Matrix Description of Non-Linear Properties of Materials or Structural Components-Idea and Application Examples.

Tomasz Janiak

doi:10.3390/ma14195837

Abstract

Numerical methods are widely used in structural analysis problems. In the cases of the most complex and practical problems, they are often the only way to obtain solutions, as analytical methods prove ineffective. The motivation for this paper was the desire to extend the scope of numerical methods to cover the problems of creating constitutive models of structural materials. The aim of this research was to develop a matrix or numerical discrete constitutive model of materials. It presents the general assumptions of the developed method for modeling the physical properties of materials. The matrix model is only useful with an appropriate numerical algorithm. Such an algorithm was created and described in this paper. Based on its findings, computer software was developed to perform numerical simulations. Presented calculation examples confirmed the effectiveness of the developed method to create constitutive matrix models of various typical materials, such as steel, but also, e.g., hyper-elastic materials. It also presents the usefulness of constitutive matrix models for simulations of simple stress states and analyses of structural elements such as reinforced concrete. All presented examples involved the physical nonlinearity of the materials. It is proved that the developed matrix constitutive model of materials is efficient and quite versatile. In complex analyses of structures made of nonlinear materials, it can be used as an effective alternative to classical constitutive or analytical models based on elementary mathematical functions.

Highlights

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Structural materials used in the construction industry feature a number of parameters that are important primarily in terms of material strength and structure mechanics, and in terms of other parameters related to, for example, building physics
The situation is completely different in case of reinforced concrete structures

Summary

Introduction

Basic construction materials (steel and concrete in particular) behave in a non-linear way through the whole operating range. This means that their stiffness changes along with the increase of strain and stress. This level is related to material specification (e.g., a clear yield point) or it is a defined arbitrary limit This approach means that steel structures almost always operate in constant stiffness range and it is justified to assume the constant material stiffness in static calculations. Most static analyses of reinforced concrete structures are carried out in a simplified way, assuming that the geometric characteristics of cross-sections correspond to an uncracked concrete crosssection (without any reinforcement) Significant errors appear in the results of internal forces

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