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The theory of a Cosserat point has been used to develop a 3D brick Cosserat point element (CPE) for the numerical solution of elastic structures that undergo finite deformations. The Cosserat approach postulates an average form of the deformation measure and connects the kinetic quantities to derivatives of a strain energy function. Once this strain energy has been specified, the procedure for obtaining the kinetic quantities needs no integration over the element region and it ensures that the response of the CPE is hyperelastic. Also, the constitutive equations of the CPE were designed to analytically satisfy a nonlinear form of the patch test. Specifically, the strain energy function is additively decomposed into two parts: one controlling the homogeneous deformations and the other controlling the inhomogeneous deformations. Developing a functional form for the strain energy of the inhomogeneous deformations has proven to be challenging. Recently, a functional form of the inhomogeneous strain energy function was developed, which causes the CPE to be a truly user friendly element that can be used with confidence for problems of finite elasticity including: three-dimensional bodies, thin shells and thin rods.

computation, modeling, simulation, numerical methods, algorithm