# Material simulation

Z-sim is a constitutive equation driver, allowing the user to load any representative volume element (RVE) and thus perform fast simulations on material elements without using any FEA.

## Constitutive simulation driver

Z-sim has been developed to compute the response of all constitutive laws available in Z-mat under either stress or strain control loading instead of forces and displacements. The simulator allows dramatic CPU time gains with respect to the equivalent FE calculation on a single element.

The main strengths of Z-sim are the following:

- A very simple input file, including the description of the loading history in terms of stresses, strains and external parameters (e.g., temperature), the name of the material file and the management of the integration algorithm and of the output
- The loading can be hybrid (mixed stresses and strains), with an unlimited number of loading blocks, a simple definition of cyclic loadings and possible on-the-fly modifications of the control variables (switch from stress to strain control, etc.)
- Loading history can be directly written in the input file or taken from an external ASCII file
- In the case of finite strains, the loading history can be introduced in terms of the transformation gradient directly
- Definition of the constitutive law in a Z-mat input file
- Choice of the integration method (explicit, implicit or mixed)
- Powerful output data management.

Material models are 100% shared between Z-sim and Z-mat. User models implemented in Z-mat by means of the ZebFront preprocessor are also available in Z-sim. Other functionalities are provided to plot yield or damage surfaces (actually any potential) in the stress space at different points of the loading history.

## Material parameter identification

Along with Z-opt, Z-sim is a core software application integrated in Z-simopt GUI for material parameter identification applications. The methods used in the application allow the optimization problem to be solved in such a way that the least-square distance between the simulated curves and the experimentally observed response is minimized. Such an approach requires a high number of simulations to be performed. Using the Z-sim software allows the simulation time to be significantly reduced and accelerates the optimization process.

## … and much more

In fact, Z-sim capabilities also include the integration of any system of ordinary differential equations. The user only provides, in a header, the list of variables that must be integrated with respect to time or any other kinematics. A list of parameters can also be given. The equations are then specified in a special environment. The type of problem that can be addressed ranges from reduced order models like Neuber’s approach, or three bar systems, to rather large finite difference schemes.