Constitutive equations are meant to describe the physics of a material behavior. Calculations involving these material models are crucial to producing reliable results out of your simulations. The unique design of Z-mat Library addresses these needs through its modular frameworks, and a vast collection of mathematical models.
Verification & Validation: Most of these constitutive models have been subject to V&V through carefully designed testing programs and calibration of parameters in our testing facilities for each relevant physical mechanism, an all-too-important factor that makes your simulations truly reliable.
Physical Mechanisms: such as elasticity (hypo and hyper), time-independent- and visco-plasticity, hardening, creep, relaxation, damage and aging can be simulated using physically motivated phenomenological models in Z-mat Library. For each physical mechanism there are several models to choose from – for example, about 20 models are available for each of these mechanisms: yielding, plastic flow and kinematic hardening. The material coefficients in these models can have spatial (constant, analytical and N-dim tabular functions) and directional (isotropic, orthotropic and anisotropic behavior) heterogeneity.
Frameworks: Each framework combines several of the above physical mechanisms (and their respective mathematical models) to produce a fully specified constitutive model. Being able to combine visco-plastic flow and kinematic hardening (physical) mechanisms in gen_evp framework means that, all mathematical models of the former can be combined with all models of the latter.
The key frameworks supported in Z-mat Library are:
- gen_evp – In generalized elastic visco-plastic framework, one can combine small strain elastic, large strain visco-plastic (and time-independent), including isotropic and kinematic hardening, creep, relaxation, and damage models. It also supports multiple potentials in series, and possible interaction between them. This is an extremely powerful tool in modeling different deformation mechanisms that are activated, say at different strain rates.
- reduced_plastic – This is the same as gen_evp with the difference that the equations are formulated in terms of a different set of unknowns, and its flexibility in admitting different integration operators. Both gen_evp and reduced_plastic have been successfully used with production simulation of metals across a wide range of temperatures and strain rates.
- porous_plastic – This framework is suitable for damage or densification of porous materials, and supports various visco-plastic, creep and hardening models, and void nucleation criteria. This framework is useful for modeling metals and granular materials, including soils.
- finite_strain_plasticity – This framework performs computations using finite strain mechanics for both elastic and inelastic mechanisms, by combining any of the hyper-elastic models with visco-plastic models including isotropic and kinematic hardening laws. Materials that have been successfully modeled include elastomers, polymers and plastics. Real life applications include engineering components (seals, gaskets, tires), bio-medical devices (syringes, prosthetics), and consumer goods (bottles, wearables), to name a few.
- multi_mat – This framework is useful in modeling composite materials that require multi-scale methods because of their microstructures. Several homogenization techniques, based on continuum or RVE meshes, are available. In general, any model in the Z-mat Library, or another multi_mat model can be used in this framework.
Algorithms and Controls: Several integrators including generalized theta (forward Euler, backward Euler, mid-point), Runge-Kutta, asymptotic and root-finding techniques, and their controls along with fail-safe and load-cut-back options are available.
In summary, Z-mat Library is a flexible and powerful Material Modeling and Simulation framework that is at the heart of our materials solution. It is not just a collection of user material models.