Computer-implemented method and system for simulating and analyzing material deformation based on principles of linear elasticity, data processing system, computer program product, and computer-readable data carrier

Abstract

A computer-based method for simulating and analyzing material deformation using the principle of linear elasticity is disclosed. The method includes: decomposing a geometry into multiple simple domains and calculating mesh tensors in the form of tensor network vectors for all dimensions, specifying corresponding coordinates for any given input in one or more mesh tensors using a defined mesh function; using the mesh tensors defined for all available dimensions for each simple domain; calculating the Jacobian components and Jacobian determinants of element transformations and mapping reference elements to small elements of each simple domain to calculate them all at once using TN operations; processing the stress and strain fields within the material, the forces applied to the material, and the defined test function equations on local elements of the stiffness and mass matrices on a storage medium using the Jacobian components calculated in the previous steps; assembling stiffness TN operators and mass TN operators for each simple domain; stitching the stiffness TN operators and mass TN operators together to enhance continuity at the joint; and applying the mass TN operator to the external force TN vector.

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