A novel framework for elastoplastic behaviour of anisotropic solids
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A novel framework for elastoplastic behaviour of anisotropic solids Zhou Lei1 · Christopher R. Bradley1 · Antonio Munjiza2 · Esteban Rougier1 · Bryan Euser1 Received: 3 February 2020 / Revised: 8 May 2020 / Accepted: 5 June 2020 © OWZ 2020
Abstract A general framework for developing nonlinear hyperelastic/plastic constitutive laws for anisotropic solids experiencing large strains and strain rates has been developed. The proposed framework does not rely on the “a priori” known strain energy function, but instead introduces a physical decomposition of the material element into seven physically independent stress bearing mechanisms, each of which has a constitutive law in terms of internal moments described by a scalar function of a single variable. The model has been encoded into a combined finite-discrete element method and tested against static geomechanical test data. The numerical validation experiments show the model can reproduce plastic anisotropic behaviour in both biaxial and uniaxial loading of a geomaterial. Keywords Continuum damage · Anisotropic solid · Large deformation · Large rotation · Hyperelastic formulation
1 Introduction Within the state-of-the-art finite element methods, discrete element methods, and hybrid methods, large strains and large displacements play an important role for dynamic and static modelling of geomaterials. The conventional approach utilizes either the traditional rate-based or co-rotational strain energy-based solutions in formulating both deformation kinematics and constitutive laws. The ability of these methods to properly capture large strain behaviour becomes problematic when the strain energy function is not known and/or where material anisotropy plays an important role. For instance, within the combined finite-discrete element method framework the solid domains (called discrete elements) are discretized into finite elements, where finite rotations and large element displacements and strains are assumed “a priori” [1–3]. In general, to describe material constitutive laws under large strains, two approaches have been introduced in computational mechanics: hypoelastic and hyperelastic formulations. The classic hypoelastic formulation results in the final stress state being dependent on the loading path and therefore not being objective [4–6]. To * Zhou Lei [email protected] 1
Geophysics Group, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545, USA
FGAG, University of Split, Split, Croatia
2
counteract these problems associated with hypoelasticity, many research and commercial implementations of large strain elasticity employ the hyperelastic formulation [1, 3, 7]. The cornerstone of the hyperelastic formulation is the utilization of a strain energy function [7]. The strain energy function is the potential energy of internal forces measured per unit mass of the solid material. Cauchy stress components are obtained as the derivative of the strain energy function with respect to the associated strain tensor in the current deformed configuration [7
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