Abstract
In this paper, the partition of the unity property of finite element shape functions is used to introduce displacement discontinuities into finite elements. The discontinuous character of the displacement field is captured with the Heaviside step function. Using the partition of unity concept, the governing equation of the continuum and the discontinuity are separated and are consequently described by different constitutive laws. Inside the discontinuity, a plasticity based constitutive law is used to describe the decrease of tractions in function of the crack opening while the continuum is assumed to remain elastic. The methodology will be described and validated with a comparison between numerical simulations and experimental results.This paper is dedicated to J. Sejnoha, TU Prague, with respect and admiration for his scientific achievement.
Highlights
A variety of computational techniques exist to describe the fracture behaviour of quasi-brittle materials
These models can be classified into two main groups: continuous and discontinuous models
A major problem with classical continuum models is that the governing equations lose ellipticity for quasi-static problems and hyperbolicity for dynamic problems if strain softening is introduced
Summary
The partition of the unity property of finite element shape functions is used to introduce displacement discontinuities into finite elements. The discontinuous character of the displacement field is captured with the Heaviside step function. Using the partition of unity concept, the governing equation of the continuum and the discontinuity are separated and are described by different constitutive laws. A plasticity based constitutive law is used to describe the decrease of tractions in function of the crack opening while the continuum is assumed to remain elastic. The methodology will be described and validated with a comparison between numerical simulations and experimental results. TU Prague, with respect and admiration for his scientific achievement
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