CAE-Companion-2018-2019

Modeling of Materials & Connections WISSEN CAE

Material Parameter Identification - Reverse Engineering

Johnson Cook)

The utilization of newmaterials such as plastics, composites, foams, textiles or high-strength steels requires the application of highly complex material models. These material models generally bring along numerous material parameters, which are difficult to define. Design optimization can be a useful method to identify those parameters. Design optimization can be defined as an automated proce- dure for achieving the best outcome of a given operationwhile satisfying certain restrictions. This objective has always been central to the design process, but is nowassuming greater significance than ever because of thematurity of mathematical and computational tools available for design optimization. These tools are used in different scenarios. Mathematically the problem is always reduced to minimizing a system outcome criterion while satisfying other system responses. A typical example would be the weight reduction of a car body by changing sheet thicknesses under achieving different NVH and crash criteria. Reverse engineering Nowadays these optimization tools are often used for “reverse engineering”. This method is applied due to the fact that complex interacting problems in measurement and simulation often can’t be transformed into a simple problem description, e.g. in the process of material calibration: „ „ σ(ε,έ) couldn’t be measured directly or the effort to measure it is too high (e.g. bending test) „ „ sample preparation doesn’t allow or the effort is too high to gain specimens for each loading condition (e.g. compression, shear, tension, ... ) or material (e.g. sandwich, glue,...) needed „ „ the material model parameters are interacting with simulation parameters (e.g. hour glassing) or model idealization (e.g. mesh size, contact formulation of multi material mix) Parameter identification is commonly used to solve those issues. Parameter identification problems are non-linear inverse problems which can be solved using mathematical optimiza- tion. In most cases the objective is to minimize the mismatch between two curves, typically a two-dimensional experi- mental target curve, e.g. a stress-strain curve or a force-dis- placement curve, and the corresponding computed curve extracted from a simulation. The computed curve depends on system parameters that can be varied, e.g. material con- stants. The main essential components of such an algorithm designed for system identification are „ „ the optimization algorithm (e.g. metamodel-based or direct optimization) „ „ the curve matching metric (e.g. Mean Squared Error) „ „ the formulation of the material “parameter” law (e.g.

Figure 1: Reverse Engineering - Parameter Identification

Figure 2: Optimization process diagram

Optimization algorithm The idea of direct optimization is to use only simulation results to find the optimal value. A typical algorithm is the Ge- netic Algorithm, e.g. MOGA-NSGA II. The GA is a population based stochastic optimizer inspired by Darwin’s “Survival of the fittest” principle. But since direct optimization requires many simulation runs, this method is usually too expensive and hence rarely used. The idea of metamodel-based optimization is to approximate the relation between parameters and simulation output by simple functions (e.g. a linear polynomial) and perform the optimization on that surrogate model. Only a few simula- tion runs are required to fit the metamodel. The method is very effective, especially for highly non-linear optimization problems. The nature and capacity of the simulation environment as well as the purpose of the optimization effort typically dictate the strategies for metamodel-based optimization. The strategies depend mostly on whether the user wants to build a metamodel that can be used for global exploration or he is only interested in finding an optimal set of parameters.

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