put a sharp pencil toward a numerical evaluation or design solution. Since inception, PEC we has solved a wide range of complex problems including performance evaluation and design support for architecturally complex glazed building facades subject to high-wind and blast events, vulnerability assessments of safety-related structures and equipment for beyond-design-basis seismic and high-wind events, numerical evaluation and protective design of bridge and vehicle armor subject to precision explosive devices, damage and residual capacity predictions for critical building components subject to severe explosive threats, anti-ram and debris impact barrier design support, and consequence analysis support for postulated industrial accident scenarios. We can also assist with quantifying vibratory load effects associated with ground shock, seismic activity, rotating equipment, or construction activities.

Computational Fluid Dynamics

Computational fluid dynamics (CFD)—sometimes referred to as hydrocodes—is a typical modeling approach often applied to problems involving hydrodynamic material response, significant material flow, and problems where detailed state variable information is not needed at every material point throughout the computational domain. Typical CFD codes operate within a Eulerian mesh description wherein the computational domain consists of a fixed spatial grid and materials flow, or advect, through the fixed spatial grid. This is in contrast to a Lagrangian mesh description typically used for solid mechanics applications wherein the spatial grid deforms with material points. A hybrid mesh approach,  referred to as Arbitrary Lagrangian-Eulerian (ALE), leverages the benefits of both types of mesh descriptions.

At PEC, we use CFD and ALE modeling approaches to help clients with problems involving things like wind-induced vibrations and wind loading on non-conventional geometries, complex blast environments in confined and urban spaces, high kinetic energy penetrators and consequent hydrodynamic material behavior, and fluid-structure interaction analysis. We have access to commercial and open-source tools, such as LS-DYNA, OpenFoam, and BlastFoam, as well as Government hydrocodes like CTH.

Material Model Development

One of the most critical and challenging aspects of computational modeling is the appropriate definition of material models—particularly when exercising materials well beyond their elastic limit and to failure.  Strain-rate effects on strength, triaxiality effects on failure strain, pressure and thermal dependencies, and availability and use of test data are all important facets. Many computational modeling tools come with an extensive library of off-the-shelf material models. The correct material model must be selected, and key model inputs defined for the problem and governing physics at hand.

PEC has extensive experience defining material models for a wide range of material types and extreme loading applications. When available, we prefer to use material-level test data as a basis for defining material model inputs. If test data are not available, we can first assist in material-level testing, or we can make use of nominal input parameters from industry standards and guidance documents.

For situations where off-the-shelf material models cannot capture the predominant behavior and governing failure mechanisms of a material, we will develop a specific user-defined material model.  We typically employ user-defined material models for non-conventional materials and/or loading conditions. Depending on whether model development can start from an existing baseline model or needs to be built from the ground up, the level-of-effort can vary from moderate to significant. Recent examples where we successfully employed a user-defined material model include a probabilistic flaw-based glass failure prediction model for blast-loaded window and curtainwall assemblies and a unique pressure-dependent plasticity model that coupled deviatoric-related damage to volumetric behavior for a glass foam aggregate material application. In both cases, these user-defined materials models were coded and compiled into an LS-DYNA executable for subsequent high-fidelity simulations.

Crowd Modeling for Security Applications

The active shooter (armed aggressor) is a growing threat as the number of incidents nationwide continues to increase. At PEC, we work with architects, design teams, and asset owners to develop risk-informed threat mitigation strategies using computational “agent behavior” modeling tools. Given a set of active shooter threat scenarios, we use these tools to quantify building occupant egress times and identify potential egress chokepoints. This information is then used to establish architectural, structural, and operational mitigation measures.

Our modeling process begins with the development of a 3-dimensional model of the site incorporating important obstructions and occupancy flow features. An egress model is developed wherein building occupants are represented and an active shooter threat scenario is selected. Occupants are referred to as “agents” and are populated with a set density throughout the site (interior and exterior).

Egress simulations are carried out, and occupant risk is evaluated using an assessment of the time taken for individual agents to evacuate the premises and avoid the active shooter. The potential benefits of forced-entry/ballistic resistant (FE/BR) engineering features can be considered. Once the baseline set of threat scenarios has been evaluated, the egress model can then be used to explore the effect of different mitigation measures on both egress time and chokepoint generation.

Our risk-based approach for the active shooter threat can bring value to both new construction projects and existing facilities or buildings. For new construction, the results of such an assessment can identify modifications to floor plans and exit locations to minimize occupant risk. For existing construction, our risk-based approach can be used to identify where FE/BR features can be added or where operational security enhancements can be made. We have successfully applied our risk-based approach to large transportation hubs and entertainment venues, and we have presented on this topic for both the American Society for Industrial Security (ASIS) and the Society of American Military Engineers (SAME). We are also working with ASTM F12.10 and E54.05 in the development of a new standard focused on mitigating the armed aggressor threat specifically at educational institutions.

Related Resources

Fragment Field Modeling Using Digital Twins and Generative Adversarial Networks (GAN)

Assessment, Design, and Construction Support to Mitigate Hostile Vehicle Ramming Threats

Modeling Armed Aggressor, Active Shooter, and MTFA Scenarios


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